This ontology covers the terminology of the Distributed Ontology, Model, and Specification Language (DOL) and is an informative part of its specification.
Distributed Ontology, Model, and Specification Language (DOL) Terminology Ontology
is strictly stronger than
supports symbol kind
supports symbol kind
object is a conservative extension of the subject
conservatively extends to
object is a definitional extension of the subject
definitionally extends to
relation of logical entailment, expressing that all realizations of the subject are also realizations of the object
entails
subject is a mapping of an extension, the object is the target of the extension mapping, i.e. the extended OMS
extends to
subject is a precise mathematical entity capturing the object (which is an informal or semi-formal entity)
formalizes
subject is a DOL library, in which the object is an alignment between two participating OMS
has alignment
subject language has exactly the expressivity of the object logic
has exact logical expressivity
relationship between the subject and a heterogeneous environment in which it is embedded or is associated with
has heterogeneous environment
subject is a DOL library, in which the object is an interpretation between two participating OMS
has interpretation
relation between an OMS language and its language aspects
has language aspect
specification of valid reasoning that comprises signatures (user defined vocabularies), realizations (interpretations of these), sentences (constraints on realizations), and a satisfaction relation between realizations and sentences, i.e., the logic in which an OMS is formalized
has logic
subject is a DOL library, in which the object is a mapping between two participating OMS
has mapping
inverse of the set membership relation
has member
OMS (resp. its semantic object) has an associated class of realizations (models), which is the class of realizations of the OMS
has realizations
subject is a DOL library, in which the object is a participating heterogeneous OMS
has OMS
relationship between two things were the second is a component of the first
has part
property of a tool that is capable of implementing a process
has proficiency
OMS (resp. its semantic object) has an associated set of sentences, that is the set of sentences of the OMS
has sentences
inverse of the sequence membership relation
has sequence member
OMS (resp. its semantic object) has an associated signature, which is the signature of the OMS
has signature
source OMS of a mapping
has source
target OMS of a mapping
has target
relation of a model-theoretic conservative extension that does not introduce new non-logical symbols
implied extends to
subject is a translation (or reduction) that shares its sentence and realization translation with the object reduction (or translation)
is adjoint of
object is a DOL library, in which the subject is an alignment between two participating OMS
is alignment in
approximation (in the sense of a logically implied theory, possibly aftersuitable translation) of an OMS in a smaller signature or OMS language
is approximant of
aggregation of all the OMS in an OMS network, where non-logical symbols are shared according to the OMS mappings in the OMS network
is combination of OMS
subject mapping is the composition of the object list of mapping
is composition of
subject OMS is a consequence-theoretic conservative extension of the object OMS
is consequence theoretically conservative extension of
subject is a conservative extension of the object
is conservative extension of
extension whose newly introduced non-logical symbols are interpreted in a unique way
is definitional extension of
any resource in an OMS (e.g. a non-logical symbol, a sentence, a correspondence, the OMS itself, ...) or a named set of such resources
is element of OMS
subject is embeddable into the object logic
is embeddable into
inverse of relation of logical entailment
is entailed by
an exact mapping from the subject to the object logic
is exactly mappable to
relation between two OMS whereby the subject OMS is an extension of the object OMS, i.e. the sets of non-logical symbols and sentences of the subject OMS are supersets of those of the object OMS
a faithful mapping from the subject to the object logic
is faithfully mappable to
object is a precise mathematical entity capturing the subject (which is an informal or semi-formal entity)
is formalized by
model-theoretic conservative extension that does not introduce new non-logical symbols
is implied extension of
object is a DOL library in which the subject is an interpretation between two participating OMS
is interpretation in
set of language constructs of a given language, not necessarily forming a sublanguage
is language aspect of
language of an OMS
is language of
relation between linguistic entities
is linguistically related to
property of structured OMS, which may be written in different OMS languages supporting different logics, of being usable jointly in a coherent way (via suitable OMS language translations), such that the notions of their overall consistency and logical entailment have a precise logical semantics
is logically interoperable with
relation between lingustic entities that has a logical, semantic nature
is logically related to
indicates that there is a mapping from the object to the subject
is mappable from
indicates that there is a mapping from the object language to the subject language
mappable from language
indicates that there is a mapping from the object logic to the subject logic
mappable from logic
indicates that there is a mapping from the subject to the object
is mappable to
indicates a realization-bijective mapping from the subject to the object logic
is mappable to bijectively on models
indicates that there is a mapping from the subject language to the object language
is mappable to language
indicates that there is a mapping from the subject logic to the object logic
is mappable to logic
object mapping maps from the subject into something of the same type as the subject
is mapped by
object is a DOL library, in which the subject is a mapping between two participating OMS
is mapping in
relation between mathematical entities
is mathematically related to
set membership relation
is member of
indicates that there is a realization-expansive mapping from the subject to the object logic
is model expansively mappable to
relationship between a realization and an OMS where the realization is a member of the realization class of the OMS (which for flattenable OMS is equivalent to being a realization of the signature of the OMS and satisfying all sentences in the OMS)
is a realization of the OMS
relationship between a realization and a signature (vocabulary) such that the realization provides a semantic interpretation of all non-logical symbols in the signature
is a realization of the signature
the subject OMS is a model-theoretic conservative extension of the object OMS. A model-theoretic conservative extension is an extension that does not lead to a restriction of class of realizations (models) of an OMS
is model theoretically conservative extension of
relationship between two OMS where the first conservatively extends to the second OMS
is module of
subject OMS is a monomorphic extension of the object OMS
is monomorphic extension of
relationship between an OMS documentation and the documented OMS
is OMS documentation of
structured OMS expressing the combination of all constraints of a sequences of OMS
is union of OMS
subject is an OMS participating in a DOL library, which is the object
is OMS in
indicates that there is a plain mapping from the subject to the object logic
is plainly mappable to
subject is a profile of the object language
is profile of
indicates that there is a reduction from the object to the subject
is reducible from
indicates that there is a reduction from the subject to the object
is reducible to
property used in the context of mappings, for both linguistic and mathematical entities
is related as part of maps to
relation that has a semantic nature
is semantically related to
sequence membership relation
is sequence memberOf
the textual syntax in which an OMS is written
is serialized in
indicates that there is a simple theoroidal mapping from the subject to the object logic
is simply theoroidally mappable to
object mapping maps from the subject into something of the same type as the subject
is source of mapping
syntactically specified subset of a given language, consisting of a subset of its terminal and nonterminal symbols and grammar rules
is sublanguage of
logic that is a syntactic restriction of another logic, inheriting its semantics
is sublogic of
OMS whose sets of non-logical symbols and sentences are subsets of those present in a given larger OMS
is subOMS of
indicates that there is a translation from the object to the subject
is translatable from
indicates that there is a translation from the subject to the object
is translatable to
subject OMS is a weak definitional extension of the object OMS
is weak definitional extension of
indicates that there is a weakly exact mapping from the subject to the object logic
is weakly exactly mappable to
relationship between a mapping and its domain
maps from
The subject mapping maps from the object into something of the same type as the object.
relationship between a mapping and its codomain
maps to
The subject mapping maps from something into the object (which is of the same type). Enforcing the latter constraint goes beyond OWL.
