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

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

• ??apa??stas? ?a? ?pe?e??as?a G??s??
• ?????? 2009

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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.

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Defeasible Logic Syntax (1/2)

• A defeasible theory D is a triple (F,R,gt), where
  F is a finite set of
• facts, R a finite set of rules, and gt 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)

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Defeasible Logic Syntax (2/2)

• Superiority relations
• A superiority relation on R is an acyclic
  relation gt on R.
• When r1 gt 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 gt 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,gt), where F is
  the set of the facts,
• R is the set of the rules, and gt 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 rgts

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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 rgts sup(r,s).
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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).

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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)).

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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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Adams Requirements in DL

• r1 from(X,athens), includesResort(X,Y),
  breakfast(Y,true), swimmingPool(Y,true) gt
  accept(X).
• r2 from(X,athens), includesResort(X,Y),
  breakfast(Y,true),includesService(X,Z),hasVehicle(
  S,W), vehicleAC(W,true) gt accept(X).
• r3 includesResort(X,Y),parking(Y,false) gt
  accept(X).
• r4 includesTransportation(X,Z) gt accept(X).
• r1 gt r3.
• r4 gt r1.
• r4 gt r2.
• r3 gt r2.

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Adams 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)), (includesTransportat
  ion(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)).
• XIT1
• no

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DR-Prolog Web Environment
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