van Harmelen, Hitzler, Wache ● ESSLLI 2006 ● Malaga, Spain ● August 2006 AIFB Approximate Reasoning for the Semantic Web Part II OWL Semantics and Tableau Reasoning Frank van Harmelen Pascal Hitzler Holger Wache ESSLLI 2006 Summer School Malaga, Spain, August 2006 Slide 1 van Harmelen, Hitzler, Wache ● ESSLLI 2006 ● Malaga, Spain ● August 2006 AIFB Introducing the speaker • 1998 Diplom (Master) in Mathematics – Uni Tübingen (Helmut Salzmann) • 1999-2001 PhD in Mathematics – Cork, Irland (Tony Seda) – Formal Aspects of Knowledge Representation • 2001-2004 Postdoc – TU Dresden, Artificial Intelligence (Steffen Hölldobler) • since 2004 Assistant Professor – AIFB Univ. Karlsruhe, Semantic Web (Rudi Studer) • 2005 Habilitation in Computer Science Main Interests: Semantic Web (Knowledge Representation/Logic) Neural-symbolic Integration Mathematical Foundations of Artificial Intelligence Slide 2
van Harmelen, Hitzler, Wache ● ESSLLI 2006 ● Malaga, Spain ● August 2006 AIFB Karlsruhe: Location for Semantic Technologies and Applications Semantic Karlsruhe AIFB Application-oriented Basic Research Application-oriented Research Research Application-oriented Know-how Transfer Research Product Development Realizing new Scenarios Innovative Solutions Knowledge Management B2B, EAI Semantic Web Infrastructure Business Intelligence Ontology Management Electronic Markets Data, Web & Text Mining eGovernment Peer-to-Peer, Semantic Grid Semantic Web Services Slide 3 van Harmelen, Hitzler, Wache ● ESSLLI 2006 ● Malaga, Spain ● August 2006 AIFB Who are we? ... Semantic Web Research Group AIFB FZI Sudhir Agarwal Anupriya Ankolekar Andreas Abecker Rudi Studer Stephan Bloehdorn Simone Braun Sebastian Blohm Saartje Brockmans Knowledge Management Stephan Grimm Philipp Cimiano Peter Haase Semantic Web Jens Hartmann Heiko Haller Intelligent WWW-Applications Pascal Hitzler Markus Krötzsch Business Intelligence Hans-Jörg Happel Steffen Lamparter eGovernment Holger Lewen Mark Hefke Guilin Qi Ontology Engineering Sebastian Rudolph Ljiljana Stojanovic Data/Text Mining York Sure Julien Tane Nenad Stojanovic Ontology Learning Thanh Tran Duc Peer-to-Peer Tuvshintur Tserendorj Max Völkel Christoph Tempich Web Services Yimin Wang Valentin Zacharias Johanna Völker Denny Vrandecic & ~40 people at Ontoprise Slide 4
van Harmelen, Hitzler, Wache ● ESSLLI 2006 ● Malaga, Spain ● August 2006 AIFB Partners and Projects Slide 5 van Harmelen, Hitzler, Wache ● ESSLLI 2006 ● Malaga, Spain ● August 2006 AIFB Semantic Web Layer Cake + + now L W O Slide 6
van Harmelen, Hitzler, Wache ● ESSLLI 2006 ● Malaga, Spain ● August 2006 AIFB What is Semantics? Syntax: strings without meaning Semantics: meaning of syntax show pixel set „_354“ on screen if „A“ is of type "B". IF cond(A,B) THEN display(_354) syntax meaning assignment of meaning e.g. „the world“ Why logic is so successful: Semantics can be captured syntactically! Slide 7 van Harmelen, Hitzler, Wache ● ESSLLI 2006 ● Malaga, Spain ● August 2006 AIFB What is semantics? Example programming language computing factorial intended semantics syntax FUNCTION f(n:natural):natural; BEGIN IF n=0 THEN f:=1 ELSE f:=n*f(n-1); END; formal semantics What the program does when exectued procedural semantics Slide 8
van Harmelen, Hitzler, Wache ● ESSLLI 2006 ● Malaga, Spain ● August 2006 AIFB Semantics of logics/knowledge representation languages all humans syntax are mortal intended semantics ∀ X (p(X) → q(X)) logical ² consequence model theoretic semantics ` deducible in proof theoretic semantics a calculus Slide 9 van Harmelen, Hitzler, Wache ● ESSLLI 2006 ● Malaga, Spain ● August 2006 AIFB Part II contents 1. OWL Model-theoretic Semantics a. Description Logics: ALC b. OWL as SHOIN(D) c. OWL Examples 2. Proof Theory a. Reasoning as Satisfiability checking b. Tableaux Reasoning Slide 10
van Harmelen, Hitzler, Wache ● ESSLLI 2006 ● Malaga, Spain ● August 2006 AIFB Description Logics, DLs • FOL (First-Order Logic) fragments • usually decidable • "expressive" • come from semantic networks and frame systems • close relation with multi-modal logics • W3C Standard OWL DL is the description logic SHOIN(D) • We first talk about the simpler ALC Slide 11 van Harmelen, Hitzler, Wache ● ESSLLI 2006 ● Malaga, Spain ● August 2006 AIFB General DL Architecture Knowledge Base I nference System Tbox (schema) Man ≡ Hum an u Male I nterface Happy-Father ≡ Man u ∃ has-child.Fem ale u … Abox (data) Happy-Father( John) has-child( John, Mary) Slide 12