subject property is reified by the object class
is reified by
subject class reifies the object property
reifies
relationship between a realization and a sentence indicating that the sentence holds true in the realization
satisfies
relation between a linguistic entity and its semantic denotation
semantically denotes
subject is a serialization for the object language; for example, Manchester syntax serializes OWL
serializes
property of OMS symbols being mapped to the same symbol when computing a combination of an OMS network
shares with
indicates that the semantics of [a subset of] the object language can be specified in terms of the subject logic
specifies semantics of
logic represented by a satisfaction relation of the language
supports logic
subject language mapping corresponds to the object logic mapping
supports logic mapping
OMS in the subject language can be serialized in the object serialization
supports serialization
Note that the serialization should be as specific as possible, i.e. one should not say that 'OWL can be serialized in XML' and 'Common Logic can be serialized in XML', but instead 'OWL can be serialized in OWL XML' and 'Common Logic can be serialized in XCL', taking into account that OWL XML and XCL are two different XML languages.
relation between something and a language used by one or more components of it
uses language
an alternative filename extension for a serialization
the media type (MIME type) of a serialization
the preferred filename extension for a serialization
subject class denotes a kind of mapping that, if it holds for a translation, also holds for the adjoint reduction
propagates to adjoint
term language for representing documents in a machine-processable way
abstract syntax
an OMS mapping expressing a collection of relations between entities of the two OMS
alignment
an alignment between two heterogeneous OMS in a DOL library
additional information without a logical semantics that is attached to an element of an OMS
annotation expression
the (unique) language aspect of an OMS language that enables the expression of comments and annotations
annotation expression language aspect
substitution that, when applied to a given query, turns the latter into a logical consequence of a given OMS
answer substitution
logically implied theory (possibly after suitable translation) of an OMS in a smaller signature or a sublanguage
approximant
structured OMS that expresses a maximum approximant
approximation
sentence postulated to be valid (i.e., true in every realization)
axiom
axiom that used in a simple theoroidal mapping
infrastructure axiom
unstructured native OMS that may be used as a building block for a larger OMS, denoting a logical theory
basic OMS
a basic OMS (in a single language, logic, and serialization)
a class of objects with suitable morphisms between them
category
a class of realizations (over some signature in some logic)
class of realizations
structured OMS expressing a variant of the closed world assumption by restricting the realizations to those that are minimal or maximal (with respect to the local environment)
closure
special type of closure, restriction of realizations to those that are cofree (with respect to the local environment)
cofreeness
collection whose members are expressions
collection of expressions
structured OMS expressing the aggregation of all the OMS in an OMS network, where non-logical symbols are shared according to the OMS mappings in the OMS network
combination
extension that does not add new theorems (in terms of the unextended signature)
consequence-theoretic conservative extension
mapping of a consequence-theoretic conservative extension
consequence-theoretic conservative extension mapping
extension that does not add new logical properties with respect to the signature of the extended OMS
conservative extension
extension mapping of a consequence-theoretic or model-theoretic conservative extension
conservative extension mapping
OMS that has a non-trivial set of logical consequences in the sense that not every sentence follows from the OMS
consistent OMS
relationship between a non-logical symbol e_1 from an OMS O_1 and a non-logical symbol e_2 from an OMS O_2, or between a non-logical symbol e_1 from O_1 and a term t_2 formed from non-logical symbols from O_2
correspondence
document containing a DOL library
DOL document
entity that is used in DOL texts
DOL entity
collection of named OMS and OMS networks, possibly written in different OMS languages, linked by named OMS mappings
DOL library
syntactically valid DOL expression denoting an OMS that is built from smaller OMS as building blocks
DOL structured OMS
logic mapping that will be chosen by default if only the source and target logic are given
default logic mapping
language mapping that will be chosen by default if only the source and target language are given
default language mapping
mapping that will be chosen by default if only the source and target are given
default mapping
extension whose newly introduced non-logical symbols are interpreted in a unique way
definitional extension
mapping of a definition extension
definitional extension mapping
text that typically is the result of serializing an object using a given serialization
document
OMS that is not flattenable
elusive OMS
logic mapping that embeds the source into the target logic, using components that are injections and (in the case of realization translations) isomorphism
embedding
a relation between two OMS (or an OMS and a sentence, or two OMS networks, or an OMS network and an OMS) expressing that the second item (the conclusion) is logically implied by the first one (the premise)
entailment
OMS mapping ensuring that two OMS share the same definable concepts
equivalence
logic mapping that is compatible with certain DOL structuring constructs
exact mapping
a finite combination of symbols that are well-formed according to applicable rules (depending on the language)
expression
structured OMS extending a given OMS with new symbols and sentences
extension
mapping of an extension
extension mapping
logic mapping that preserves and reflects logical consequence
faithful mapping
structured OMS expressing the verbatim removal of symbols or axioms from an OMS
filtering
OMS that can be seen, by purely syntactical means, to be logically equivalent to a basic OMS
flattenable OMS
process of transforming an OMS to an equivalent basic OMS
flattening
assignment of mathematical meaning to a language by mapping abstract syntax to suitable semantic domains
formal semantics
special type of closure, restriction of realizations to those that are free (with respect to the local environment)
freeness
mapping from identifiers (IRIs) to values in semantics domains representing semantic information about a set of documents (the latter typically being distributed over the internet)
global environment
set of objects (nodes) that are connected by links (edges)
graph
environment for the expression of homogeneous and heterogeneous OMS, comprising a logic graph, an OMS language graph and a supports relation
heterogeneous environment
OMS whose parts are supported by different logics
heterogeneous OMS
OMS whose parts are supported by one logic
homogeneous OMS
model-theoretic conservative extension that does not introduce new non-logical symbols
implied extension
mapping of an implied extension
implied extension mapping
reference to an OMS or DOL library behaving as if it were verbatim included
import
OMS that has a trivial set of logical consequences in the sense that every sentence follows from the OMS
inconsistent OMS
metaframework mathematically formalizing the notion of a logic in terms of notions of signature, signature morphism, realization, sentence and satisfaction
institution
signature mediating between an OMS and a module of that OMS in the sense that it contains those non-logical symbols that the sentences of the module and the sentences of the OMS have in common
interface signature
OMS mapping that postulates a specialization relation between two OMS along a morphism between their signatures
interpretation
collection of expressions, following formal rules of well-formedness
formal language
a body of words, following a set of methods of combining them (called a grammar), understood by a community and used as a form of communication
language
syntactic pattern that is part of a language
construct
set of language constructs of a given language, not necessarily forming a sublanguage
language aspect
graph with OMS languages as nodes and OMS language translations and OMS language reductions as edges, typically used in a heterogeneous environment
OMS language graph
mapping between languages
language mapping
entity that is of linguistic, syntactic nature
linguistic entity
structured data that is published on the Web in a machine-processable way, according to principles explained in http://linkeddata.org/
linked data
signature built from all previously-declared symbols and axioms
local environment
specification of monotonic valid reasoning that comprises signatures, sentences, realizations, and a satisfaction relation between realizations and sentences
monotonic logic
a (monotonic) logic that defines the semantics of an language
specification of (possibly non-monotonic) valid reasoning that comprises signatures, sentences, realizations, and a satisfaction relation between realizations and sentences
logic
a (possibly non-monotonic) logic that defines the semantics of an language
graph with logics as nodes and logic translations and logic reductions as edges, typically used in a heterogeneous environment
logic graph
mapping between logics
logic mapping
a mapping (translation or reduction) between two logics consisting of mappings for signatures, sentences and realizations
reduction of a source logic onto a (usually less expressive) target logic (mapping signatures, sentences and realizations) that simply forgets those parts of the logical structure not fitting the target logic
logic reduction
reduction of a source onto a (usually less expressive) target that simply forgets those parts of the source not fitting the target
