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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.inference;
import java.util.ArrayList;
import java.util.List;
import java.util.Map;
import java.util.Set;
import aima.core.logic.fol.inference.proof.Proof;
import aima.core.logic.fol.inference.proof.ProofFinal;
import aima.core.logic.fol.inference.proof.ProofStep;
import aima.core.logic.fol.inference.proof.ProofStepFoChAlreadyAFact;
import aima.core.logic.fol.inference.proof.ProofStepFoChAssertFact;
import aima.core.logic.fol.kb.FOLKnowledgeBase;
import aima.core.logic.fol.kb.data.Clause;
import aima.core.logic.fol.kb.data.Literal;
import aima.core.logic.fol.parsing.ast.AtomicSentence;
import aima.core.logic.fol.parsing.ast.NotSentence;
import aima.core.logic.fol.parsing.ast.Sentence;
import aima.core.logic.fol.parsing.ast.Term;
import aima.core.logic.fol.parsing.ast.Variable;
/**
* Artificial Intelligence A Modern Approach (3rd Edition): Figure 9.3, page
* 332.
*
*
*
* function FOL-FC-ASK(KB, alpha) returns a substitution or false
* inputs: KB, the knowledge base, a set of first order definite clauses
* alpha, the query, an atomic sentence
* local variables: new, the new sentences inferred on each iteration
*
* repeat until new is empty
* new <- {}
* for each rule in KB do
* (p1 ˆ ... ˆ pn => q) <- STANDARDIZE-VARAIBLES(rule)
* for each theta such that SUBST(theta, p1 ˆ ... ˆ pn) = SUBST(theta, p'1 ˆ ... ˆ p'n)
* for some p'1,...,p'n in KB
* q' <- SUBST(theta, q)
* if q' does not unify with some sentence already in KB or new then
* add q' to new
* theta <- UNIFY(q', alpha)
* if theta is not fail then return theta
* add new to KB
* return false
*
*
* Figure 9.3 A conceptually straightforward, but very inefficient
* forward-chaining algo- rithm. On each iteration, it adds to KB all the atomic
* sentences that can be inferred in one step from the implication sentences and
* the atomic sentences already in KB. The function STANDARDIZE-VARIABLES
* replaces all variables in its arguments with new ones that have not been used
* before.
*
* @author Ciaran O'Reilly
*
*/
public class FOLFCAsk implements InferenceProcedure {
public FOLFCAsk() {
}
//
// START-InferenceProcedure
/**
* FOL-FC-ASK returns a substitution or false.
*
* @param KB
* the knowledge base, a set of first order definite clauses
* @param query
* the query, an atomic sentence
*
* @return a substitution or false
*/
public InferenceResult ask(FOLKnowledgeBase KB, Sentence query) {
// Assertions on the type of queries this Inference procedure
// supports
if (!(query instanceof AtomicSentence)) {
throw new IllegalArgumentException(
"Only Atomic Queries are supported.");
}
FCAskAnswerHandler ansHandler = new FCAskAnswerHandler();
Literal alpha = new Literal((AtomicSentence) query);
// local variables: new, the new sentences inferred on each iteration
List newSentences = new ArrayList();
// Ensure query is not already a know fact before
// attempting forward chaining.
Set> answers = KB.fetch(alpha);
if (answers.size() > 0) {
ansHandler.addProofStep(new ProofStepFoChAlreadyAFact(alpha));
ansHandler.setAnswers(answers);
return ansHandler;
}
// repeat until new is empty
do {
// new <- {}
newSentences.clear();
// for each rule in KB do
// (p1 ^ ... ^ pn => q) <-STANDARDIZE-VARIABLES(rule)
for (Clause impl : KB.getAllDefiniteClauseImplications()) {
impl = KB.standardizeApart(impl);
// for each theta such that SUBST(theta, p1 ^ ... ^ pn) =
// SUBST(theta, p'1 ^ ... ^ p'n)
// --- for some p'1,...,p'n in KB
for (Map theta : KB.fetch(invert(impl
.getNegativeLiterals()))) {
// q' <- SUBST(theta, q)
Literal qDelta = KB.subst(theta, impl.getPositiveLiterals()
.get(0));
// if q' does not unify with some sentence already in KB or
// new then do
if (!KB.isRenaming(qDelta)
&& !KB.isRenaming(qDelta, newSentences)) {
// add q' to new
newSentences.add(qDelta);
ansHandler.addProofStep(impl, qDelta, theta);
// theta <- UNIFY(q', alpha)
theta = KB.unify(qDelta.getAtomicSentence(),
alpha.getAtomicSentence());
// if theta is not fail then return theta
if (null != theta) {
for (Literal l : newSentences) {
Sentence s = null;
if (l.isPositiveLiteral()) {
s = l.getAtomicSentence();
} else {
s = new NotSentence(l.getAtomicSentence());
}
KB.tell(s);
}
ansHandler.setAnswers(KB.fetch(alpha));
return ansHandler;
}
}
}
}
// add new to KB
for (Literal l : newSentences) {
Sentence s = null;
if (l.isPositiveLiteral()) {
s = l.getAtomicSentence();
} else {
s = new NotSentence(l.getAtomicSentence());
}
KB.tell(s);
}
} while (newSentences.size() > 0);
// return false
return ansHandler;
}
// END-InferenceProcedure
//
//
// PRIVATE METHODS
//
private List invert(List lits) {
List invLits = new ArrayList();
for (Literal l : lits) {
invLits.add(new Literal(l.getAtomicSentence(), (l
.isPositiveLiteral() ? true : false)));
}
return invLits;
}
class FCAskAnswerHandler implements InferenceResult {
private ProofStep stepFinal = null;
private List proofs = new ArrayList();
public FCAskAnswerHandler() {
}
//
// START-InferenceResult
public boolean isPossiblyFalse() {
return proofs.size() == 0;
}
public boolean isTrue() {
return proofs.size() > 0;
}
public boolean isUnknownDueToTimeout() {
return false;
}
public boolean isPartialResultDueToTimeout() {
return false;
}
public List getProofs() {
return proofs;
}
// END-InferenceResult
//
public void addProofStep(Clause implication, Literal fact,
Map bindings) {
stepFinal = new ProofStepFoChAssertFact(implication, fact,
bindings, stepFinal);
}
public void addProofStep(ProofStep step) {
stepFinal = step;
}
public void setAnswers(Set> answers) {
for (Map ans : answers) {
proofs.add(new ProofFinal(stepFinal, ans));
}
}
}
}