Three Theses of Representation in the Semantic Web Ian Horrocks University of Manchester Manchester,...
-
Upload
gia-canterbury -
Category
Documents
-
view
217 -
download
4
Transcript of Three Theses of Representation in the Semantic Web Ian Horrocks University of Manchester Manchester,...
![Page 1: Three Theses of Representation in the Semantic Web Ian Horrocks University of Manchester Manchester, UK horrocks@cs.man.ac.uk Peter F. Patel-Schneider.](https://reader035.fdocuments.us/reader035/viewer/2022070307/551ae6a15503466b6a8b5e8e/html5/thumbnails/1.jpg)
Three Theses of Representationin the Semantic Web
Ian Horrocks
University of Manchester
Manchester, UK
Peter F. Patel-Schneider
Bell Labs Research
Murray Hill, NJ, USA
![Page 2: Three Theses of Representation in the Semantic Web Ian Horrocks University of Manchester Manchester, UK horrocks@cs.man.ac.uk Peter F. Patel-Schneider.](https://reader035.fdocuments.us/reader035/viewer/2022070307/551ae6a15503466b6a8b5e8e/html5/thumbnails/2.jpg)
Semantic Web Languages• SemWeb aims to make content accessible to automated processes
– Add semantic markup (meta-data) describing content/function of resources
• Need a common way of providing meta-data so that:– It can be understood and manipulated by automated processes (“agents”)– Agents can integrate meta-data from different sources
• Proposed solution is famous language “layer cake”:
![Page 3: Three Theses of Representation in the Semantic Web Ian Horrocks University of Manchester Manchester, UK horrocks@cs.man.ac.uk Peter F. Patel-Schneider.](https://reader035.fdocuments.us/reader035/viewer/2022070307/551ae6a15503466b6a8b5e8e/html5/thumbnails/3.jpg)
Language Architecture• Relationship between adjacent layers not clear
– XML $ RDF relationship purely syntactic
– RDF $ Ontology layer relationship should be something more?
• RDF is proposed as base for SemWeb languages– Used to add metadata annotations to resources
– Also used to define syntax and semantics of subsequent layers
• Not clear that RDF is appropriate for all these functions– Limited set of syntax constructs (triples)
– Not possible to extend syntax (as it is, e.g., when using XML)
– Uniform semantic treatment of triple syntax
– Non standard KR thesis and model theory
• May facilitate development of SemWeb to use more standard KR thesis…
![Page 4: Three Theses of Representation in the Semantic Web Ian Horrocks University of Manchester Manchester, UK horrocks@cs.man.ac.uk Peter F. Patel-Schneider.](https://reader035.fdocuments.us/reader035/viewer/2022070307/551ae6a15503466b6a8b5e8e/html5/thumbnails/4.jpg)
Ontology Language Layer• Ontologies set to play key role in SemWeb
– source of shared and precisely defined terms for use in meta-data
• RDF already extended to RDFS– Hierarchies of classes and properties
– Domain and range constraints on properties
• More expressive ontology languages clearly required– With logical connectives, quantifiers, transitive properties, etc.