reduction
reduction of a source language onto a (usually less expressive) target language that simply forgets those parts of the source language not fitting the target language
OMS language reduction
translation of a source logic into a target logic (mapping signatures, sentences and realizations) that keeps or encodes the logical content of OMS
logic translation
mapping of a source into a target that keeps or encodes the content of the source
translation
the (unique) language aspect of an OMS language that enables the expression of non-logical symbols and sentences in a logical language
logical language aspect
a signature together with a set of sentences (over that signature)
logical theory
representation of (the development of) a system (e.g., hardware, software, information system, or organization), or a domain related to a system, used in model-driven engineering (MDE)
model
relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output
mapping
a generic set-theoretic mapping or family of set-theoretic mappings (translation or reduction)
tool that implements matching
matcher
algorithmic procedure that generates an alignment for two given OMS
matching
entity that is part of a mathematical theory
mathematical entity
form of closure that restricts the realizations to those that are maximal (with respect to the local environment)
maximization
best possible (in the sense of a maximum set of logical consequences) approximant of an OMS in a smaller signature or a sublanguage
maximum approximant
form of closure that restricts the realizations to those that are minimal (with respect to the local environment)
minimization
semantic interpretation of all non-logical symbols of a signature
realization
logic mapping that has a bijective mapping of realizations (models)
model bijective mapping
logic mapping that has a surjective realization (model) translation (ensuring faithfulness of the mapping)
model expansive mapping
tool that implements realization (model) finding
model finder
process that finds realizations (models) of an OMS and thus proves it to be satisfiable
model finding
extension that does not lead to a restriction of class of models of an OMS
model-theoretic conservative extension
mapping of a model-theoretic conservative extension
model-theoretic conservative extension mapping
structured OMS expressing a subOMS that conservatively extends to conservative extension the whole OMS
module
activity of obtaining from an OMS concrete modules to be used for a particular purpose (e.g., to contain a particular sub-signature of the original OMS)
module extraction
tool that implements module extraction
module extractor
extension whose newly introduced non-logical symbols are interpreted in a way unique up to isomorphism
monomorphic extension
mapping of a monomorphic extension
monomorphic extension mapping
document containing a native OMS
native document
sequence of expressions (like non-logical symbols, sentences and structuring elements) from a given OMS language
native OMS
symbol that requires an interpretation through a realization
non-logical symbol
a non-logical symbol in an OMS
symbol whose interpretation is fixed by the logic
logical symbol
atomic expression or syntactic constituent of an OMS
symbol
a basic or structured ontology, specification or model
OMS (ontology, specification or model)
set of all annotations to an OMS, plus any other documents and explanatory comments generated during the entire OMS building process
OMS documentation
language equipped with a formal, declarative, logic-based semantics, plus non-logical annotations
OMS language
a language for OMS (ontologies, models or specifications)
a translation between two OMS languages that keeps or encodes the content of the source
OMS language translation
relationship between two OMS, typically given as a set of correspondences
OMS mapping
a mapping between two heterogeneous OMS in a DOL library
collection of named OMS, possibly written in different OMS languages, linked by named OMS mappings and named OMS networks
OMS network
DOL structured OMS expressing the restriction of an OMS to a smaller signature
OMS reduction
object giving the semantics of an OMS
OMS Semantic Object
DOL structured OMS expressing the assignment of new names to some non-logical symbols of an OMS, or translation of an OMS along a language translation
OMS translation
explicit and shared formal representation of the entities and their interrelationships of a given domain of discourse or of fundamental notions
ontology
logic mapping that maps signatures to signatures and therefore does not use infrastructure axioms
plain mapping
Developers' note: ProtÃ©gÃ© 4.2 doesn't like 'Class: OMSMapping DisjointUnionOf: PlainMapping, SimpleTheoroidalMapping', so we do it this way:
algorithmic procedure working on DOL-related linguistic entities as input
process
(syntactic) sublanguage of an OMS language interpreting according to a particular logic that targets specific applications or reasoning methods}
profile
sentence containing variables that can be instantiated by a substitution
query
OMS language specifically dedicated to queries
query language
symbol that will be used in a query and a substitution
query variable
OMS mapping that postulates a specialization relation between two OMS along a morphism between their signatures
refinement
refinement
something that can be globally identified
resource
relation between realizations and sentences indicating which sentences hold true in the realization
satisfaction relation
OMS that is satisfied by least one realization
satisfiable OMS
mathematically-defined set of values that can represent the intended meanings of language constructs
semantic domain
entity that is of semantic nature, i.e. relating linguistic objects with their semantic denotation in a mathematical structure
semantic entity
specification of a mapping from abstract syntax to a semantic domain
semantic rule
term that is either true or false in a given realization, i.e., which is assigned a truth value in this realization
sentence
a sentence in an OMS
ordered collection where also multiplicity of elements matters
sequence
sequence whose members are correspondences
sequence of correspondences
sequence whose members are OMS
sequence of OMS
specific syntactic encoding of a given OMS language
OMS serialization
a serialization of an language
synonymous to 'concrete syntax'
collection whose members have a certain type, as specified by the type parameter
set
set whose members are annotation expressions
set of annotation expressions
set whose members are mappings
set of mappings
set whose members are non-logical symbols
set of non-logical symbols
set whose members are sentences
set of sentences
set (or otherwise structured entity) of non-logical symbols of an OMS
signature
mapping between two signatures, preserving the structure of the source signature within the target signature
signature morphism
logic mapping that maps signatures of the source logic to theories of the target logic
simple theoroidal mapping
orthogonal to WeaklyExactMapping and FaithfulMapping
the resulting theory tpyically contains infrastructure axioms that are needed for expressing the logic mapping
formal representation of (requirements of) a data structure, an algorithm or a hardware or software system used in systems analysis, requirements analysis and systems design
specification
way of providing annotations to subjects in external resources, without embedding them into the original resource (here: OMS)
standoff markup
OMS that results from other OMS by import, union, combination, renaming or other structuring operations
structured OMS
the (unique) language aspect of an OMS language that covers structured OMS as well as the relations of basic OMS and structured OMS to each other, including, but not limited to imports, OMS mappings, conservative extensions, and the handling of prefixes for CURIEs
structuring language aspect
logic embedding that is 'syntactic' in the sense that signature and sentence translations are inclusions
sublogic
OMS mapping that maps variables of one OMS to complex terms of another OMS
substitution
relation between OMS languages and logics expressing the logical language aspect of the former, namely that the constructs of the former lead to a logical theory in the latter
supports relation
pair of symbols of two OMS, indicating how a symbol from the first OMS is mapped by a signature morphism to a symbol of the second OMS
symbol map item
syntactic expression either consisting of a single non-logical symbol or recursively composed of other terms (a.k.a. its subterms) and possibly logical symbols
term
software tool implementing theorem proving
theorem prover
process of demonstraing that a sentence (or OMS) is the logical consequence of some OMS
theorem proving
sentence that has been proven from other axioms and theorems
theorem
software for processing DOL libraries and OMS
tool
process of applying a language or logic translation, or flattening an OMS translation
translation (process)
structured OMS expressing the combination of all symbols and axioms (and more general constraints) of a sequence of OMS
union
OMS that is not satisfied by any realization
unsatisfiable OMS
OMS mapping that postulates a relation between two OMS
view
a view (also called interpretation) between two heterogeneous OMS in a DOL library
extension whose newly introduced non-logical symbols can be interpreted in at most one way
weak definitional extension
mapping of a weak definitional extension
weak definitional extension mapping
logic mapping that is weakly compatible with certain DOL structuring constructs
weakly exact mapping
entity that is related to the world wide web
web entity
unified metalanguage for the structured and heterogeneous expression of ontologies, specifications, and models, using DOL libraries of OMS, OMS mappings and OMS networks
Distributed Ontology, Model and Specification Language
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Copyright (c) 2015-2017 Object Management Group, Inc.
