net.sf.tweety.logics.cl.reasoner

Class ZReasoner

java.lang.Object

net.sf.tweety.logics.cl.reasoner.AbstractConditionalLogicReasoner

net.sf.tweety.logics.cl.reasoner.ZReasoner

All Implemented Interfaces:

ModelProvider<Conditional,ClBeliefSet,RankingFunction>, QualitativeReasoner<ClBeliefSet,PropositionalFormula>, Reasoner<java.lang.Boolean,ClBeliefSet,PropositionalFormula>

public class ZReasoner
extends AbstractConditionalLogicReasoner

This class models a z-reasoner for conditional logic. Reasoning is performed by computing a ranking function based on a tolerating partitioning of a consistent knowledge base
The conditionals of the knowledge base KB are splitted in different partitions. The first partition KB_0 contains all conditionals (B_i|A_i) that are tolerated by all other rules of the knowledge base, i.e., there exists a world w that satisfies A_iB_i and for all other conditionals (B_j|A_j) it satisfies the material implication A_j => B_j. These conditionals are removed from the knowledge base. The second partition KB_1 contains all conditionals of the remaining conditional set that are tolerated by it. This is done until the original knowledge base is the empty set. This is simultaniously a test on whether or not the knowledge base is consistent. There exists such a partitioning iff the knowledge base is consistent. A world falsifying a conditional r_i gets penalty points according to the maxium partition that contains a falsified world. The penalty points represent the ranking function and are computed as follows Z(r_i) = j iff r_i in KB_j ( 0, if w |= A_i => B_i for all 1<=i<=n Z(w) = < ( max {z(r_i)} + 1 for all conditionals r_i=(B_i|A_i) with w |= A_i !B_i

See Judea Pearl. System Z: a natural ordering of defaults with tractable applications to default reasoning. In Proceedings of the 3rd conference on Theoretical aspects of reasoning about knowledge, TARK '90, San Francicso, Morgan Kaufmann Publishers Inc. (1990) 121-135

Author:

Katharina Diekmann, Matthias Thimm

Constructor Summary

Constructors

Constructor and Description
ZReasoner()

Method Summary

Modifier and Type	Method and Description
RankingFunction	getModel(ClBeliefSet beliefset) Returns a single (dedicated) model of the given belief base.
private boolean	isTolerated(Conditional f, ClBeliefSet kb, java.util.Set<PossibleWorld> omega) Checks whether or not the given formula is tolerated by the knowledge base, i.e., there is a world omega that satisfies the formula and does not falsify each conditional (B|A) in the knowledge base (it satisfies the material implication A => B).
private java.util.ArrayList<ClBeliefSet>	partition(ClBeliefSet kb, java.util.Set<PossibleWorld> omega) Returns a partitioning of a knowledge base into partitions containing all conditionals that tolerate the remaining set of conditionals of a knowledge base.

Methods inherited from class net.sf.tweety.logics.cl.reasoner.AbstractConditionalLogicReasoner

getModels, query

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

ZReasoner

public ZReasoner()

Method Detail

partition

private java.util.ArrayList<ClBeliefSet> partition(ClBeliefSet kb,
                                                   java.util.Set<PossibleWorld> omega)

Returns a partitioning of a knowledge base into partitions containing all conditionals that tolerate the remaining set of conditionals of a knowledge base.

Parameters:

Knowledge - base that needs to be partitioned

Returns:

ArrayList containing consistent belief sets

isTolerated

private boolean isTolerated(Conditional f,
                            ClBeliefSet kb,
                            java.util.Set<PossibleWorld> omega)

Checks whether or not the given formula is tolerated by the knowledge base, i.e., there is a world omega that satisfies the formula and does not falsify each conditional (B|A) in the knowledge base (it satisfies the material implication A => B).

Parameters:

Conditional - f - formula that should be tolerated by the knowledge base

ClBeliefSet - kb - corresponding knowledge base

Returns:

true if the Conditional f is tolerated, false otherwise

getModel

public RankingFunction getModel(ClBeliefSet beliefset)

Description copied from interface: ModelProvider

Returns a single (dedicated) model of the given belief base. If the implemented method allows for more than one dedicated model, the selection may be non-deterministic.

Specified by:

getModel in interface ModelProvider<Conditional,ClBeliefSet,RankingFunction>

Specified by:

getModel in class AbstractConditionalLogicReasoner

Returns:

a selected model of the belief base.