– E.g., OIL, DAML+OIL, and now OWL
• Possible choices for language layering:– Base ontology language layer(s) on RDF(S)
– Base ontology language layer(s) on “classical” FOL
– Base ontology language layer(s) on SKIF/Lbase/CL languages
![Page 5: Three Theses of Representation in the Semantic Web Ian Horrocks University of Manchester Manchester, UK horrocks@cs.man.ac.uk Peter F. Patel-Schneider.](https://reader035.fdocuments.us/reader035/viewer/2022070307/551ae6a15503466b6a8b5e8e/html5/thumbnails/5.jpg)
Semantics and Model Theories• Ontology/KR languages aim to model (part of) world• Constructs in language correspond to entities in world• Meaning given by mapping to some formal system
– E.g., a logic such as FOL with its own well defined semantics– or a data model such as XQuery data model for XML– or (for more expressive languages) a Model Theory (MT)
• MT defines relationship between syntax and interpretations– Can be many interpretations (models) of one piece of syntax– Models supposed to be analogue of (part of) world
• E.g., elements of model correspond to objects in world– Formal relationship between syntax and models
• Structure of models must reflect relationships specified in syntax– Inference (e.g., entailment) defined in terms of MT
• E.g., A ² B iff every model of A is also a model of B
![Page 6: Three Theses of Representation in the Semantic Web Ian Horrocks University of Manchester Manchester, UK horrocks@cs.man.ac.uk Peter F. Patel-Schneider.](https://reader035.fdocuments.us/reader035/viewer/2022070307/551ae6a15503466b6a8b5e8e/html5/thumbnails/6.jpg)
FOL Thesis• Base SW languages on established
FO hierarchy– Propositional logic
– Decidable FOL subsets (e.g., DL, Horn)
– Undecidable FOL subsets
– Full FOL (and even HOL)
• Higher layers extend syntax– Upwards compatibility, i.e., syntax retains
same meaning in higher layers
• Semantics via FOL mapping or standard FO model theory
– Individual i ! element of domain (iI 2 D)
– Class C ! sets of elements (CI µ D)
– Property P ! binary rel on D (PI µ D £ D)
![Page 7: Three Theses of Representation in the Semantic Web Ian Horrocks University of Manchester Manchester, UK horrocks@cs.man.ac.uk Peter F. Patel-Schneider.](https://reader035.fdocuments.us/reader035/viewer/2022070307/551ae6a15503466b6a8b5e8e/html5/thumbnails/7.jpg)
(Dis)advantages of FOL Thesis• Pros
– Based on well known and extensively studied formalism– Wealth of theoretical knowledge and practical experience– Family of sub-languages with well known formal properties
• E.g., decidability, complexity– Highly optimised reasoners for FOL and many sub-languages
• E.g., DL reasoners, Horn (rule) reasoners, FOL provers– Mapping to FOL provides easy integration, e.g., of DL and Horn
languages– FO subset of RDFS fits well in this framework
• Cons– No classes as instances (unless extended to HOL)– Relatively poor fit with full RDFS
• Can be axiomatised in FOL, but may damage semantic interoperability and computational properties
![Page 8: Three Theses of Representation in the Semantic Web Ian Horrocks University of Manchester Manchester, UK horrocks@cs.man.ac.uk Peter F. Patel-Schneider.](https://reader035.fdocuments.us/reader035/viewer/2022070307/551ae6a15503466b6a8b5e8e/html5/thumbnails/8.jpg)
Axiomatisation• An Axiomatisation can be used to embed RDFS in FOL, e.g.:
– Triple x P y translated as holds2(P,x,y)– Axioms capture semantics of language, e.g.:
• Problems with axiomatisations include– May require large and complex set of axioms– Difficult to prove semantics have been correctly captured– Axiomatisation may greatly increase computational complexity
• RDFS ! undecidable (subset of) FOL– No interoperability unless all languages similarly axiomatised
• E.g., in DAML+OIL, C subClassOf D equivalent to 8 x.C(x) ! D(x)
• But have to axiomatise as holds2(subClass, C, D)
![Page 9: Three Theses of Representation in the Semantic Web Ian Horrocks University of Manchester Manchester, UK horrocks@cs.man.ac.uk Peter F. Patel-Schneider.](https://reader035.fdocuments.us/reader035/viewer/2022070307/551ae6a15503466b6a8b5e8e/html5/thumbnails/9.jpg)
SKIF/Lbase/CL Thesis• Base SW languages on SKIF/Lbase/CL
– Similar to FOL thesis, but FOL replaced with CL
• Higher layers extend syntax– Upwards compatibility, i.e., syntax retains
same meaning in higher layers
• Semantics via mapping into CL
• CL provides model theory– Individual i ! element of domain (iV 2 D)
– Class C ! element of domain (CV 2 D)
– Property P ! element of domain (PV 2 D)
Second mapping (ext)
– Class elt w ! set of elts (ext(w) µ D)
– Prop elt k ! binary rel (ext(P) µ D £ D)
