CS6999 Presentation

Introduction to Description Logic and Ontology Languages

Jidi (Judy) Zhao April 25, 2020

Talk Outline

• Introduction to Ontologies • Introduction to Description Logic (DL) • Reasoning in DL • Introduction to Ontology Languages: OWL • Extensions of DL and Research Challenges 2



What is an ontology?

Many

definitions

    have been given: from Philosophy: “

a systematic explanation of being

” Neches gives some guidelines:

“…defines the basic terms and relations including the vocabulary of a topic area as well as the rules for combining terms and relations to define extensions to the vocabulary.

” Gruber, the most quoted:

“…an explicit specification of a conceptualization

” An ontology defines the and represent an area of knowledge, as well as relations among them.

concepts used to describe 3

Types of Ontologies

 Top-level Ontologies  The Standard Upper Ontology (SUO): http://suo.ieee.org/ 4

Types of Ontologies

  Top-level Ontologies     The Standard Upper Ontology (SUO): http://suo.ieee.org/ WordNet: http://wordnet.princeton.edu/ Sowa’s top-level ontology Cyc’s upper ontology Domain Ontologies     E-commerce Medicine Engineering Enterprise   Chemistry ….

Living Thing Nonliving 5

Methodologies for Ontology Engineering

 Building domain ontologies from huge ontologies (SENSUS, Cyc, AKT,…)  OTK (On-To-Knowledge) Methodology  Univ. of Karlsruhe  Methontology  Univ. Politecnica de Madrid 6

Methontology: A Methodology for Building Ontologies Methontology Ontology Development Process Life Cycle (Fernández-López et al., 1997;1999) 7

Tools for Ontology Engineering

        OilEd from University of Manchester  http://oiled.man.ac.uk/ Ontolingua from KSL (Stanford University)  http://www-ksl.stanford.edu

OntoSaurus from ISI (USA)  http://www.isi.edu/isd/ontosaurus.html

OntoEdit from Karlsrhue Univ.  http://ontoserver.aifb.unikarlsruhe.de/ontoedit/ Protégé  from SMI (Stanford University) http://protege.stanford.edu/ WebOnto from KMI (Open University)  http://kmi.open.ac.uk/projects/webonto/ WebODE from UPM  http://webode.dia.fi.upm.es/webODE/ KAON from AIFB and FZI at the University of Karlsruhe  http://kaon.semanticweb.org/ 8

Talk Outline

• Introduction to Ontologies • Introduction to Description Logic (DL) • Reasoning in DL • Introduction to Ontology Languages: OWL • Extensions of DL and Research Challenges 9

Description Logic

    Brachman and Levesque [1984] using that language ” .

“ there is a tradeoff between the expressiveness of a representation language and the difficulty of reasoning over the representations built  The more expressive the language, the harder the reasoning.

Description Logics  overcome the ambiguities of early semantic networks and frames  first realized in the system KL-One [Brachman and Schmolze, 1985] Well-studied and decidable (most DL languages) Tight coupling between theory and practice

Architecture of a DL System

 from DL Handbook

    

DL Basics

Concepts  (unary predicates/formulae with one free variable) E.g., Person , Female Roles  (binary predicates/formulae with two free variables) E.g., hasChild Individuals  (constants) E.g., Mary, John Constructors         Union t , Intersection u Exists restriction 9 : 9 hasChild.Doctor

Value restriction 8 : 8 hasChild.Doctor

Complement /negation : : : Mother Number restriction ≥ n , ≤n Inverse role (-): isChildOf ≡ hasChild – transitive role (+): hasSister Role hierarchy : hasDaughter v hasChild

Axioms

  Subsumption v : Mother v Parent Assertion: Mary: Mother, Mary hasChild John 12

What does

8

R.C and

9

R.C mean?

  A DogLover is someone whose pets are all dogs, in this case {C} A hasPet Fido DogLover = 8 hasPet.Dog

{p | 8 a, (p, a) 2 hasPet !

a 2 Dog} Also writen more simply as {p | hasPet(p, a) !

Dog(a) } A B C C Cat Fluffy A DogLiker is someone who owns a dog , in this case {A, C} Tabby Dog Fido DogLiker = 9 hasPet.Dog

Rover Flip {p | hasPet(p, a) Æ Dog(a) } This slide is from Dr. Bruce Spencer ’ s slides (2007).

Fluffy Tabby Rover Flip

The DL Family

 Smallest propositionally closed DL is ALC  Concepts constructed using boolean operators t , u , : plus restricted quantifiers 9 , 8  Only atomic roles E.g., Person u 8 hasChild.(Doctor t 9 hasChild.Doctor) 14

  

The DL Family (cont.)

