DR-Prolog : A System for Defeasible Reasoning with Rules and Ontologies on the Semantic Web

DR-Prolog: A System for Defeasible Reasoning with Rules and Ontologies on the Semantic Web Αναπαράσταση και Επεξεργασία Γνώσης Άνοιξη 2009

Defeasible Logic: Basic Characteristics • Defeasible logics are rule-based, without disjunction • Classical negation is used in the heads and bodies of rules. • Rules may support conflicting conclusions • The logics are skeptical in the sense that conflicting rules do not fire. Thus consistency is preserved. • Priorities on rules may be used to resolve some conflicts among rules • They have linear computational complexity. Αναπαράσταση και Επεξεργασία Γνώσης

Defeasible Logic – Syntax (1/2) A defeasible theory D is a triple (F,R,>), where F is a finite set of facts, R a finite set of rules, and > a superiority relation on R. There are two kinds of rules (fuller versions of defeasible logics include also defeaters): strict rules, defeasible rules • Strict rules: Ap Whenever the premises are indisputable then so is the conclusion. • penguin(X) bird(X) • Defeasible rules: Ap They can be defeated by contrary evidence. • bird(X) fly(X) Αναπαράσταση και Επεξεργασία Γνώσης

Defeasible Logic – Syntax (2/2) • Superiority relations A superiority relation on R is an acyclic relation > on R. When r1 > r2, then r1 is called superior to r2, and r2 inferior to r1. This expresses that r1 may override r2. • Example: r: bird(X) flies(X) r’: penguin(X) ¬flies(X) r’ > r Αναπαράσταση και Επεξεργασία Γνώσης

DR-Prolog Features DR-Prolog is a rule system for the Web that: • reasons both with classical and non-monotonic rules • handles priorities between rules • reasons with RDF data and RDFS/OWL ontologies • translates rule theories into Prolog using the well-founded semantics • complies with the Semantic Web standards (e.g. RuleML) • has low computational complexity Αναπαράσταση και Επεξεργασία Γνώσης

System Architecture Αναπαράσταση και Επεξεργασία Γνώσης

Translation of Defeasible Theories (1/3) • The translation of a defeasible theory D into a logic program P(D) has a certain goal: to show that p is defeasibly provable in D  p is included in the Well-Founded Model of P(D) • The translation is based on the use of a metaprogram which simulates the proof theory of defeasible logic Αναπαράσταση και Επεξεργασία Γνώσης

Translation of Defeasible Theories (2/3) For a defeasible theory D = (F,R,>), where F is the set of the facts, R is the set of the rules, and > is the set of the superiority relations in the theory, we add facts according to the following guidelines: • fact(p)for each pF • strict(ri , p,[q1 ,…,qn])for each rule ri: q1,…,qn  pR • defeasible(ri ,p,[q1 ,…,qn]) for each rule ri: q1,…,qn pR • sup(r,s) for each pair of rules such that r>s Αναπαράσταση και Επεξεργασία Γνώσης

Translation of Defeasible Theories (3/3) Αναπαράσταση και Επεξεργασία Γνώσης

Prolog Metaprogram (1/3) • Class of rules in a defeasible theory supportive_rule(Name,Head,Body):- strict(Name,Head,Body). supportive_rule(Name,Head,Body):- defeasible(Name,Head,Body). • Definite provability definitely(X):- fact(X). definitely(X):- strict(R,X,[Y1 ,Y2 ,…,Yn]), definitely(Y1), definitely(Y2), …, definitely(Yn). Αναπαράσταση και Επεξεργασία Γνώσης

Prolog Metaprogram (2/3) • Defeasible provability defeasibly(X):- definitely(X). defeasibly(X):- supportive_rule(R, X, [Y1 ,Y2 ,…,Yn]), defeasibly(Y1), defeasibly(Y2), …, defeasibly(Yn), sk_not(overruled(R,X)), sk_not(definitely(¬X)). Αναπαράσταση και Επεξεργασία Γνώσης

Prolog Metaprogram (3/3) • Overruled(R,X) overruled(R,X):- supportive_rule(S, ¬X, [Y1 ,Y2 ,…,Yn]), defeasibly(Y1), defeasibly(Y2), …, defeasibly(Yn), sk_not(defeated(S, ¬X)). • Defeated(S,X) defeated(S,X):- supportive_rule(T, ¬X, [Y1 ,Y2 ,…,Yn]), defeasibly(Y1), defeasibly(Y2), …, defeasibly(Yn), sup(T, S). Αναπαράσταση και Επεξεργασία Γνώσης

An Application Scenario • Adam visits a Web Travel Agency and states his requirements for the trip he plans to make. • Adam wants • to depart from Athens and considers that the hotel at the place of vacation must offer breakfast. • either the existence of a swimming pool at the hotel to relax all the day, or a car equipped with A/C, to make daily excursions at the island. • if there is no parking area at the hotel, the car is useless • if the tickets for the transportation to the island are not included in the travel package, the customer is not willing to accept it Αναπαράσταση και Επεξεργασία Γνώσης

Adam’s Requirements in DL r1: from(X,athens), includesResort(X,Y), breakfast(Y,true), swimmingPool(Y,true) => accept(X). r2: from(X,athens), includesResort(X,Y), breakfast(Y,true),includesService(X,Z),hasVehicle(S,W),vehicleAC(W,true) => accept(X). r3: includesResort(X,Y),parking(Y,false) => ~accept(X). r4: ~includesTransportation(X,Z) => ~accept(X). r1 > r3. r4 > r1. r4 > r2. r3 > r2. Αναπαράσταση και Επεξεργασία Γνώσης

Adam’s Requirements in Prolog defeasible(r1,accept(X),[from(X,athens),includesResort(X,Y),breakfast(Y,true),swimmingPool(Y,true)]). defeasible(r2,accept(X),[from(X,athens),includesResort(X,Y),breakfast(Y,true),includesService(X,Z),hasVehicle(Z,W),vehicleAC(W,true)]). defeasible(r3,~(accept(X)),[includesResort(X,Y),parking(Y,false)]). defeasible(r4,~(accept(X)),[~(includesTransportation(X,Y))]). sup(r1,r3). sup(r4,r1). sup(r4,r2). sup(r3,r2). Αναπαράσταση και Επεξεργασία Γνώσης

Knowledge Base (facts) in Prolog fact(from(‘IT1’,athens)). fact(to(‘IT1’,crete)). fact(includesResort(‘IT1’,’CretaMareRoyal’). fact(breakfast(‘CretaMareRoyal’,true). fact(swimmingPool(‘CretaMareRoyal’,true). fact(includesTransportation(‘IT1’,’Aegean’). fact(from(‘IT2’,athens)). fact(to(‘IT2’,crete)). fact(includesResort(‘IT2’,’Atlantis’). fact(breakfast(‘Atlantis’,true). fact(swimmingPool(‘Atlantis’,false). fact(includesTransportation(‘IT2’,’Aegean’). … Αναπαράσταση και Επεξεργασία Γνώσης

Queries ?- defeasibly(accept(‘IT2’)). no ?- defeasibly(accept(X)). X=IT1; no Αναπαράσταση και Επεξεργασία Γνώσης

DR-Prolog Web Environment Visit: http://www.csd.uoc.gr/~bikakis/DR-Prolog Αναπαράσταση και Επεξεργασία Γνώσης

DR-Prolog Web Environment Αναπαράσταση και Επεξεργασία Γνώσης

:- Thank You! Αναπαράσταση και Επεξεργασία Γνώσης

DR-Prolog : A System for Defeasible Reasoning with Rules and Ontologies on the Semantic Web