Copyright (c) 2014-2017 Thematix Partners LLC
Copyright (c) 2014-2017 Fraunhofer Fokus
Copyright (c) 2014-2017 MITRE
Copyright (c) 2014-2017 Otto-von-Guericke University of Magdeburg
Copyright (c) 2014-2017 Athan Services
http://www.omg.org/techprocess/ab/SpecificationMetadata/MITLicense
DOL-terms.rdf
dol
This ontology covers the terminology of the Distributed Ontology, Model, and Specification Language (DOL) and is an informative part of its specification.
When using this ontology for implementation purposes including complete DOL FOL or rules support, see annotations marked as 'beyond OWL'. They can be modeled in FOL or using rules.
http://www.omg.org/spec/ODM/
http://www.w3.org/standards/techs/owl#w3c_all
Intended domain - OMSLanguage, intended range - owl:Class that rdfs:subClassOf value NonLogicalSymbol
Intended inverse - supportsSymbolKind
object is a conservative extension of the subject
object is a definitional extension of the subject
relation of logical entailment, expressing that all realizations of the subject are also realizations of the object
subject is a mapping of an extension, the object is the target of the extension mapping, i.e. the extended OMS
subject is a precise mathematical entity capturing the object (which is an informal or semi-formal entity)
subject is a DOL library, in which the object is an alignment between two participating OMS
subject language has exactly the expressivity of the object logic
relationship between the subject and a heterogeneous environment in which it is embedded or is associated with
subject is a DOL library, in which the object is an interpretation between two participating OMS
relation between an OMS language and its language aspects
The reasoners in Protege don't like us to say the following, which makes hasLogic a non-simple property. hasLogic is not used in cardinality restrictions, so it _should_ be OK to say the following, but in practice it doesn't work.
SubPropertyChain: semanticallyDenotes o hasLogic
specification of valid reasoning that comprises signatures (user defined vocabularies), realizations (interpretations of these), sentences (constraints on realizations), and a satisfaction relation between realizations and sentences, i.e., the logic in which an OMS is formalized
subject is a DOL library, in which the object is a mapping between two participating OMS
inverse of the set membership relation
OMS (resp. its semantic object) has an associated class of realizations (models), which is the class of realizations of the OMS
subject is a DOL library, in which the object is a participating heterogeneous OMS
relationship between two things were the second is a component of the first
property of a tool that is capable of implementing a process
OMS (resp. its semantic object) has an associated set of sentences, that is the set of sentences of the OMS
inverse of the sequence membership relation
This is a lingustic property, because it is about sequences of linguistic entities that occur in a text.
OMS (resp. its semantic object) has an associated signature, which is the signature of the OMS
source OMS of a mapping
target OMS of a mapping
relation of a model-theoretic conservative extension that does not introduce new non-logical symbols
subject is a translation (or reduction) that shares its sentence and realization translation with the object reduction (or translation)
The signature translations are adjoint to each other (in the sense of category theory).
object is a DOL library, in which the subject is an alignment between two participating OMS
approximation (in the sense of a logically implied theory, possibly aftersuitable translation) of an OMS in a smaller signature or OMS language
Consider an ontology involving a concept Person, and another one involving Human being, and an alignment that relates these to concepts. In the combination of the ontologies along the alignment, there is only one concept, representing both Person and Human being.
aggregation of all the OMS in an OMS network, where non-logical symbols are shared according to the OMS mappings in the OMS network
subject mapping is the composition of the object list of mapping
Essentially, this means list item 1 composed with list item 2 composed with â€¦ composed with list item n. All elements of the latter list must be instances of the same class as the subject. (Note that enforcing the latter constraint goes beyond OWL, and the range cannot be specified in OWL DL.)
subject OMS is a consequence-theoretic conservative extension of the object OMS
A consequence-theoretic conservative extension is an extension that does not add new theorems (in terms of the unextended signature).
subject is a conservative extension of the object
$O_2$ being a definitional extension of $O_1$ implies a bijective correspondence between the classes of realizations of $O_2$ and $O_1$.
An extension $O_2$ of an OMS $O_1$ is a definitional extension, if each realization of $O_1$ can be uniquely expanded to a realization of $O_2$.
Each definitional extension is also a monomorphic extension but not vice versa.
We need FOL, or the same reification approach as chosen for the different kinds of translations, for capturing that an extension is definitional if and only if it is weakly definitional and model-theoretically conservative.
extension whose newly introduced non-logical symbols are interpreted in a unique way
isMonomorphicExtensionOf
any resource in an OMS (e.g. a non-logical symbol, a sentence, a correspondence, the OMS itself, ...) or a named set of such resources
subject is embeddable into the object logic
inverse of relation of logical entailment
an exact mapping from the subject to the object logic
relation between two OMS whereby the subject OMS is an extension of the object OMS, i.e. the sets of non-logical symbols and sentences of the subject OMS are supersets of those of the object OMS
extends
is extension of
a faithful mapping from the subject to the object logic
object is a precise mathematical entity capturing the subject (which is an informal or semi-formal entity)
A conservative extension $O_2$ of an OMS $O_1$ is an implied extension, if and only if the signature of $O_2$ is the signature of $O_1$. $O_2$ is an implied extension of $O_1$ if and only if the realization class of $O_2$ is the realization class of $O_1$.
Each implied extension is also a definitional extension but not vice versa.
model-theoretic conservative extension that does not introduce new non-logical symbols
isConservativeExtensionOf
object is a DOL library in which the subject is an interpretation between two participating OMS
set of language constructs of a given language, not necessarily forming a sublanguage
The reasoners in Protege don't like us to say the following. Together with the SubPropertyChain specified for supportsSerialization it would go beyond OWL DL anyway.
SubPropertyChain: serialization o serializes
language of an OMS
relation between linguistic entities
property of structured OMS, which may be written in different OMS languages supporting different logics, of being usable jointly in a coherent way (via suitable OMS language translations), such that the notions of their overall consistency and logical entailment have a precise logical semantics
relation between lingustic entities that has a logical, semantic nature
indicates that there is a mapping from the object to the subject
indicates that there is a mapping from the object language to the subject language
indicates that there is a mapping from the object logic to the subject logic
indicates that there is a mapping from the subject to the object
indicates a realization-bijective mapping from the subject to the object logic
indicates that there is a mapping from the subject language to the object language
indicates that there is a mapping from the subject logic to the object logic
object mapping maps from the subject into something of the same type as the subject
object is a DOL library, in which the subject is a mapping between two participating OMS
relation between mathematical entities
set membership relation
indicates that there is a realization-expansive mapping from the subject to the object logic
relationship between a realization and an OMS where the realization is a member of the realization class of the OMS (which for flattenable OMS is equivalent to being a realization of the signature of the OMS and satisfying all sentences in the OMS)
relationship between a realization and a signature (vocabulary) such that the realization provides a semantic interpretation of all non-logical symbols in the signature
the subject OMS is a model-theoretic conservative extension of the object OMS. A model-theoretic conservative extension is an extension that does not lead to a restriction of class of realizations (models) of an OMS
isConsequenceTheoreticallyConservativeExtensionOf
relationship between two OMS where the first conservatively extends to the second OMS
subject OMS is a monomorphic extension of the object OMS
A monomorphic extension is an extension whose newly introduced non-logical symbols are interpreted in a way unique up to isomorphism.
