Logics and Reasoning - SESA Reasoning is an act of deriving a conclusion from certain premises. The

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  • Logics and Reasoning - SESA Tutorial

    Darko Anicic darko.anicic@deri.org

    Digital Enterprise Research Institute (DERI) Leopold-Franzens Universität

    Innsbruck, Austria

    Seoul – September 10-13, 2007

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    Introduction Ontologies and Reasoning

    Ontology Languages & WSML IRIS Reasoner

    Hands-on Session

    Agenda

    Logics and Reasoning

    Agenda for day 2nd: Logics and Reasoning

    1 Ontologies and Reasoning 2 The WSML Language 3 IRIS Reasoner 4 Hands-on Session

    Darko Anicic SESA Tutorial - Logics and Reasoning

  • ����

    Introduction Ontologies and Reasoning

    Ontology Languages & WSML IRIS Reasoner

    Hands-on Session

    Introduction

    Ontology Definition

    Figure: Ontology Definition

    Darko Anicic SESA Tutorial - Logics and Reasoning

  • ����

    Introduction Ontologies and Reasoning

    Ontology Languages & WSML IRIS Reasoner

    Hands-on Session

    Introduction

    Ontology Example

    Darko Anicic SESA Tutorial - Logics and Reasoning

  • ����

    Introduction Ontologies and Reasoning

    Ontology Languages & WSML IRIS Reasoner

    Hands-on Session

    Introduction

    Reasoning

    Reasoning is an act of deriving a conclusion from certain premises. The process of inferring implicit knowledge about some domain of discourse from a given (formal) knowledge of that domain. Reasoning is a critical success factor for Semantic Web applications. Reasoning problems: satisfiability, model finding, deduction...

    Darko Anicic SESA Tutorial - Logics and Reasoning

  • ����

    Introduction Ontologies and Reasoning

    Ontology Languages & WSML IRIS Reasoner

    Hands-on Session

    Introduction

    Practical Reasons Given key role of ontologies in e-Science and Semantic Web, it is essential to provide tools and services to help users:

    Design and maintain high quality ontologies, e.g.:

    Meaningful - all named classes can have instances Correct - captured intuitions of domain experts Minimally redundant - no unintended synonyms Richly axiomatised - (sufficiently) detailed descriptions

    Store (large numbers) of instances of ontology classes, e.g.:

    Annotations from web pages (or gene product data) Answer queries over ontology classes and instances, e.g.:

    Find more general/specific classes Retrieve annotations/pages matching a given description

    Integrate and align multiple ontologies

    Darko Anicic SESA Tutorial - Logics and Reasoning

  • ����

    Introduction Ontologies and Reasoning

    Ontology Languages & WSML IRIS Reasoner

    Hands-on Session

    Ontology Languages RDF (S) OWL First Order Logic WSML

    Ontology Languages

    Requirements: - Expressivity

    knowledge representation and ontology theory support Dimensions to Consider: Open vs. Closed World Semantics, Classical vs. Default neg, performance etc.

    - Reasoning support

    sound (unambiguous, decidable) support reasoners / inference engines (query answering, classification, logical ent., consistency check...)

    Semantic Web languages: - Web compatibility - Existing W3C Recommendations: XML, RDF, OWL

    Darko Anicic SESA Tutorial - Logics and Reasoning

  • ����

    Introduction Ontologies and Reasoning

    Ontology Languages & WSML IRIS Reasoner

    Hands-on Session

    Ontology Languages RDF (S) OWL First Order Logic WSML

    Layer Cake 2005

    Figure: Tim Berners Lee, International Semantic Web Conference, 2005

    Darko Anicic SESA Tutorial - Logics and Reasoning

  • ����

    Introduction Ontologies and Reasoning

    Ontology Languages & WSML IRIS Reasoner

    Hands-on Session

    Ontology Languages RDF (S) OWL First Order Logic WSML

    Simplified Stack (from a logicians point of view)

    Darko Anicic SESA Tutorial - Logics and Reasoning

  • ����

    Introduction Ontologies and Reasoning

    Ontology Languages & WSML IRIS Reasoner

    Hands-on Session

    Ontology Languages RDF (S) OWL First Order Logic WSML

    Open-World Assumption vs. Closed-World Assumption

    Logic Programming

    hasFather(peter,john) hasFather(john,michael) grandchild(x)←hasFather(x,y), hasFather(y,z), Person(x).

