Description Logics

Outline Knowledge Representation Knowledge Representation Ontology Language Ontology Language Description Logics Description Logics Application Application

Knowledge Representation Object: find implicit meaning in explicit knowledge Object: find implicit meaning in explicit knowledge Concentration: since 1970, research of this field falls into two division—logic-based and cognitive method (network structure or problem solving) Concentration: since 1970, research of this field falls into two division—logic-based and cognitive method (network structure or problem solving) Logic in Knowledge Representation: Logic in Knowledge Representation: 1 Formalized semantics (reasoning function to symbol) 2 Operators and interpretation (semantics of logic expression) 3 Functional explanation of other methods (semantic web, frame-based) 4 In structure-based KR (OWL), reasoning service is related with computing complexity

Ontology Language Classification by structure: Classification by structure: Frame-based: FLogic, OKBC, KM Description logic-based: OWL First order logic-based: Cycl, KIF frame: definition and restriction of expressiveness, formalism and characteristics Logic in Ontology: Logic in Ontology: 1 Ontology designing: contradiction and hierarchies in concepts 2 Ontology building: consistency, inclusion of instances

Description Logics Components Components Research Research Example: SHIQ Example: SHIQ

Description Logics Component Constructors: existential restriction Constructors: existential restriction value restriction value restriction number restriction number restriction Terminological axioms: definition & restriction Terminological axioms: definition & restriction Assertion Formalism: attributes of instance Assertion Formalism: attributes of instance Subsumption Algorithm Subsumption Algorithm Instance Algorithm Instance Algorithm Consistency Algorithm: check consistency in terminological axioms and assertions Consistency Algorithm: check consistency in terminological axioms and assertions

Research in Description Logics Key Problem in the field: Key Problem in the field: Tradeoff between expressiveness and reasoning complexity of Description Logics Tradeoff between expressiveness and reasoning complexity of Description Logics

Research Stages Phase 1 ( ) Phase 1 ( ) System implementation implying structural subsumption algorithm, but it’s not complete for expressive Description Logics. Computing complexity of most DLs’ reasoning service exceeds polynomial. System implementation implying structural subsumption algorithm, but it’s not complete for expressive Description Logics. Computing complexity of most DLs’ reasoning service exceeds polynomial. Example: KL-ONE, K-REP, BACK, LOOM, CLASSIC

Research Stages Phase 2 ( ) Phase 2 ( ) 1 Tableau-based algorithms are used for reasoning services in DLs, especially for propositionally closed DLs (DLs with all of Boolean constructors) and it is complete for expressive DLs. 2 A thorough examination into various DLs. 3 Subsumption and satisfiability are ascribed to consistency in propositionally closed DLs, thus consistency algorithm can solve three reasoning problems in DLs. KRIS and CRACK show optimized implementation of such algorithm is acceptable, though its worst-case complexity is not polynomial. 4 Description Logics is relevant to modal logic.

Research Stages Phase 3 ( ) Phase 3 ( ) Research of reasoning service in very expressive DLs falls into two concentrations: tableau-based methods and transfering to modal logic. Highly optimized system like FaCT, RACE, DLP show tableau-based algorithms obtain preferable performance even for expressive DLs with large knowledge base.

Research Stages Phase 4 (2001-) Phase 4 (2001-) Industrial strength Description Logics System and tableau –based algorithms research Industrial strength Description Logics System and tableau –based algorithms research Application: Semantic Web, Knowledge Representation and Integration in Bioinformatics Application: Semantic Web, Knowledge Representation and Integration in Bioinformatics

Facilities in Description Logics A navigator for the complexity of description logics by Evgeny Zolin. A navigator for the complexity of description logics by Evgeny Zolin.navigator

SHIQ It is a kind of Description Logics. It is a kind of Description Logics. Components: Components: value restriction, terminological axioms value restriction, terminological axioms inverse roles inverse roles subroles subroles Extensions: Extensions: Concrete Domain: real number, integer, strings, built-in predicates(eg, <=, <=13, isPrefixof). Non restricted use of concrete domain will largely affect decidability and complexity of underlying DLs. Concrete Domain: real number, integer, strings, built-in predicates(eg, <=, <=13, isPrefixof). Non restricted use of concrete domain will largely affect decidability and complexity of underlying DLs. Nominals: sets of unique instance Nominals: sets of unique instance

SHIQ Basically, OWL is based on SHIQ, though its underlying DL is more expressive than SHIQ. Basically, OWL is based on SHIQ, though its underlying DL is more expressive than SHIQ. OWL has a very restricted ways of using concrete domain. OWL has a very restricted ways of using concrete domain. Reasoning problem in SHIQ is decidable, though its worst-case complexity is EXPTIME. Reasoning problem in SHIQ is decidable, though its worst-case complexity is EXPTIME.

Application Selection and combination of language structure matter to reasoning characteristics and complexity. Selection and combination of language structure matter to reasoning characteristics and complexity. There are three ways of implementing knowledge representation system: There are three ways of implementing knowledge representation system: 1 limited language + complete polynomial reasoning algorithms eg, CLASSIC eg, CLASSIC 2 expressive language + incomplete reasoning algorithms eg, BACK, LOOM eg, BACK, LOOM 3 expressive language + complete reasoning algorithm eg, KRIS eg, KRIS

Application: System Composition Two ways for application + Description Logics Two ways for application + Description Logics 1 Description Logics -- integrated development environment for the system and it interacts loosely with application program 2 Description Logics is the reasoning component of the system, functions like data management is implemented by other techniques. It depends on the application

Application: Knowledge Vagueness Probabilistic logic Probabilistic logic Knowledge: probabilistic terminological axioms (information) + probabilistic assertions (credibility) Knowledge: probabilistic terminological axioms (information) + probabilistic assertions (credibility) Reasoning for finding subsumption and assertion probability Reasoning for finding subsumption and assertion probability Fuzzy Logic Fuzzy Logic