Description LogicsDescription Logics

OutlineOutline

• Knowledge RepresentationKnowledge Representation

• Ontology LanguageOntology Language

• Description LogicsDescription Logics

• ApplicationApplication

Knowledge RepresentationKnowledge Representation

• Object: find implicit meaning in explicit knowledgeObject: find implicit meaning in explicit knowledge

• Concentration: since 1970, research of this field falls Concentration: since 1970, research of this field falls into two division—logic-based and cognitive method into two division—logic-based and cognitive method (network structure or problem solving)(network structure or problem solving)

• Logic in Knowledge Representation:Logic in Knowledge Representation:

1 Formalized semantics (reasoning function to symbol)1 Formalized semantics (reasoning function to symbol)

2 Operators and interpretation (semantics of logic 2 Operators and interpretation (semantics of logic expression)expression)

3 Functional explanation of other methods (semantic 3 Functional explanation of other methods (semantic web, frame-based)web, frame-based)

4 In structure-based KR (OWL), reasoning service is 4 In structure-based KR (OWL), reasoning service is related with computing complexityrelated with computing complexity

Ontology LanguageOntology Language

• Classification by structure:Classification by structure:Frame-based: FLogic, OKBC, KMFrame-based: FLogic, OKBC, KMDescription logic-based: OWLDescription logic-based: OWLFirst order logic-based: Cycl, KIFFirst order logic-based: Cycl, KIFframe: definition and restriction of expressiveness, forframe: definition and restriction of expressiveness, for

malism and characteristicsmalism and characteristics• Logic in Ontology:Logic in Ontology:1 Ontology designing: contradiction and hierarchies in c1 Ontology designing: contradiction and hierarchies in c

onceptsoncepts2 Ontology building: consistency, inclusion of instances2 Ontology building: consistency, inclusion of instances

Description LogicsDescription Logics

• ComponentsComponents

• ResearchResearch

• Example: SHIQExample: SHIQ

Description Logics ComponentDescription Logics Component

• Constructors: existential restrictionConstructors: existential restriction

value restrictionvalue restriction

number restrictionnumber restriction

• Terminological axioms: definition & restrictionTerminological axioms: definition & restriction

• Assertion Formalism: attributes of instanceAssertion Formalism: attributes of instance

• Subsumption AlgorithmSubsumption Algorithm

• Instance AlgorithmInstance Algorithm

• Consistency Algorithm: check consistency in Consistency Algorithm: check consistency in terminological axioms and assertionsterminological axioms and assertions

Research in Description LogicsResearch in Description Logics

• Key Problem in the field:Key Problem in the field:

Tradeoff between expressiveness and Tradeoff between expressiveness and reasoning complexity of Description Logicsreasoning complexity of Description Logics

Research StagesResearch Stages

• Phase 1 (1980-1990)Phase 1 (1980-1990) System implementation implying structural suSystem implementation implying structural su

bsumption algorithm, but it’s not complete fbsumption algorithm, but it’s not complete for expressive Description Logics. Computing cor expressive Description Logics. Computing complexity of most DLs’ reasoning service excomplexity of most DLs’ reasoning service exceeds polynomial. eeds polynomial.

Example: KL-ONE, K-REP, BACK, LOOM, CLASSIC Example: KL-ONE, K-REP, BACK, LOOM, CLASSIC

Research StagesResearch Stages

• Phase 2 (1990-1995)Phase 2 (1990-1995)1 Tableau-based algorithms are used for reasoning services in 1 Tableau-based algorithms are used for reasoning services in

DLs, especially for propositionally closed DLs (DLs with all of DLs, especially for propositionally closed DLs (DLs with all of Boolean constructors) and it is complete for expressive DLs. Boolean constructors) and it is complete for expressive DLs.

2 A thorough examination into various DLs.2 A thorough examination into various DLs.3 Subsumption and satisfiability are ascribed to consistency in 3 Subsumption and satisfiability are ascribed to consistency in

propositionally closed DLs, thus consistency algorithm can spropositionally closed DLs, thus consistency algorithm can solve three reasoning problems in DLs. KRIS and CRACK show olve three reasoning problems in DLs. KRIS and CRACK show optimized implementation of such algorithm is acceptable, toptimized implementation of such algorithm is acceptable, though its worst-case complexity is not polynomial.hough its worst-case complexity is not polynomial.

