Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Description Logics: Logic foundation of Semantic Web Semantic Web - Fall 2005 Computer Engineering Department Sharif University of Technology

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Outline  First order logic and Models  Introduction to Description Logics  Reasoning on Description Logics

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Prepositional Logic

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Truth Tables

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall First Order Logic (FOL)

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Models

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Important Equivalences

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Example of a model

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Knowledge Representation with FOL

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Knowledge Representation with FOL

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall What Are Description Logics?  A family of logic based Knowledge Representation formalisms Based on concepts and roles  Concepts are interpreted as sets of objects.  Roles are interpreted as binary relations between objects. Descendants of semantic networks and KL-ONE  Key features of DLs are: Formal semantics  Decidable fragments of FOL  Closely related to Propositional Modal & Dynamic Logics Provision of inference services  Sound and complete decision procedures for key problems  Implemented systems (highly optimised)  Trade-off between expressive power and computational complexity.

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Description Logic Family  Particular languages mainly characterised by: Set of constructors for building complex concepts and roles from simpler ones. Set of axioms for asserting facts about concepts, roles and individuals. Simplest logic in this family is named AL Others are specified by adding some suffixes like U  NC : ALC ALCU …

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Description logic AL

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Fundamental Equivalences

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Interpretation (model)

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Example of a model

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall AL Constructors at Work

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Additional Constructors (1)

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Additional Constructors (2)

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall  The “Happy Father” concept:  A person who has at most one child or has at least 3 children from which at least one of them is female. Some Examples

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Some more examples! Π

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Classes

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Semantic Networks

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Rule Constructors

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Examples  Expressing what we stated in slides 9 and 10 with DL: There is a lecturer who teaches INFS4201 Guido teaches every course Bob teaches some courses

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall DL as fragments of Predicate Logic

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Lisp like style for DL

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Normal Forms

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Representing Knowledge in DL

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall DL Architecture

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Terminologies or TBoxes

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Terminologies or Tboxes (cont.)

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Reasoning about TBoxes

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Reduction to Subsumption

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Reduction to Unsatisfiability

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Reducing Unsatisfiability

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Inference services

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Inference service: concept satisfiability

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Inference services based on satisfiability

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Inference service: concept subsumption

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Concept examples

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Example taxonomy

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall World description: ABox

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall ABox inference services

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Abox inference services (cont.)

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall ABox example

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall TBox taxonomy plus individuals

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Open world assumption

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Reasoning Procedures

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Structural Subsumption

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Examples

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Example (do it yourself !)

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Tableaux  The Tableaux Algorithm is a decision procedure solving the problem of satisfiability.  If a formula is satisfiable, the procedure will constructively exhibit a model of the formula.  The basic idea is to incrementally build the model by looking at the formula, by decomposing it in a top/down fashion. The procedure exhaustively looks at all the possibilities, so that it can eventually prove that no model could be found for unsatisfiable formulas.

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Tableaux Algorithm

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Negation Normal Form

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Completion Rules: the AND rule

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall The AND rule

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall The OR rule

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall The SOME rule

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall The FORALL rule

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Clash

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Completion rules for the logic ALC

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Example inference

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall Example inference

Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall References  Chapters 1 and 2 of DLHB.