isModelTheoreticallyConservativeExtensionOf
relationship between an OMS documentation and the documented OMS
structured OMS expressing the combination of all constraints of a sequences of OMS
subject is an OMS participating in a DOL library, which is the object
indicates that there is a plain mapping from the subject to the object logic
subject is a profile of the object language
This is a stronger notion than just being a sublanguage. Supported serializations are shared along this property.
indicates that there is a reduction from the object to the subject
indicates that there is a reduction from the subject to the object
property used in the context of mappings, for both linguistic and mathematical entities
relation that has a semantic nature
sequence membership relation
the textual syntax in which an OMS is written
indicates that there is a simple theoroidal mapping from the subject to the object logic
object mapping maps from the subject into something of the same type as the subject
syntactically specified subset of a given language, consisting of a subset of its terminal and nonterminal symbols and grammar rules
Supported logics are shared along the inverse of this property.
logic that is a syntactic restriction of another logic, inheriting its semantics
OMS whose sets of non-logical symbols and sentences are subsets of those present in a given larger OMS
indicates that there is a translation from the object to the subject
indicates that there is a translation from the subject to the object
subject OMS is a weak definitional extension of the object OMS
A weak definitional extension is an extension whose newly introduced non-logical symbols can be interpreted in at most one way.
indicates that there is a weakly exact mapping from the subject to the object logic
Enforcing the constraint that a mapping must map into something of the same type goes beyond OWL.
relationship between a mapping and its domain
relationship between a mapping and its codomain
subject property is reified by the object class
subject class reifies the object property
Because of the punning issue in OWL DL, this property is used in restrictions that explicitly do not include the target object property. The target property is identified instead in a usage note on the class that reifies that property, which can be codified in a rule or FOL.
relationship between a realization and a sentence indicating that the sentence holds true in the realization
relation between a linguistic entity and its semantic denotation
subject is a serialization for the object language; for example, Manchester syntax serializes OWL
Sharing is always relative to a given OMS network that relates different OMS. That is, two given OMS symbols
can share with respect to one OMS network, and not share with respect to some other OMS network.
property of OMS symbols being mapped to the same symbol when computing a combination of an OMS network
indicates that the semantics of [a subset of] the object language can be specified in terms of the subject logic
The semantics of [a subset of] the subject language can be specified in terms of the object logic.
logic represented by a satisfaction relation of the language
subject language mapping corresponds to the object logic mapping
The reasoners in Protege don't like us to say the following. Together with the SubPropertyChain specified for language it would go beyond OWL DL anyway.
SubPropertyChain: isProfileOf o supportsSerialization
OMS in the subject language can be serialized in the object serialization
relation between something and a language used by one or more components of it
an alternative filename extension for a serialization
the media type (MIME type) of a serialization
the preferred filename extension for a serialization
subject class denotes a kind of mapping that, if it holds for a translation, also holds for the adjoint reduction
An abstract syntax can be specified as a MOF metamodel. Then abstract abstract syntax documents can be represented as XMI documents.
term language for representing documents in a machine-processable way
an OMS mapping expressing a collection of relations between entities of the two OMS
Formally, an annotation can be specified as a (subject, predicate, object) triple, as defined in the RDF 1.1 W3C Recommendations. In the case of an annotation on an OMS, the subject of an annotation is an element of an OMS. The predicate is an RDF property defined in an external OMS that describes the way in which the annotation object is related to the annotation subject. Given this representation approach, it is possible to interpret annotations under an RDF semantics. 'Without a logical semantics' under this definition means that annotations to an OMS are not considered sentences of that OMS.
additional information without a logical semantics that is attached to an element of an OMS
the (unique) language aspect of an OMS language that enables the expression of comments and annotations
substitution that, when applied to a given query, turns the latter into a logical consequence of a given OMS
logically implied theory (possibly after suitable translation) of an OMS in a smaller signature or a sublanguage
structured OMS that expresses a maximum approximant
sentence postulated to be valid (i.e., true in every realization)
axiom that used in a simple theoroidal mapping
unstructured native OMS that may be used as a building block for a larger OMS, denoting a logical theory
In DOL, objects of a category are usually signatures or OMS, and morphisms are signature morphisms, or OMS mappings. In principle, no assumption about the exact nature of objects and morphisms is made.
The morphisms determine which part of the structure of the objects is relevant, i.e. preserved by morphisms. Hence, objects can be seen as 'sets with structure', and morphisms as 'structure-preserving maps'. However note that not all categories can be obtained in this way.
a class of objects with suitable morphisms between them
a class of realizations (over some signature in some logic)
DOL supports four different forms of closure: minimization and maximization as well as freeness and cofreeness.
Symbols from the local environment are assumed to have a fixed interpretation. Only the symbols newly declared in the closure are forced to have minimal or maximal interpretation.
structured OMS expressing a variant of the closed world assumption by restricting the realizations to those that are minimal or maximal (with respect to the local environment)
The closed world assumption is a default assumption about facts whose status in unknown.
In first-order-like logics, cofreeness means maximal interpretation of predicates and equality being observable equivalence. Cofreeness can be used for the specification of coinductive datatypes like infinite lists and streams.
special type of closure, restriction of realizations to those that are cofree (with respect to the local environment)
collection whose members are expressions
Consider an ontology involving a concept Person, and another one involving Human being, and an alignment that relates these to concepts. In the combination of the ontologies along the alignment, there is only one concept, representing both Person and Human being.
structured OMS expressing the aggregation of all the OMS in an OMS network, where non-logical symbols are shared according to the OMS mappings in the OMS network
An extension O_2 of an OMS O_1 is a consequence-theoretic conservative extension, if all properties formulated in the signature of O_1 hold for O_1 whenever they hold for O_2.
extension that does not add new theorems (in terms of the unextended signature)
An extension O_2 of an OMS O_1 is a consequence-theoretic conservative extension, if all properties formulated in the signature of O_1 hold for O_1 whenever they hold for O_2.
mapping of a consequence-theoretic conservative extension
reifies property isConsequenceTheoreticallyConservativeExtensionOf
extension that does not add new logical properties with respect to the signature of the extended OMS
If used without qualification, the consequence-theoretic version is meant.
extension mapping of a consequence-theoretic or model-theoretic conservative extension
reifies property isConservativeExtensionOf
OMS that has a non-trivial set of logical consequences in the sense that not every sentence follows from the OMS
A correspondence is given as a quadruple (e_1, R, e_2, c), where R denotes the type of relationship that is asserted to hold between the two non-logical symbols or terms, and 0<=c<=1 is a confidence value. R and c may be omitted: When R is omitted, it defaults to the equivalence relation, unless another defaultrelation has been explicitly specified; when c is omitted, it defaults to 1.
relationship between a non-logical symbol e_1 from an OMS O_1 and a non-logical symbol e_2 from an OMS O_2, or between a non-logical symbol e_1 from O_1 and a term t_2 formed from non-logical symbols from O_2
document containing a DOL library
entity that is used in DOL texts
Collection is used here in the sense of syntactic collection.
collection of named OMS and OMS networks, possibly written in different OMS languages, linked by named OMS mappings
DOL structured OMS, typically, use basic OMS as building blocks for defining other structured OMS, OMS mappings or OMS networks.
syntactically valid DOL expression denoting an OMS that is built from smaller OMS as building blocks
logic mapping that will be chosen by default if only the source and target logic are given
language mapping that will be chosen by default if only the source and target language are given
mapping that will be chosen by default if only the source and target are given
An extension O_2 of an OMS O_1 is a definitional extension, if each realization (model) of O_1 can be uniquely expanded to a realization of O_2.
extension whose newly introduced non-logical symbols are interpreted in a unique way
O_2 being a definitional extension of O_1 implies a bijective correspondence between the classes of realizations of O_2 and O_1.