4 Description Logics is relevant to modal logic.4 Description Logics is relevant to modal logic.

Research StagesResearch Stages

• Phase 3 (1995-2000)Phase 3 (1995-2000)Research of reasoning service in very expressive Research of reasoning service in very expressive

DLs falls into two concentrations: tableau-basDLs falls into two concentrations: tableau-based methods and transfering to modal logic. Hied methods and transfering to modal logic. Highly optimized system like FaCT, RACE, DLP shghly optimized system like FaCT, RACE, DLP show tableau-based algorithms obtain preferablow tableau-based algorithms obtain preferable performance even for expressive DLs with lare performance even for expressive DLs with large knowledge base. ge knowledge base.

Research StagesResearch Stages

• Phase 4 (2001-) Phase 4 (2001-)

Industrial strength Description Logics System and Industrial strength Description Logics System and tableau –based algorithms researchtableau –based algorithms research

Application: Semantic Web, Knowledge Application: Semantic Web, Knowledge Representation and Integration in BioinformaticsRepresentation and Integration in Bioinformatics

Facilities in Description LogicsFacilities in Description Logics

• A A navigatornavigator for the complexity of descrip for the complexity of description logics by Evgeny Zolin. tion logics by Evgeny Zolin.

SHIQSHIQ

• It is a kind of Description Logics.It is a kind of Description Logics.• Components:Components: value restriction, terminological axiomsvalue restriction, terminological axioms inverse rolesinverse roles subrolessubroles• Extensions:Extensions: Concrete Domain: real number, integer, strings, built-iConcrete Domain: real number, integer, strings, built-i

n predicates(eg, <=, <=13, isPrefixof). Non restricted usn predicates(eg, <=, <=13, isPrefixof). Non restricted use of concrete domain will largely affect decidability ane of concrete domain will largely affect decidability and complexity of underlying DLs.d complexity of underlying DLs.

Nominals: sets of unique instanceNominals: sets of unique instance

SHIQSHIQ

• Basically, OWL is based on SHIQ, though its Basically, OWL is based on SHIQ, though its underlying DL is more expressive than SHIQ. underlying DL is more expressive than SHIQ.

• OWL has a very restricted ways of using concrete OWL has a very restricted ways of using concrete domain.domain.

• Reasoning problem in SHIQ is decidable, though Reasoning problem in SHIQ is decidable, though its worst-case complexity is EXPTIME.its worst-case complexity is EXPTIME.

ApplicationApplication

• Selection and combination of language structure matter to rSelection and combination of language structure matter to reasoning characteristics and complexity. easoning characteristics and complexity.

• There are three ways of implementing knowledge representThere are three ways of implementing knowledge representation system:ation system:

1 limited language + complete polynomial reasoning algorithm1 limited language + complete polynomial reasoning algorithmss

eg, CLASSICeg, CLASSIC2 expressive language + incomplete reasoning algorithms2 expressive language + incomplete reasoning algorithms eg, BACK, LOOMeg, BACK, LOOM3 expressive language + complete reasoning algorithm3 expressive language + complete reasoning algorithm eg, KRISeg, KRIS

Application: System CompositionApplication: System Composition

• Two ways for application + Description LogicsTwo ways for application + Description Logics

1 Description Logics -- integrated development 1 Description Logics -- integrated development environment for the system and it interacts environment for the system and it interacts loosely with application programloosely with application program

2 Description Logics is the reasoning component of 2 Description Logics is the reasoning component of the system, functions like data management is the system, functions like data management is implemented by other techniques.implemented by other techniques.

It depends on the applicationIt depends on the application

Application: Knowledge VaguenessApplication: Knowledge Vagueness

• Probabilistic logicProbabilistic logic Knowledge: probabilistic terminological axioms Knowledge: probabilistic terminological axioms

(information) + probabilistic assertions (credib(information) + probabilistic assertions (credibility)ility)

Reasoning for finding subsumption and assertiReasoning for finding subsumption and assertion probabilityon probability

• Fuzzy LogicFuzzy Logic