// Note: see - // http://logic.stanford.edu/classes/cs157/2008/lectures/lecture15.pdf // slide 12 for where this test example was taken from. public static FOLKnowledgeBase createABCEqualityKnowledgeBase( InferenceProcedure infp, bool includeEqualityAxioms) { FOLDomain domain = new FOLDomain(); domain.addConstant("A"); domain.addConstant("B"); domain.addConstant("C"); FOLKnowledgeBase kb = new FOLKnowledgeBase(domain, infp); kb.tell("B = A"); kb.tell("B = C"); if (includeEqualityAxioms) { // Reflexivity Axiom kb.tell("x = x"); // Symmetry Axiom kb.tell("(x = y => y = x)"); // Transitivity Axiom kb.tell("((x = y AND y = z) => x = z)"); } return(kb); }
public void testNegativeTermEquality() { FOLDomain domain = new FOLDomain(); domain.addConstant("A"); domain.addConstant("B"); domain.addConstant("C"); domain.addPredicate("P"); domain.addFunction("F"); FOLParser parser = new FOLParser(domain); ICollection <Literal> lits = CollectionFactory.CreateQueue <Literal>(); AtomicSentence a1 = (AtomicSentence)parser.parse("P(y, F(A,y))"); lits.Add(new Literal(a1)); Clause c1 = new Clause(lits); lits.Clear(); a1 = (AtomicSentence)parser.parse("F(x,B) = x"); lits.Add(new Literal(a1, true)); Clause c2 = new Clause(lits); ISet <Clause> paras = paramodulation.apply(c1, c2); Assert.AreEqual(0, paras.Size()); }
// Note: see - // http://logic.stanford.edu/classes/cs157/2008/lectures/lecture15.pdf // slide 16,17, and 18 for where this test example was taken from. public static FOLKnowledgeBase createABCDEqualityAndSubstitutionKnowledgeBase( InferenceProcedure infp, bool includeEqualityAxioms) { FOLDomain domain = new FOLDomain(); domain.addConstant("A"); domain.addConstant("B"); domain.addConstant("C"); domain.addConstant("D"); domain.addPredicate("P"); domain.addFunction("F"); FOLKnowledgeBase kb = new FOLKnowledgeBase(domain, infp); kb.tell("F(A) = B"); kb.tell("F(B) = A"); kb.tell("C = D"); kb.tell("P(A)"); kb.tell("P(C)"); if (includeEqualityAxioms) { // Reflexivity Axiom kb.tell("x = x"); // Symmetry Axiom kb.tell("(x = y => y = x)"); // Transitivity Axiom kb.tell("((x = y AND y = z) => x = z)"); // Function F Substitution Axiom kb.tell("((x = y AND F(y) = z) => F(x) = z)"); // Predicate P Substitution Axiom kb.tell("((x = y AND P(y)) => P(x))"); } return(kb); }
public void testSimpleClauseNonExample() { FOLDomain domain = new FOLDomain(); domain.addConstant("A"); domain.addConstant("B"); domain.addConstant("C"); domain.addPredicate("P"); domain.addFunction("F"); FOLParser parser = new FOLParser(domain); ICollection <Literal> lits = CollectionFactory.CreateQueue <Literal>(); Predicate p1 = (Predicate)parser.parse("P(y, F(A,y))"); lits.Add(new Literal(p1)); Clause clExpression = new Clause(lits); TermEquality assertion = (TermEquality)parser.parse("F(x,B) = C"); Clause altClExpression = demodulation.apply(assertion, clExpression); Assert.IsNull(altClExpression); }
static void fOL_Demodulation() { System.Console.WriteLine("-----------------"); System.Console.WriteLine("Demodulation Demo"); System.Console.WriteLine("-----------------"); FOLDomain domain = new FOLDomain(); domain.addConstant("A"); domain.addConstant("B"); domain.addConstant("C"); domain.addConstant("D"); domain.addConstant("E"); domain.addPredicate("P"); domain.addFunction("F"); domain.addFunction("G"); domain.addFunction("H"); domain.addFunction("J"); FOLParser parser = new FOLParser(domain); Predicate expression = (Predicate)parser.parse("P(A,F(B,G(A,H(B)),C),D)"); TermEquality assertion = (TermEquality)parser.parse("B = E"); Demodulation demodulation = new Demodulation(); Predicate altExpression = (Predicate)demodulation.apply(assertion, expression); System.Console.WriteLine("Demodulate '" + expression + "' with '" + assertion + "' to give"); System.Console.WriteLine(altExpression.ToString()); System.Console.WriteLine("and again to give"); System.Console.WriteLine(demodulation.apply(assertion, altExpression).ToString()); System.Console.WriteLine(""); }