van Harmelen, Hitzler, Wache ● ESSLLI 2006 ● Malaga, Spain ● August 2006 AIFB DLs – general remarks • DLs are a family of logic-based KR formalisms • DLs characterised by: – Different constructors for generating complex class expressions. – Axioms for describing properties for roles. • ALC is the smalles DL which is propositionally closed – Conjunction, disjunction, negation are constructors, written as u , t , ¬ . – Quantifiers used only together with roles: Man u ∃ hasChild.Female u u ∃ hasChild.Male u u ∀ hasChild.(Rich t Happy) Slide 13 van Harmelen, Hitzler, Wache ● ESSLLI 2006 ● Malaga, Spain ● August 2006 AIFB Other DL language components • E.g. – Number restrictions (cardinality constraints) for Roles: ≥ 3 hasChild, · 1hasMother – Qualified number restrictions: ≥ 2 hasChild.Female, · 1 hasParent.Male – Nominals (definition by extension): {Italy, France, Spain} – Concrete domains (datatypes): hasAge.( ≥ 21) hasChild – ≡ hasParent – Inverse roles: hasAncestor v + hasAncestor – Transitive roles: – Role composition: hasParent.hasBrother(uncle) Slide 14
van Harmelen, Hitzler, Wache ● ESSLLI 2006 ● Malaga, Spain ● August 2006 AIFB ALC: basic language elements • basic language components: – classes – roles – individuals • Professor(RudiStuder) – Individual RudiStuder is in class Professor • affiliation(RudiStuder,AIFB) – RudiStuder has affiliation AIFB Slide 15 van Harmelen, Hitzler, Wache ● ESSLLI 2006 ● Malaga, Spain ● August 2006 AIFB ALC: subclass relation • Professor v Faculty – translates to ( ∀ x)(Professor(x) → Faculty(x)) – corresponds to owl:subClassOf • Professor ≡ Faculty – translates to ( ∀ x)(Professor(x) ↔ Faculty(x)) – corresponds to owl:equivalentClass Slide 16
van Harmelen, Hitzler, Wache ● ESSLLI 2006 ● Malaga, Spain ● August 2006 AIFB ALC: complex class descriptions • conjunction u • disjunction t • negation ¬ • Professor v (Person u Faculty) t (Person u ¬ PhDStudent) ( ∀ x)(Professor(x) → ((Person(x) ∧ Faculty(x)) ∨ (Person(x) ∧ ¬ PhDStudent(x))) Slide 17 van Harmelen, Hitzler, Wache ● ESSLLI 2006 ● Malaga, Spain ● August 2006 AIFB ALC: Quantifiers • Exam v ∀ hasExaminer.Professor ( ∀ x)(Exam(x) → ( ∀ y)(hasExaminer(x,y) → Professor(y))) – corresponds to owl:allValuesFrom • Exam v ∃ hasExaminer.Person ( ∀ x)(Exam(x) → ( ∃ y)(hasExaminer(x,y) ∧ Person(y))) – corresponds to owl:someValuesFrom Slide 18
van Harmelen, Hitzler, Wache ● ESSLLI 2006 ● Malaga, Spain ● August 2006 AIFB Modelling in ALC • owl:nothing: ⊥ ≡ C u ¬ C • owl:thing: > ≡ C t ¬ C • owl:disjointWith: C u D ≡ ⊥ equivalently: C v ¬ D • rdfs:range: > v ∀ R.C • rdfs:domain: ∃ R. > v C Slide 19 van Harmelen, Hitzler, Wache ● ESSLLI 2006 ● Malaga, Spain ● August 2006 AIFB ALC: Syntax • The following rules generate classes in ALC, where A is an atomic (named) class and R is a role. C,D → A | > | ⊥ | ¬ C | C u D | C t D | ∀ R.C | ∃ R.C • An ALC TBox consists of assertions (axioms) of the form C v D and C ≡ D, where C,D are classes. • An ALC ABox consists of assertions of the form C(a) and R(a,b), where C is a complex class, R is a role and a,b are individuals. • An ALC-knowledge base consists of an ABox and a TBox. Slide 20
van Harmelen, Hitzler, Wache ● ESSLLI 2006 ● Malaga, Spain ● August 2006 AIFB ALC: Semantics Defined by translating TBox axioms into FOL via the mapping π (shown to the right). Here, C,D are complex A ( y ) classes, R is a role and A is an atomic class. Slide 21 van Harmelen, Hitzler, Wache ● ESSLLI 2006 ● Malaga, Spain ● August 2006 AIFB DL knowledge bases • DL knowledge bases consist of two parts: – TBox: Axioms containing schema knowledge: • HappyFather ≡ Man u ∃ hasChild.Female u … • Elephant v Animal u Large u Grey • transitive(hasAncestor) – Abox: Axioms describing data: • HappyFather(John) • hasChild(John, Mary) • Distinction between ABox and TBox has no logical significance whatsoever …but it makes some things easier to talk about. Slide 22
van Harmelen, Hitzler, Wache ● ESSLLI 2006 ● Malaga, Spain ● August 2006 AIFB Simple example Terminological knowledge ( TBox ): Human v ∃ parentOf.Human Orphan ≡ Human u ¬ ∃ hasParent.Alive Data ( ABox ): Orphan(harrypotter) hasParent(harrypotter,jamespotter) Semantics and logical consequences are understood via translation to FOL. Slide 23 van Harmelen, Hitzler, Wache ● ESSLLI 2006 ● Malaga, Spain ● August 2006 AIFB Part II contents 1. OWL Model-theoretic Semantics a. Description Logics: ALC b. OWL as SHOIN(D) c. OWL Examples 2. Proof Theory a. Reasoning as Satisfiability checking b. Tableaux Reasoning Slide 24
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