    Every person is a grandchild is not deducible due to closed domain of interpretation! Domain bounded to known objects: peter is a grandchild. No tree model property required

    Darko Anicic SESA Tutorial - Logics and Reasoning

  • ����

    Introduction Ontologies and Reasoning

    Ontology Languages & WSML IRIS Reasoner

    Hands-on Session

    Ontology Languages RDF (S) OWL First Order Logic WSML

    Open-World Assumption vs. Closed-World Assumption

    Description Logic Person(peter ) Peter is a person. Person v ∃ father.Person Each person has a father

    who is a person. ∃ father.(∃ father.Person) v Grandchild Things having a father of

    a father who is a person are grandchildren.

    Every person is a grandchild is deducible due to open domain of interpretation! hasAunt(x,y) ← hasParent(x,z), hasSibling(z,y), Female(y) Arbitrary rule is not possible to express due to the need for tree model property

    Darko Anicic SESA Tutorial - Logics and Reasoning

  • ����

    Introduction Ontologies and Reasoning

    Ontology Languages & WSML IRIS Reasoner

    Hands-on Session

    Ontology Languages RDF (S) OWL First Order Logic WSML

    Classical vs. Default Negation

    Default Negation(i.e., negation as failure)

    Rules: male(x) :- father(x). female(x) :- person(x), ¬male(x). grandchild(x)←hasFather(x,y), hasFather(y,z), Person(x).

    Facts: person(joe), person(bill), father(joe)

    Value Computation: male(joe) female(bill)

    Darko Anicic SESA Tutorial - Logics and Reasoning

  • ����

    Introduction Ontologies and Reasoning

    Ontology Languages & WSML IRIS Reasoner

    Hands-on Session

    Ontology Languages RDF (S) OWL First Order Logic WSML

    Classical vs. Default Negation

    Classical Negation

    Rules: male(x) :- father(x). female(x) :- person(x), ¬male(x). grandchild(x)←hasFather(x,y), hasFather(y,z), Person(x).

    Facts: person(joe), person(bill), father(joe)

    Value Computation: male(joe)

    Darko Anicic SESA Tutorial - Logics and Reasoning

  • ����

    Introduction Ontologies and Reasoning

    Ontology Languages & WSML IRIS Reasoner

    Hands-on Session

    Ontology Languages RDF (S) OWL First Order Logic WSML

    Basic Model of RDF (S)

    RDF triples:

    A model is a set of statements Statement := (predicate,subject,object) Predicate is a resource Subject is a resource Object is either a resource or a literal

    Darko Anicic SESA Tutorial - Logics and Reasoning

  • ����

    Introduction Ontologies and Reasoning

    Ontology Languages & WSML IRIS Reasoner

    Hands-on Session

    Ontology Languages RDF (S) OWL First Order Logic WSML

    RDF(S) - Core Classes and Properties

    RDFS CLASS represents the generic concept of a type or category and can be defined to represent almost everything, e.g. Web pages, people, document types...

    RDFS PROPERTY represents the subset of RDFS resources that are properties

    RDFS SubClassOf defines a subset or superset relation between classes. This property is transitive!

    RDFS SubPropertyOf is used to indicate that one property is a specialization of another property

    RDFS RANGE is used to define that the values of a property are instances of one or more stated classes

    RDFS DOMAIN is used to state that any resource that has a given property is an instance of one or more classes

    Darko Anicic SESA Tutorial - Logics and Reasoning

  • ����

    Introduction Ontologies and Reasoning

    Ontology Languages & WSML IRIS Reasoner

    Hands-on Session

    Ontology Languages RDF (S) OWL First Order Logic WSML

    RDF(S) - Schema Example

    Darko Anicic SESA Tutorial - Logics and Reasoning

  • ����

    Introduction Ontologies and Reasoning

    Ontology Languages & WSML IRIS Reasoner

    Hands-on Session

    Ontology Languages RDF (S) OWL First Order Logic WSML

    RDF(S) - Summary

    Simple Triple Data Model Basic Ontology Modeling Primitives URIs for Identification RDFS too weak to describe resources in sufficient detail

    No localised range and domain constraints No existence/cardinality constraints No transitive, inverse or symmetrical properties

    Difficult to provide reasoning support (No "native" reasoners for non-standard semantics)

    Darko Anicic SESA Tutorial - Logics and Reasoning

  • ����

    Introduction Ontologies and Reasoning

    Ontology Languages & WSML IRIS Reasoner

    Hands-on Session

    Ontology Languages RDF (S) OWL First Order Logic WSML

    OWL - DL based ontology language

    DLs are a family of logic based KR formalisms DLs - 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 indi