An extension O_2 of an OMS O_1 is a definitional extension, if each realization of O_1 can be uniquely expanded to a realization of O_2.
Each definitional extension is also a monomorphic extension but not vice versa.
mapping of a definition extension
reifies property isDefinitionalExtensionOf
text that typically is the result of serializing an object using a given serialization
In other words, typical documentthat is a linguistic entity used in context of the DOL standard contain an OMS or DOL library.
OMS that is not flattenable
logic mapping that embeds the source into the target logic, using components that are injections and (in the case of realization translations) isomorphism
reifies property isEmbeddableInto
Entailment expresses that each realization satisfying the first OMS also satisfies the second OMS (or the sentence, respectively).
Entailments can also be stated between networks, or networks and OMS.
logical consequence
a relation between two OMS (or an OMS and a sentence, or two OMS networks, or an OMS network and an OMS) expressing that the second item (the conclusion) is logically implied by the first one (the premise)
Two OMS are equivalent if they have a common definitional extension. The OMS may be written in different OMS languages.
OMS mapping ensuring that two OMS share the same definable concepts
logic mapping that is compatible with certain DOL structuring constructs
reifies property isExactlyMappableTo
a finite combination of symbols that are well-formed according to applicable rules (depending on the language)
The new symbols and sentences are interpreted relative to the local envorinment, which is the signature of the 'given OMS'.
structured OMS extending a given OMS with new symbols and sentences
This definition differs from that in the Terms and Definition section of the DOL specification by focussing on the mapping rather than the codomain of the mapping.
mapping of an extension
logic mapping that preserves and reflects logical consequence
reifies property isFaithfullyMappableTo
If a symbol is removed, all axioms containing that symbol are removed, too.
structured OMS expressing the verbatim removal of symbols or axioms from an OMS
More precisely, an OMS is flattenable if and only if it is either a basic OMS or it is an extension, union, translation, module extraction, approximation, filtering, or reference of named OMS involving only flattenable OMS.
OMS that can be seen, by purely syntactical means, to be logically equivalent to a basic OMS
process of transforming an OMS to an equivalent basic OMS
A formal semantics is a formalization of the meaning of a language.
assignment of mathematical meaning to a language by mapping abstract syntax to suitable semantic domains
In first-order logic (and similar logics), freeness means minimal interpretation of predicates and minimal equality among data values. Freeness can be used for the specification of inductive datatypes like numbers, lists, trees, bags etc. In order to specify, e.g., lists over some elements, the specification of the elements should be in the local environment.
special type of closure, restriction of realizations to those that are free (with respect to the local environment)
mapping from identifiers (IRIs) to values in semantics domains representing semantic information about a set of documents (the latter typically being distributed over the internet)
network
set of objects (nodes) that are connected by links (edges)
environment for the expression of homogeneous and heterogeneous OMS, comprising a logic graph, an OMS language graph and a supports relation
The support relations specify which language supports which logics and which serializations, and which language translation supports which logic translation or reduction. Moreover, each language has a default logic and a default serialization.
Although in principle, there can be many heterogeneous environments, for ensuring interoperability, there will be a global heterogeneous environment (maintained in some registry), with subenvironments for specific purposes.
OMS whose parts are supported by different logics
OMS whose parts are supported by one logic
A conservative extension O_2 of an OMS O_1 is an implied extension, if and only if the signature of O_2 is the signature of O_1. O_2 is an implied extension of O_1 if and only if the realization class of O_2 is the realization class of O_1.
model-theoretic conservative extension that does not introduce new non-logical symbols
A conservative extension O_2 of an OMS O_1 is an implied extension, if and only if the signature of O_2 is the signature of O_1. O_2 is an implied extension of O_1 if and only if the realization class of O_2 is the realization class of O_1.
Each implied extension is also a definitional extension but not vice versa.
mapping of an implied extension
reifies property isImpliedExtensionOf
An owl:import in OWL is an import.
Importing O_1 into O_2 turns O_2 into an extension of O_1.
Semantically, an import of O_2 into O_1 is equivalent to the verbatim inclusion of O_2 in place of the import declaration.
The import of a whole DOL library into another DOL library is also called import.
The purpose of O_2 importing O_1 is to make non-logical symbols and sentences of O_1 available in O_2.
reference to an OMS or DOL library behaving as if it were verbatim included
OMS that has a trivial set of logical consequences in the sense that every sentence follows from the OMS
metaframework mathematically formalizing the notion of a logic in terms of notions of signature, signature morphism, realization, sentence and satisfaction
signature mediating between an OMS and a module of that OMS in the sense that it contains those non-logical symbols that the sentences of the module and the sentences of the OMS have in common
OMS mapping that postulates a specialization relation between two OMS along a morphism between their signatures
refinement
view
Collection is used here in the sense of syntactic collection.
collection of expressions, following formal rules of well-formedness
a body of words, following a set of methods of combining them (called a grammar), understood by a community and used as a form of communication
syntactic pattern that is part of a language
set of language constructs of a given language, not necessarily forming a sublanguage
graph with OMS languages as nodes and OMS language translations and OMS language reductions as edges, typically used in a heterogeneous environment
mapping between languages
entity that is of linguistic, syntactic nature
RDF, serialized as RDF/XML, is the most common format for publishing linked data. However, its usage is not mandatory.
Linked data principles, as interpreted herein, are as follows: (a) Use IRIs as names for things; (b) Use HTTP IRIs so that these things can be referred to and looked up (dereferenced) by people and user agents; i.e., the IRI is treated as a URL (uniform resource locator); (c) Provide useful machine-processable (plus optionally human-readable) information about the thing when its IRI is dereferenced, using standard formats; (d) Include links to other, related IRIs in the exposed data to improve discovery of other related information on the Web.
Using HTTP content negotiation, it is possible to serve representations in different formats from the same URL.
structured data that is published on the Web in a machine-processable way, according to principles explained in http://linkeddata.org/
signature built from all previously-declared symbols and axioms
SROIQ(D) is the logic underlying OWL 2 DL.
Most OMS languages have an underlying logic.
See the annexes in the DOL specification for an explanation of the organization of the relation between OMS languages and their logics and serializations.
specification of monotonic valid reasoning that comprises signatures, sentences, realizations, and a satisfaction relation between realizations and sentences
SROIQ(D) is the monotonic logic underlying OWL 2 DL.
Reiter's default logic is a logic that is not monotonic.
Most OMS languages have an underlying logic.
