net.sf.tweety.logics.cl

Class ZReasoner

java.lang.Object

net.sf.tweety.commons.Reasoner

net.sf.tweety.logics.cl.ZReasoner

public class ZReasoner
extends Reasoner

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

Field Summary

Fields

Modifier and Type	Field and Description
private RankingFunction	ocf The ranking function for this knowledge base based on penalty points of System Z.
private java.util.Set<PossibleWorld>	omega

Constructor Summary

Constructors

Constructor and Description
ZReasoner(BeliefBase beliefBase) Creates a new System Z reasoner for the given knowledge base.

Method Summary

Modifier and Type	Method and Description
private RankingFunction	computeOCF() Returns a ranking functions based on penalty points of System Z.
RankingFunction	getOCF() Returns the ranking function this reasoner bases on.
private boolean	isTolerated(Conditional f, ClBeliefSet kb) 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(BeliefBase kb) Returns a partitioning of a knowledge base into partitions containing all conditionals that tolerate the remaining set of conditionals of a knowledge base.
Answer	query(Formula query) This method determines the answer of the given query wrt.

Methods inherited from class net.sf.tweety.commons.Reasoner

getKnowledgeBase

Methods inherited from class java.lang.Object

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

Field Detail

ocf

private RankingFunction ocf

The ranking function for this knowledge base based on penalty points of System Z. Once this ranking function has been computed it is used for subsequent queries in order to avoid unnecessary computations.

omega

private java.util.Set<PossibleWorld> omega

Constructor Detail

ZReasoner

public ZReasoner(BeliefBase beliefBase)

Creates a new System Z reasoner for the given knowledge base.

Parameters:

beliefBase - a knowledge base.

Method Detail

query

public Answer query(Formula query)

Description copied from class: Reasoner

This method determines the answer of the given query wrt. to the given knowledge base.

Specified by:

query in class Reasoner

Parameters:

query - a query.

Returns:

the answer to the query.

getOCF

public RankingFunction getOCF()

Returns the ranking function this reasoner bases on.

Returns:

the ranking function this reasoner bases on.

computeOCF

private RankingFunction computeOCF()

Returns a ranking functions based on penalty points of System Z.

Returns:

A ranking function for this reasoner's knowledge base.

partition

private java.util.ArrayList<ClBeliefSet> partition(BeliefBase kb)

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)

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