DR-Prolog: A System for Defeasible Reasoning with Rules and Ontologies on the Semantic Web CS566 – Διαχειριση Γνώσης στο Διαδίκτυο Άνοιξη 2010

21/6/20152 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. Defeasible Logic: Basic Characteristics

21/6/20153 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)

21/6/20154 Defeasible Logic – Syntax (2/2) Superiority relations A superiority relation on R is an acyclic relation > on R. When r 1 > r 2, then r 1 is called superior to r 2, and r 2 inferior to r 1. This expresses that r 1 may override r 2.  Example: r: bird(X)  flies(X) r’: penguin(X)  ¬flies(X) r’ > r

21/6/20155 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

21/6/20156 System Architecture

21/6/20157 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

21/6/20158 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(r i, p,[q 1,…,q n ]) for each rule r i : q 1,…,q n  p  R defeasible(r i,p,[q 1,…,q n ]) for each rule r i : q 1,…,q n  p  R sup(r,s) for each pair of rules such that r>s

21/6/20159 Translation of Defeasible Theories (3/3) Element of the dl theoryLP element negated literal ~p ~(p) dl facts p fact(p). dl strict rules r: q 1,q 2,…,q n → p strict(r,p,[q 1,…,q n ]). dl defeasible rules r: q 1,…,q n  p defeasible(r,p,[q 1,…,q n ]). priority on rules r>s sup(r,s).

21/6/ 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,[Y 1,Y 2,…,Y n ]), definitely(Y 1 ), definitely(Y 2 ), …, definitely(Y n ).

21/6/ Prolog Metaprogram (2/3) Defeasible provability defeasibly(X):- definitely(X). defeasibly(X):- supportive_rule(R, X, [Y 1,Y 2,…,Y n ]), defeasibly(Y 1 ), defeasibly(Y 2 ), …, defeasibly(Y n ), sk_not(overruled(R,X)), sk_not(definitely(¬X)).

21/6/ Prolog Metaprogram (3/3) Overruled(R,X) overruled(R,X):- supportive_rule(S, ¬X, [Y 1,Y 2,…,Y n ]), defeasibly(Y 1 ), defeasibly(Y 2 ), …, defeasibly(Y n ), sk_not(defeated(S, ¬X)). Defeated(S,X) defeated(S,X):- supportive_rule(T, ¬X, [Y 1,Y 2,…,Y n ]), defeasibly(Y 1 ), defeasibly(Y 2 ), …, defeasibly(Y n ), sup(T, S).

21/6/ 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

21/6/ Adam’s Requirements in DL r 1 : from(X,athens), includesResort(X,Y), breakfast(Y,true), swimmingPool(Y,true) => accept(X). r 2 : from(X,athens), includesResort(X,Y), breakfast(Y,true),includesService(X,Z),hasVehicle(S,W), vehicleAC(W,true) => accept(X). r 3 : includesResort(X,Y),parking(Y,false) => ~accept(X). r 4 : ~includesTransportation(X,Z) => ~accept(X). r 1 > r 3. r 4 > r 1. r 4 > r 2. r 3 > r 2.

21/6/ 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).

21/6/ 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’). …

21/6/ Queries ?- defeasibly(accept(‘IT2’)). no ?- defeasibly(accept(X)). X=IT1; no

21/6/ DR-Prolog Web Environment

21/6/ DR-Prolog Web Environment

21/6/ DR-Prolog Web Environment

21/6/ DR-Prolog Web Environment

21/6/ DR-Prolog Web Environment

21/6/ DR-Prolog Web Environment

21/6/ DR-Prolog Web Environment

21/6/ :- Thank You!