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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.fol;

import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Set;

import aima.core.logic.fol.kb.data.Clause;

/**
 * Artificial Intelligence A Modern Approach (3rd Edition): page 356.

 * 

 * The subsumption method eliminates all sentences that are subsumed by (that
 * is, more specific than) an existing sentence in the KB. For example, P(x) is
 * in the KB, then there is no sense in adding P(A) and even less sense in
 * adding P(A) V Q(B). Subsumption helps keep the KB small and thus helps keep
 * the search space small.

 * 

 * Note: From slide 17. 

 * 

 * Relational Subsumption

 * 

 * A relational clause Φ subsumes Ψ if and only if there is a
 * substitution δ that, when applied to Φ, produces a clause Φ'
 * that is a subset of Ψ.
 * 
 * @author Ciaran O'Reilly
 * @author Mike Stampone
 */
public class SubsumptionElimination {
	/**
	 * Returns the clauses that are subsumed by (that is, more specific than) an
	 * existing clause in the specified set of clauses.
	 * 
	 * @param clauses
	 *            a set of clauses in first order logic
	 * 
	 * @return the clauses that are subsumed by (that is, more specific than) an
	 *         existing clause in the specified set of clauses.
	 */
	public static Set findSubsumedClauses(Set clauses) {
		Set subsumed = new HashSet();

		// Group the clauses by their # of literals.
		// Keep track of the min and max # of literals.
		int min = Integer.MAX_VALUE;
		int max = 0;
		Map> clausesGroupedBySize = new HashMap>();
		for (Clause c : clauses) {
			int size = c.getNumberLiterals();
			if (size < min) {
				min = size;
			}
			if (size > max) {
				max = size;
			}
			Set cforsize = clausesGroupedBySize.get(size);
			if (null == cforsize) {
				cforsize = new HashSet();
				clausesGroupedBySize.put(size, cforsize);
			}
			cforsize.add(c);
		}
		// Check if each smaller clause
		// subsumes any of the larger clauses.
		for (int i = min; i < max; i++) {
			Set scs = clausesGroupedBySize.get(i);
			// Ensure there are clauses with this # of literals
			if (null != scs) {
				for (int j = i + 1; j <= max; j++) {
					Set lcs = clausesGroupedBySize.get(j);
					// Ensure there are clauses with this # of literals
					if (null != lcs) {
						for (Clause sc : scs) {
							// Don't bother checking clauses
							// that are already subsumed.
							if (!subsumed.contains(sc)) {
								for (Clause lc : lcs) {
									if (!subsumed.contains(lc)) {
										if (sc.subsumes(lc)) {
											subsumed.add(lc);
										}
									}
								}
							}
						}
					}
				}
			}
		}

		return subsumed;
	}
}