![Page 10: Three Theses of Representation in the Semantic Web Ian Horrocks University of Manchester Manchester, UK horrocks@cs.man.ac.uk Peter F. Patel-Schneider.](https://reader035.fdocuments.us/reader035/viewer/2022070307/551ae6a15503466b6a8b5e8e/html5/thumbnails/10.jpg)
(Dis)advantages of CL Thesis• Pros
– Classes as individuals without HOL extension– Can use as a basis for a family of sub-languages– Mapping to CL provides easy integration of sub-languages– Better fit with RDFS
• Cons– Relatively new and untried– Little known about CL sub-languages– Confusion w.r.t. FOL compatibility– RDFS still requires axiomatisation due, e.g., to rdf:type being in
domain of discourse• Still no direct semantic interoperability with RDFS
– Computational pathway only via (performance-damaging) FOL mapping
![Page 11: Three Theses of Representation in the Semantic Web Ian Horrocks University of Manchester Manchester, UK horrocks@cs.man.ac.uk Peter F. Patel-Schneider.](https://reader035.fdocuments.us/reader035/viewer/2022070307/551ae6a15503466b6a8b5e8e/html5/thumbnails/11.jpg)
Confusion w.r.t. FOL Compatibility• SKIF/Lbase/CL use same syntax as FOL
– But allow variables to occur in predicate positions
• Originally asserted that SKIF semantics coincide with FOL for well formed FOL sentences
• Subsequently shown to be wrong for FOL with equality– E.g.,
• Moral of the story– May confuse users more familiar with
classical FOL– Easy to make mistakes with complex new
formalisms– Risky to base future of SemWeb on such a
new formalism
![Page 12: Three Theses of Representation in the Semantic Web Ian Horrocks University of Manchester Manchester, UK horrocks@cs.man.ac.uk Peter F. Patel-Schneider.](https://reader035.fdocuments.us/reader035/viewer/2022070307/551ae6a15503466b6a8b5e8e/html5/thumbnails/12.jpg)
RDF Thesis• All SW languages based on triples
– Triple based syntax– Semantics compatible with semantics of
triples as defined by RDF MT
• Upwards & downwards compatibility– Syntax retains same meaning in higher
layers– Higher layer syntax is valid in lower layers
• Semantics via RDF model theory– Similar to CL, but only binary predicates– Language syntax also in domain of
discourse– Higher layers impose additional
constraints on models
• Syntax must be encoded as triples– Awkward for complex constructs– Resulting triples also have meaning
![Page 13: Three Theses of Representation in the Semantic Web Ian Horrocks University of Manchester Manchester, UK horrocks@cs.man.ac.uk Peter F. Patel-Schneider.](https://reader035.fdocuments.us/reader035/viewer/2022070307/551ae6a15503466b6a8b5e8e/html5/thumbnails/13.jpg)
(Dis)advantages of RDF Thesis• Pros
– (Supposed) interoperability between language layers– RDF tools can be used to parse all SW languages into triples– Large ontologies/KBs can be stored in triple DBs
• Cons– Achieving real (semantic) interoperability may be difficult or impossible
• E.g., efforts to layer OWL on top of RDF(S)– Triple encoding of complex languages such as OWL is very clumsy– Triples introduced by encodings have semantic consequences
• E.g., first-rest triples used in list syntax have same consequences as ground facts (even though ordering of list may be arbitrary)
– Not clear if technique can be extended to more expressive languages• E.g., full FOL
– Computational pathway only via (performance-damaging) FOL mapping
![Page 14: Three Theses of Representation in the Semantic Web Ian Horrocks University of Manchester Manchester, UK horrocks@cs.man.ac.uk Peter F. Patel-Schneider.](https://reader035.fdocuments.us/reader035/viewer/2022070307/551ae6a15503466b6a8b5e8e/html5/thumbnails/14.jpg)
Summary• Formal meaning of SW languages crucial to interoperability
– Common semantic underpinning facilitates layered architecture
• Widely assumed that RDF will provide this underpinning– But layering on top of RDF(S) may be difficult/impossible and does
not lead to any direct computational pathway– Moreover, benefits are not clear
• Alternative would be to use standard FOL as underpinning– Well established and well understood– Established family of languages capturing different trade-offs– Direct computational pathway for FOL and many sub-languages– FO subset of RDF(S) would fit well in this framework
• Third approach is to use CL as underpinning– Relatively new and untested– May not solve problems with RDF(S)
![Page 15: Three Theses of Representation in the Semantic Web Ian Horrocks University of Manchester Manchester, UK horrocks@cs.man.ac.uk Peter F. Patel-Schneider.](https://reader035.fdocuments.us/reader035/viewer/2022070307/551ae6a15503466b6a8b5e8e/html5/thumbnails/15.jpg)
Perhaps we should consider recalling the Semantic Web
bandwagon in order to carry out a safety modification on the RDF
component!