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AIMA-Java Core Algorithms from the book Artificial Intelligence a Modern Approach 3rd Ed.

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package aima.core.logic.propositional.visitors;

import aima.core.logic.propositional.parsing.AbstractPLVisitor;
import aima.core.logic.propositional.parsing.ast.ComplexSentence;
import aima.core.logic.propositional.parsing.ast.Connective;
import aima.core.logic.propositional.parsing.ast.Sentence;

/**
 * Artificial Intelligence A Modern Approach (3rd Edition): page 253.

 * 

 * Eliminate <=>, replacing α <=> β

 * with (α => β) & (β => α)
 * 
 * @author Ciaran O'Reilly
 * 
 */
public class BiconditionalElimination extends AbstractPLVisitor {

	/**
	 * Eliminate the biconditionals from a sentence.
	 * 
	 * @param sentence
	 *            a propositional logic sentence.
	 * @return an equivalent Sentence to the input with all biconditionals
	 *         eliminated.
	 */
	public static Sentence eliminate(Sentence sentence) {
		BiconditionalElimination eliminator = new BiconditionalElimination();

		Sentence result = sentence.accept(eliminator, null);

		return result;
	}

	@Override
	public Sentence visitBinarySentence(ComplexSentence s, Object arg) {
		Sentence result = null;
		if (s.isBiconditionalSentence()) {
			// Eliminate <=>, replace α <=> β
			// with (α => β) & (β => α)
			Sentence alpha = s.getSimplerSentence(0).accept(this, arg);
			Sentence beta = s.getSimplerSentence(1).accept(this, arg);
			Sentence alphaImpliesBeta = new ComplexSentence(
					Connective.IMPLICATION, alpha, beta);
			Sentence betaImpliesAlpha = new ComplexSentence(
					Connective.IMPLICATION, beta, alpha);

			result = new ComplexSentence(Connective.AND, alphaImpliesBeta,
					betaImpliesAlpha);
		} else {
			result = super.visitBinarySentence(s, arg);
		}
		return result;
	}
}
 















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