See the annexes in the DOL specification for an explanation of the organization of the relation between OMS languages and their logics and serializations.
specification of (possibly non-monotonic) valid reasoning that comprises signatures, sentences, realizations, and a satisfaction relation between realizations and sentences
In a logic graph, some of the logic translations and reductions can be marked to be default translations.
graph with logics as nodes and logic translations and logic reductions as edges, typically used in a heterogeneous environment
mapping between logics
mapping between logics forgetting parts of the logical structure, projection to a smaller logic, in contrast to translation
reduction of a source logic onto a (usually less expressive) target logic (mapping signatures, sentences and realizations) that simply forgets those parts of the logical structure not fitting the target logic
mapping forgetting parts of the source, projection to a smaller target, in contrast to translation
reduction of a source onto a (usually less expressive) target that simply forgets those parts of the source not fitting the target
mapping between OMS languages forgetting parts of the source, projection to a smaller language, in contrast to translation
reduction of a source language onto a (usually less expressive) target language that simply forgets those parts of the source language not fitting the target language
An OMS language reduction shall satisfy the property that the result of a reduction is a well-formed text in the target language.
mapping between logics representing all structure, in contrast to reduction
translation of a source logic into a target logic (mapping signatures, sentences and realizations) that keeps or encodes the logical content of OMS
mapping representing the source completely, in contrast to reduction
mapping of a source into a target that keeps or encodes the content of the source
the (unique) language aspect of an OMS language that enables the expression of non-logical symbols and sentences in a logical language
The sentences must use only those non-logical symbols that are present in the signature.
a signature together with a set of sentences (over that signature)
Not to be confused with the term 'model' in the sense of logic (model theory), which is termed 'realization' in this ontology.
representation of (the development of) a system (e.g., hardware, software, information system, or organization), or a domain related to a system, used in model-driven engineering (MDE)
function
in some cases is a morphism, as in Category Theory.
relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output
reifies property isMappableTo
tool that implements matching
algorithmic procedure that generates an alignment for two given OMS
entity that is part of a mathematical theory
form of closure that restricts the realizations to those that are maximal (with respect to the local environment)
Technically, a maximum approximant is a uniform interpolant
best possible (in the sense of a maximum set of logical consequences) approximant of an OMS in a smaller signature or a sublanguage
Also known as circumscription.
form of closure that restricts the realizations to those that are minimal (with respect to the local environment)
semantic interpretation of all non-logical symbols of a signature
A realization of an OMS is a realization of the signature of the OMS that also satisfies all the additional constraints expressed by the OMS. In case of flattenable OMS, these constraints are expressed by the axioms of the OMS.
This term is called 'realization' and not 'model' in order not to be confused with model in the sense of modeling (i.e., the 'M' in OMS).
logic mapping that has a bijective mapping of realizations (models)
reifies property isMappableToBijectivelyOnModels
logic mapping that has a surjective realization (model) translation (ensuring faithfulness of the mapping)
reifies property isModelExpansivelyMappableTo
tool that implements realization (model) finding
process that finds realizations (models) of an OMS and thus proves it to be satisfiable
An extension O_2 of an OMS O_1 is a model-theoretic conservative extension, if all properties formulated in the signature of O_1 hold for O_1 whenever they hold for O_2.
extension that does not lead to a restriction of class of models of an OMS
An extension O_2 of an OMS O_1 is a model-theoretic conservative extension, if all properties formulated in the signature of O_1 hold for O_1 whenever they hold for O_2.
Any model-theoretic conservative extension is also a consequence-theoretic one.
mapping of a model-theoretic conservative extension
reifies property isModelTheoreticallyConservativeExtensionOf
structured OMS expressing a subOMS that conservatively extends to conservative extension the whole OMS
Cited and slightly adapted from Suarez, Figueroa et al: Ontology Glossary 2008
The goal of module extraction is 'decomposing an OMS into smaller, more manageable modules with appropriate dependencies' \cite{DBLP:series/lncs/5445}
activity of obtaining from an OMS concrete modules to be used for a particular purpose (e.g., to contain a particular sub-signature of the original OMS)
tool that implements module extraction
An extension O_2 of an OMS O_1 is a monomorphic extension, if each realization (model) of O_1 can be expanded to a realization of O_2 that is unique up to isomorphism.
extension whose newly introduced non-logical symbols are interpreted in a way unique up to isomorphism
An extension O_2 of an OMS O_1 is a monomorphic extension, if each realization (model) of O_1 can be expanded to a realization of O_2 that is unique up to isomorphism.
Each monomorphic extension is also a model-theoretic conservative extension but not vice versa.
mapping of a monomorphic extension
reifies property isMonomorphicExtensionOf
document containing a native OMS
sequence of expressions (like non-logical symbols, sentences and structuring elements) from a given OMS language
Non-logical symbols in Common Logic (ISO/IEC 24707:2007) comprise (a) names (denoting objects from the domain of discourse), and (b) sequence markers (denoting sequences of objects). This is opposed to logical symbols in Common Logic, e.g., logical connectives and quantifiers.
Non-logical symbols in OWL (W3C/TR REC-owl2-syntax), called 'entities' therein, comprise \begin{itemize} \item individuals (denoting objects from the domain of discourse), \item classes (denoting sets of objects; also called concepts), and \item properties (denoting binary relations over objects; also called roles). \end{itemize} This is opposed to logical symbols in OWL, e.g.\ those for intersection and union of classes.
OMS symbol
The notion of 'atomic sentence' used in logic is different, it usually may involve several non-logical symbols.
symbol that requires an interpretation through a realization
Logical symbols in Common Logic include propositional connectives and quantifiers.
Logical symbols in OWL include propositional connectives (e.g. the intersection operator on classes) and quantifiers (e.g. the existential restriction operator).
symbol whose interpretation is fixed by the logic
atomic expression or syntactic constituent of an OMS
An OMS can be written in different OMS language serializations.
An OMS has a single signature and realization class over that signature as its model-theoretic semantics.
An OMS is a collection of expressions (like non-logical symbols, sentences and structuring elements) in a given OMS language (or several such languages) and denoting a class of realizations and, possibly, a logical theory
a basic or structured ontology, specification or model
collection is used here in the sense of syntactic collection
Adapted from SuarezFigueroaEtAl:OntologyGlossary2008
set of all annotations to an OMS, plus any other documents and explanatory comments generated during the entire OMS building process
An OMS language is used for the formal specification of OMS.
OMS languages include OWL, Common Logic, F-logic, UML class diagrams, RDFS, and OBO.
language equipped with a formal, declarative, logic-based semantics, plus non-logical annotations
An OMS language translation shall satisfy the property that the result of a translation is well-formed in the target language.
a translation between two OMS languages that keeps or encodes the content of the source
relationship between two OMS, typically given as a set of correspondences
reifies property isMappableTo
An OMS network is a diagram of OMS in the sense of category theory, but different from a diagram in the sense of model-driven architecture.
collection is used here in the sense of syntactic collection
collection of named OMS, possibly written in different OMS languages, linked by named OMS mappings and named OMS networks
the definition deliberately includes OMS networks; this is a recursive definition. A specific network can make use of this recursion only finitely many times.
hyperontology
DOL structured OMS expressing the restriction of an OMS to a smaller signature
reifies property isReducibleTo
object giving the semantics of an OMS
An OMS translation results in an OMS mapping between the original and the translation OMS.
DOL structured OMS expressing the assignment of new names to some non-logical symbols of an OMS, or translation of an OMS along a language translation
explicit and shared formal representation of the entities and their interrelationships of a given domain of discourse or of fundamental notions
The explicit and shared formal representation is materialised in some OMS language (or several such languages).