S often used for ALC Additional letters extended with transitive roles ( indicate other extensions, e.g.: R + )       H I O for nominals (e.g., {Mary, John}) for inverse roles N for role hierarchy for number restrictions Q R for qualified number restrictions (e.g., ≥ 2 hasChild.Doctor) for limited complex role inclusion axioms, role disjointness ALC + transitive role ( SHOIQ R + )+role hierarchy ( H ) + O + I + Q = 15

DL Semantics    Semantics given by standard FO model theory The vocabulary is the set of names (consist of concepts and roles ) we use in our model of (part of) the world  {Daisy, Cow, Animal, Person, Car, drives, …} An interpretation I is a tuple (  I , • I )   I is the domain (a set)  • I is a mapping that maps:    Names of objects (individuals/constants) to elements of  I Names of unary predicates (classes/concepts) Names of binary predicates (properties/roles) to subsets of to subsets of  I  I ×  I 16

DL Semantics

(adapted from Horrocks 2006) Individuals i I 2 Mary  I John Concepts C I µ  I Teacher Student Car Roles R I µ  I ×  I hasChild owns Interpretation function • I (Teacher u Student) 17 Interpretation domain  I

  

DL Knowledge Bases

A Knowledge Base (KB) = a Tbox + an Abox A TBox (

terminology

) is a set of inclusion axioms and equivalence axioms   the vocabulary of an application domain e.g.: { Mother v Person, GrandMother ≡ Person u 9 hasChild.Parent } An ABox (

Assertion

) is a set of assertions about individuals   about named individuals in terms of this vocabulary e.g.: {Mary: Mother, Anita hasChild Mary} 18

Talk Outline

• Introduction to Ontologies • Introduction to Description Logic (DL) • Reasoning in DL • Introduction to Ontology Languages: OWL • Extensions of DL and Research Challenges 19

      

Tableau Reasoning (1)

Key reasoning tasks Satisfiability: asat( A ) , whether the assertions in a KB have a model Instance checking: C(a)?

Concept satisfiability: C?

Retrieval: retrieve a set of individuals that instantiate C Subsumption: B v  A ?

A subsumes B if every individual of concept B is also of concept A.

Equivalence: A≡B? , B v A ? And A v B?

  Reasoning tasks reducible to     KB (un) satisfiability: asat( A ) Instance checking: instance(a, C, A ) Concept satisfiability: sat(C) , asat( , : A [ asat ( {a:C}) A [ {a: : C}) Concept subsumption: C v D w.r.t. KB A , A [ { : D u C} is

not

satisfiable , : asat( A [ {a: : D u C}) Retrieval: check each individual in the Abox, reducible to instance checking DL systems typically use tableau algorithms (consistency) of KB to decide the satisfiability 20

    

Tableau Reasoning (2)

Tableau algorithms work by trying to construct a concrete example (model) consistent with KB.

A KB A is satisfiable iff a fully expanded clash-free graph is constructed.

Tableau reasoning contains a set of constraint sets or tableau completion rules operating on Clash : a clash is an obvious contradiction, e.g., A(x), : A(x) Proof procedure:     start from assertions about individuals (ABox axioms) unfold the TBox so that atomic concepts only appear on the right side of axioms transform all concepts into negation normal form (i.e. negation only occurs in front of atomic concept names):   : (C u D) ! : C t : D : 9 R.C ! 8 R.

: C apply completion rules in arbitrary order as long as possible    stops when a clash is found terminates if no completion rule is applicable A KB is satisfiable iff a clash-free tableau can be derived 21 CS6795 Semantic Web Techniques

Tableau Reasoning (3)

completion rules 22

Tableau Reasoning (5): Concept Subsumption

KB: Reasoning task: mother v woman ?

 Exercise: Is the concept : woman u mother satisfiable?

23

   

Tableau Reasoning (4): asat(

A

)

E.g., KB: { HappyParent≡Person u ∀ hasChild.(Doctor t 9 hasChild.Doctor), John:HappyParent, John hasChild Mary, Mary: : Doctor, Wendy hasChild Mary, Wendy marriedTo John} Person ∀ hasChild.(Doctor t ∃ hasChild.Doctor)  from Harrock, 2006 24

  

Tableau Reasoning (6)

Some completion rules are nondeterministic (e.g., 9 , ≤ ).

Blocking Strategies are often needed to ensure termination .

E.g., KB: {Person v 9 hasParent.Person, John:Person} 25

Tableau Reasoning (7)

 In general, (representation of) model consists of:   Named individuals forming arbitrary directed graph Trees of anonymous individuals rooted in named individuals 26

Tableau Reasoning (8)

  Similar tableaux expansions can be designed for more expressive DL languages. A tableau algorithm has to meet three requirements:    Soundness : if a complete and clash-free graph is found by the algorithm, we can construct a model.

