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

CS566 – Διαχειριση Γνώσης στο ΔιαδίκτυοΆνοιξη 2010

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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

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Defeasible Logic – Syntax (1/2)

A defeasible theory D is a triple (F,R,>), where F is a finite set offacts, R a finite set of rules, and > a superiority relation on R. There are two kinds of rules (fuller versions of defeasible logicsinclude 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)

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Defeasible Logic – Syntax (2/2)

Superiority relationsA 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

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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

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System Architecture

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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

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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 relationsin the theory, we add facts according to the following guidelines:

fact(p) for each pF 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

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Translation of Defeasible Theories (3/3)

Element of the dl theory LP element

negated literal

~p

~(p)

dl facts

p

fact(p).

dl strict rules

r: q1,q2,…,qn → p

strict(r,p,[q1,…,qn]).

dl defeasible rules

r: q1,…,qn p

defeasible(r,p,[q1,…,qn]).

priority on rules

r>s

sup(r,s).

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Prolog Metaprogram (1/3)

Class of rules in a defeasible theorysupportive_rule(Name,Head,Body):- strict(Name,Head,Body).supportive_rule(Name,Head,Body):- defeasible(Name,Head,Body).

Definite provabilitydefinitely(X):- fact(X).definitely(X):- strict(R,X,[Y1 ,Y2 ,…,Yn]),

definitely(Y1), definitely(Y2), …, definitely(Yn).

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Prolog Metaprogram (2/3)

Defeasible provabilitydefeasibly(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)).

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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).

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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

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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.

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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).

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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’).

…

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Queries

?- defeasibly(accept(‘IT2’)).

no

?- defeasibly(accept(X)).

X=IT1;

no

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DR-Prolog Web Environment

http://www.csd.uoc.gr/~bikakis/DR-PrologVisit:

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DR-Prolog Web Environment

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DR-Prolog Web Environment

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DR-Prolog Web Environment

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DR-Prolog Web Environment

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DR-Prolog Web Environment

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DR-Prolog Web Environment

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:- Thank You!