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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 249.

 * 

 * Distributivity of & over |:

 * (α & (β | γ))

 * ≡

 * ((α & β) | (α & γ))

 * 
 * @author Ciaran O'Reilly
 * 
 */
public class DistributeAndOverOr extends AbstractPLVisitor {

	/**
	 * Distribute and (&) over or (|).
	 * 
	 * @param sentence
	 *            a propositional logic sentence. This sentence should already
	 *            have biconditionals, and implications removed and negations
	 *            moved inwards.
	 * @return an equivalent Sentence to the input with and's distributed over
	 *         or's.
	 */
	public static Sentence distribute(Sentence sentence) {
		Sentence result = null;

		DistributeAndOverOr distributeAndOverOr = new DistributeAndOverOr();
		result = sentence.accept(distributeAndOverOr, null);

		return result;
	}

	@Override
	public Sentence visitBinarySentence(ComplexSentence s, Object arg) {
		Sentence result = null;

		if (s.isAndSentence()) {
			Sentence s1 = s.getSimplerSentence(0).accept(this, arg);
			Sentence s2 = s.getSimplerSentence(1).accept(this, arg);
			if (s1.isOrSentence() || s2.isOrSentence()) {
				Sentence alpha, betaAndGamma;
				if (s2.isOrSentence()) {
					// (α & (β | γ))
					// Note: even if both are 'or' sentence
					// we will prefer to use s2
					alpha = s1;
					betaAndGamma = s2;
				} else {
					// Note: Need to handle this case too
					// ((β | γ) & α)
					alpha = s2;
					betaAndGamma = s1;
				}

				Sentence beta = betaAndGamma.getSimplerSentence(0);
				Sentence gamma = betaAndGamma.getSimplerSentence(1);

				if (s2.isOrSentence()) {
					// ((α & β) | (α & γ))
					Sentence alphaAndBeta = (new ComplexSentence(Connective.AND,
							alpha, beta)).accept(this, null);
					Sentence alphaAndGamma = (new ComplexSentence(Connective.AND,
							alpha, gamma)).accept(this, null);

					result = new ComplexSentence(Connective.OR, alphaAndBeta,
							alphaAndGamma);
				} else {
					// ((β & α) | (γ & α))
					Sentence betaAndAlpha = (new ComplexSentence(Connective.AND,
							beta, alpha)).accept(this, null);
					Sentence gammaAndAlpha = (new ComplexSentence(Connective.AND,
							gamma, alpha)).accept(this, null);

					result = new ComplexSentence(Connective.OR, betaAndAlpha,
							gammaAndAlpha);
				}
			} else {
				result = new ComplexSentence(Connective.AND, s1, s2);
			}
		} else {
			result = super.visitBinarySentence(s, arg);
		}

		return result;
	}
}
 















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