Ontologies also include definitions and explanations in natural language that capture the intended meaning of the formal expressions.
Ontologies typically include a taxonomy and, frequently, a partonomy.
logic mapping that maps signatures to signatures and therefore does not use infrastructure axioms
reifies property isPlainlyMappableTo
algorithmic procedure working on DOL-related linguistic entities as input
Profiles can have different logics, even with completely different semantics, e.g., OWL 2 DL versus OWL 2 Full.
The logic needs to support the language.
(syntactic) sublanguage of an OMS language interpreting according to a particular logic that targets specific applications or reasoning methods}
Profiles of OWL 2 include OWL 2 EL, OWL 2 QL, OWL 2 RL, OWL 2 DL, and OWL 2 Full.
Profiles typically correspond to sublogics.
sentence containing variables that can be instantiated by a substitution
SPARQL, Prolog
There are also general purpose OMS languages, which can express both OMS and quries.
OMS language specifically dedicated to queries
From an abstract point of view, query variables are just symbols; they are used in a way that they will be substituted using a substitution. Many OMS languages have special notations for (query) variables.
If there are no variables in an OMS language, constants can be used as query variables.
Usually, query variables are the free variables of a sentence, whereas there can be other (bound) variables.
symbol that will be used in a query and a substitution
OMS mapping that postulates a specialization relation between two OMS along a morphism between their signatures
Familiar examples include an electronic document, an image, a source of information with a consistent purpose (e.g., 'today's weather report for Los Angeles'), a service (e.g., an HTTP-to-SMS gateway), and a collection of other resources. A resource is not necessarily accessible via the Internet; e.g., human beings, corporations, and bound books in a library can also be resources. Likewise, abstract concepts can be resources, such as the operators and operands of a mathematical equation, the types of a relationship (e.g., 'parent' or 'employee'), or numeric values (e.g., zero, one, and infinity). \nisref{IETF/RFC 3986:2005, Section 1.1}
IETF/RFC 3986:2005, Section 1.1 deliberately defines a resource as 'in a general sense whatever might be identified by an IRI'. The original source refers to URIs, but DOL uses the compatible IRI standard IETF/RFC 3987:2005 for identification.
something that can be globally identified
relation between realizations and sentences indicating which sentences hold true in the realization
OMS that is satisfied by least one realization
mathematically-defined set of values that can represent the intended meanings of language constructs
entity that is of semantic nature, i.e. relating linguistic objects with their semantic denotation in a mathematical structure
specification of a mapping from abstract syntax to a semantic domain
A sentence can conform to one or more signatures (namely those signatures containing all non-logical symbols used in the sentence).
In a realization, on the one hand, a sentence is always true or false. In an OMS, on the other hand, a sentence can have several logical statuses: it can be an axiom, if postulated to be true; a theorem, if proven from other axioms and theorems; a conjecture, if expecting to be proven from other axioms and theorems; or have another of many possible statuses.
It is quite common that sentences are required to be closed (i.e., have no free variables). However, this depends on the OMS language at hand.
term that is either true or false in a given realization, i.e., which is assigned a truth value in this realization
sequence is used here in the sense of syntactic sequence
ordered collection where also multiplicity of elements matters
sequence is used here in the sense of syntactic sequence
sequence whose members are correspondences
sequence is used here in the sense of syntactic sequence
sequence whose members are OMS
Common Logic uses the term 'dialect'; the following are standard Common Logic dialects: Common Logic Interchange Format (CLIF), Conceptual Graph Interchange Format (GCIF), eXtended Common Logic Markup Language (XCL).
OWL uses the term 'serialization' the following are standard OWL serializations: OWL functional-style syntax, OWL/XML, OWL Manchester syntax, plus any standard serialization of RDF (e.g., RDF/XML, Turtle, ...). However, RDF/XML is the only one tools are required to implement.
Serializations serve as standard formats for exchanging OMS between tools.
specific syntactic encoding of a given OMS language
collection whose members have a certain type, as specified by the type parameter
set whose members are annotation expressions
set whose members are mappings
set whose members are non-logical symbols
set whose members are sentences
The signature of a term is the set of all non-logical symbols occuring in the term. The signature of an OMS language is the set of all non-logical symbols possible in that language.
set (or otherwise structured entity) of non-logical symbols of an OMS
A list of symbol map items induces a signature morphism.
mapping between two signatures, preserving the structure of the source signature within the target signature
logic mapping that maps signatures of the source logic to theories of the target logic
reifies property isSimplyTheoroidallyMappableTo
formal representation of (requirements of) a data structure, an algorithm or a hardware or software system used in systems analysis, requirements analysis and systems design
way of providing annotations to subjects in external resources, without embedding them into the original resource (here: OMS)
OMS that results from other OMS by import, union, combination, renaming or other structuring operations
the (unique) language aspect of an OMS language that covers structured OMS as well as the relations of basic OMS and structured OMS to each other, including, but not limited to imports, OMS mappings, conservative extensions, and the handling of prefixes for CURIEs
logic embedding that is 'syntactic' in the sense that signature and sentence translations are inclusions
reifies property isSubLogicOf
OMS mapping that maps variables of one OMS to complex terms of another OMS
There is also a supports relation between OMS languages and serializations, and one between language mappings and logic mappings.
relation between OMS languages and logics expressing the logical language aspect of the former, namely that the constructs of the former lead to a logical theory in the latter
reifies properties: supportsLogic, supportsLogicMapping, supportsSerialization
A symbol map item is given as s_1 |-> s_2, where $s_1$ is a symbol from the source OMS and $s_2$ is a symbol from the target of the OMS mapping.
pair of symbols of two OMS, indicating how a symbol from the first OMS is mapped by a signature morphism to a symbol of the second OMS
syntactic expression either consisting of a single non-logical symbol or recursively composed of other terms (a.k.a. its subterms) and possibly logical symbols
software tool implementing theorem proving
process of demonstraing that a sentence (or OMS) is the logical consequence of some OMS
sentence that has been proven from other axioms and theorems
software for processing DOL libraries and OMS
process of applying a language or logic translation, or flattening an OMS translation
structured OMS expressing the combination of all symbols and axioms (and more general constraints) of a sequence of OMS
OMS that is not satisfied by any realization
When an interpretation is given as a set of correspondences, these are given as tuples, where the type of relationship is given by the specific kind of interpretation.
An interpretation typically leads to proof obligations, \ie one has to prove that axioms of the source OMS of the mapping are theorems in the target OMS.
OMS mapping that postulates a relation between two OMS
interpretation
An extension O_2 of an OMS O_1 is a weak definitional extension, if each realization of O_1 can be expanded to at most one realization of O_2.
extension whose newly introduced non-logical symbols can be interpreted in at most one way
An extension O_2 of an OMS O_1 is a weak definitional extension, if each realization of O_1 can be expanded to at most one realization of O_2.
An extension is definitional if and only if it is both weakly definitional and model-theoretically conservative.
mapping of a weak definitional extension
reifies property isWeakDefinitionalExtensionOf
logic mapping that is weakly compatible with certain DOL structuring constructs
reifies property isWeaklyExactlyMappableTo
entity that is related to the world wide web
When viewed as an OMS language, DOL has OMS as its non-logical symbols, and OMS mappings as its sentences.
unified metalanguage for the structured and heterogeneous expression of ontologies, specifications, and models, using DOL libraries of OMS, OMS mappings and OMS networks