Completeness : Given a model, the algorithm can always find an complete and clash-free graph Termination : the algorithm can terminate in finite steps with specific result.

Software for DL Reasoning

KAON2

28

Pellet CEL

Efficiency of Tableau Reasoning

I can’t find an efficient algorithm, but neither can all these famous people.

NP-Complete Cartoons, http://max.cs.kzoo.edu/~kschultz/CS510/ClassPresentations/NPCartoons.html

Talk Outline

• Introduction to Ontologies • Introduction to Description Logic (DL) • Reasoning in DL • Introduction to Ontology Languages: OWL • Extensions of DL and Research Challenges 30

Ontology Languages

  Traditional Ontology Languages     Ontolingua and KIF LOOM OKBC F-logic Ontology Markup Languages      SHOE RDF and RDF Schema OIL DAML+OIL OWL 31

  

The Web Ontology Language OWL

Semantic Web led to requirement for a “ web ontology language ” Group set up Web-Ontology (WebOnt) Working    WebOnt developed OWL language OWL based on earlier languages OIL and DAML+OIL OWL now a W3C recommendation OIL, DAML+OIL and OWL based on Description Logic 32

      OWL Three species of OWL OWL full is the union of OWL syntax and RDF OWL DL restricted to FOL fragment (is equivalent to SHOIN (D n ) DL) OWL Lite is an “easier to implement” subset of OWL DL OWL DL Benefits from many years of DL research   Well defined semantics Formal properties well understood (complexity, decidability)   Known reasoning algorithms Implemented systems (highly optimised)

OWL RDF/XML Exchange Syntax

u ∀ hasChild.(Doctor t ∃ hasChild.Doctor): E.g., Person

onProperty rdf:parseType=“collection"> rdf:resource="#hasChild"/> rdf:resource="#hasChild"/> rdf:resource="#Doctor"/>

34

Class/Concept Constructors

35

Ontology Axioms

 OWL ontology equivalent to DL KB (Tbox + Abox) 36

Talk Outline

• Introduction to Ontologies • Introduction to Description Logic (DL) • Reasoning in DL • Introduction to Ontology Languages: OWL • Extensions of DL and Research Challenges 37

Extensions of DL

      Combinations of DL and Logic Programs (LP) Uncertainty extension of DL Concrete domain constraints Modal, epistemic, and temporal operators Open world vs. close world …..

38

Venn Diagram of DL, LP, and FOC

39

Motivation(1)

X    DL cannot represent “more than one free variable at a time”.

(1) A rule involving multiple variables. E.g., Man(?X) ∧ Woman(?Y) !

PotentialFriendshipBetween(?X,?Y).

(2) Chaining to derive values of Properties. E.g., Father(?X,?Y) ∧ SHOIN ) Father(?Y,?Z) ! Grandfather(?X,?Z). (not allowed in Work Work(?X, ?Y) ∧ Live(?X, ?Z) ∧ !

HomeWorker(?X).

Loc(?Y,?W) ∧ Loc(?Z,?W) Y Loc W Live Loc 40 Z

Motivation(2)

• Horn Logic cannot represent a (1) disjunction or (2) existential in the head.

• (1) State a subclass of a complex class expression which is a disjunction. E.g., (Human u Adult) v (Man t Woman) • (2) State a subclass of a complex class expression which is an existential. E.g., Radio v 9 hasPart.Tuner

41

Different approaches

1. Approaches reducing description logics to logic programs A. DLP B. OWL 2 RL 2. Homogeneous approaches A. OWL Rules B. SWRL 3. Hybrid approaches accessing description logic through queries in logic programs A. AL-Log 42

    

Uncertainty extension of DL

Handling uncertain knowledge is becoming a critical research direction for the (Semantic) Web.

knowledge on the Web is often uncertain and imprecise. E.g., many concepts needed in business domain ontology modeling lack well-defined boundaries or, precisely defined criteria of relationship between concepts Domain modeling and Ontology reasoning  Quantify degree of an individual belonging to a class  Quantify degree of

subsumption

subclasses between a class and its Concept mapping between ontologies  Quantify degree of alignment between classes of two ontologies 43

URW3 Situation Report: uncertainty ontology

 URW3 44 44

Probability, Possibility and Fuzzy logic

   Probabilistic Description Logic:   Statistical information e.g. John is a student with the probability 0.6 and a teacher with the probability 0.4 Fuzzy Description Logic:   Express vagueness and imprecision e.g. John is tall with the degree of truth 0.9

Possibilistic Description Logic:   Particular rankings and preferences e.g. John prefers an ice cream to a beer 45

Research Challenges

      Syntax and Semantics Decidability Reasoning algorithms for possible extensions Soundness and completeness Complexity/efficiency Effective methods for reasoning under uncertainty 46

Questions?