aima.core.logic.propositional.inference

Class TTEntails

java.lang.Object

aima.core.logic.propositional.inference.TTEntails

public class TTEntails
extends java.lang.Object

Artificial Intelligence A Modern Approach (3rd Edition): Figure 7.10, page 248.

 function TT-ENTAILS?(KB, α) returns true or false
   inputs: KB, the knowledge base, a sentence in propositional logic
           α, the query, a sentence in propositional logic
           
   symbols <- a list of proposition symbols in KB and &alpha
   return TT-CHECK-ALL(KB, α symbols, {})
   
 --------------------------------------------------------------------------------
 
 function TT-CHECK-ALL(KB, α symbols, model) returns true or false
   if EMPTY?(symbols) then
     if PL-TRUE?(KB, model) then return PL-TRUE?(α, model)
     else return true // when KB is false, always return true
   else do
     P <- FIRST(symbols)
     rest <- REST(symbols)
     return (TT-CHECK-ALL(KB, α, rest, model ∪ { P = true })
            and
            TT-CHECK-ALL(KB, α, rest, model ∪ { P = false }))
 

Figure 7.10 A truth-table enumeration algorithm for deciding propositional entailment. (TT stands for truth table.) PL-TRUE? returns true if a sentence holds within a model. The variable model represents a partional model - an assignment to some of the symbols. The keyword "and" is used here as a logical operation on its two arguments, returning true or false.

Author:

Ciaran O'Reilly, Ravi Mohan, Mike Stampone

Constructor Summary

Constructors

Constructor and Description
TTEntails()

Method Summary

Modifier and Type	Method and Description
boolean	ttCheckAll(KnowledgeBase kb, Sentence alpha, java.util.List<PropositionSymbol> symbols, Model model) function TT-CHECK-ALL(KB, α symbols, model) returns true or false
boolean	ttEntails(KnowledgeBase kb, Sentence alpha) function TT-ENTAILS?(KB, α) returns true or false.

Methods inherited from class java.lang.Object

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

Constructor Detail

TTEntails

public TTEntails()

Method Detail

ttEntails

public boolean ttEntails(KnowledgeBase kb,
                         Sentence alpha)

function TT-ENTAILS?(KB, α) returns true or false.

Parameters:

kb - KB, the knowledge base, a sentence in propositional logic

alpha - α, the query, a sentence in propositional logic

Returns:

true if KB entails α, false otherwise.

ttCheckAll

public boolean ttCheckAll(KnowledgeBase kb,
                          Sentence alpha,
                          java.util.List<PropositionSymbol> symbols,
                          Model model)

function TT-CHECK-ALL(KB, α symbols, model) returns true or false

Parameters:

kb - KB, the knowledge base, a sentence in propositional logic

alpha - α, the query, a sentence in propositional logic

symbols - a list of currently unassigned propositional symbols in the model.

model - a partially or fully assigned model for the given KB and query.

Returns:

true if KB entails α, false otherwise.