public void testBypassReflexivityAxiom() { FOLDomain domain = new FOLDomain(); domain.addConstant("A"); domain.addConstant("B"); domain.addConstant("C"); domain.addPredicate("P"); domain.addFunction("F"); FOLParser parser = new FOLParser(domain); List <Literal> lits = new List <Literal>(); Predicate p1 = (Predicate)parser.parse("P(y, F(A,y))"); lits.Add(new Literal(p1)); Clause clExpression = new Clause(lits); TermEquality assertion = (TermEquality)parser.parse("x = x"); Clause altClExpression = demodulation.apply(assertion, clExpression); Assert.IsNull(altClExpression); }
public void testBypassReflexivityAxiom() { FOLDomain domain = new FOLDomain(); domain.addConstant("A"); domain.addConstant("B"); domain.addConstant("C"); domain.addPredicate("P"); domain.addFunction("F"); FOLParser parser = new FOLParser(domain); List <Literal> lits = new List <Literal>(); AtomicSentence a1 = (AtomicSentence)parser.parse("P(y, F(A,y))"); lits.Add(new Literal(a1)); Clause c1 = new Clause(lits); lits.Clear(); a1 = (AtomicSentence)parser.parse("x = x"); lits.Add(new Literal(a1)); Clause c2 = new Clause(lits); List <Clause> paras = paramodulation.apply(c1, c2); Assert.AreEqual(0, paras.Count); }
public void testSimpleAtomicNonExample() { FOLDomain domain = new FOLDomain(); domain.addConstant("A"); domain.addConstant("B"); domain.addConstant("C"); domain.addConstant("D"); domain.addConstant("E"); domain.addPredicate("P"); domain.addFunction("F"); domain.addFunction("G"); domain.addFunction("H"); domain.addFunction("J"); FOLParser parser = new FOLParser(domain); Predicate expression = (Predicate)parser.parse("P(A,G(x,B),C)"); TermEquality assertion = (TermEquality)parser.parse("G(A,y) = J(y)"); Predicate altExpression = (Predicate)demodulation.apply(assertion, expression); Assert.IsNull(altExpression); }
public void testDefaultClauseSimplifier() { FOLDomain domain = new FOLDomain(); domain.addConstant("ZERO"); domain.addConstant("ONE"); domain.addPredicate("P"); domain.addFunction("Plus"); domain.addFunction("Power"); FOLParser parser = new FOLParser(domain); ICollection <TermEquality> rewrites = CollectionFactory.CreateQueue <TermEquality>(); rewrites.Add((TermEquality)parser.parse("Plus(x, ZERO) = x")); rewrites.Add((TermEquality)parser.parse("Plus(ZERO, x) = x")); rewrites.Add((TermEquality)parser.parse("Power(x, ONE) = x")); rewrites.Add((TermEquality)parser.parse("Power(x, ZERO) = ONE")); DefaultClauseSimplifier simplifier = new DefaultClauseSimplifier(rewrites); Sentence s1 = parser.parse("((P(Plus(y,ZERO),Plus(ZERO,y)) OR P(Power(y, ONE),Power(y,ZERO))) OR P(Power(y,ZERO),Plus(y,ZERO)))"); CNFConverter cnfConverter = new CNFConverter(parser); CNF cnf = cnfConverter.convertToCNF(s1); Assert.AreEqual(1, cnf.getNumberOfClauses()); Clause simplified = simplifier.simplify(cnf.getConjunctionOfClauses().Get(0)); Assert.AreEqual("[P(y,y), P(y,ONE), P(ONE,y)]", simplified.ToString()); }
public void testAdditionalVariableMixtures() { FOLDomain domain = new FOLDomain(); domain.addConstant("A"); domain.addConstant("B"); domain.addFunction("F"); domain.addFunction("G"); domain.addFunction("H"); domain.addPredicate("P"); FOLParser parser = new FOLParser(domain); // Test Cascade Substitutions handled correctly Sentence s1 = parser.parse("P(z, x)"); Sentence s2 = parser.parse("P(x, a)"); IMap <Variable, Term> result = unifier.unify(s1, s2); Assert.AreEqual("[[z, a], [x, a]]", result.ToString()); s1 = parser.parse("P(x, z)"); s2 = parser.parse("P(a, x)"); result = unifier.unify(s1, s2); Assert.AreEqual("[[x, a], [z, a]]", result.ToString()); s1 = parser.parse("P(w, w, w)"); s2 = parser.parse("P(x, y, z)"); result = unifier.unify(s1, s2); Assert.AreEqual("[[w, z], [x, z], [y, z]]", result.ToString()); s1 = parser.parse("P(x, y, z)"); s2 = parser.parse("P(w, w, w)"); result = unifier.unify(s1, s2); Assert.AreEqual("[[x, w], [y, w], [z, w]]", result.ToString()); s1 = parser.parse("P(x, B, F(y))"); s2 = parser.parse("P(A, y, F(z))"); result = unifier.unify(s1, s2); Assert.AreEqual("[[x, A], [y, B], [z, B]]", result.ToString()); s1 = parser.parse("P(F(x,B), G(y), F(z,A))"); s2 = parser.parse("P(y, G(F(G(w),w)), F(w,z))"); result = unifier.unify(s1, s2); Assert.IsNull(result); s1 = parser.parse("P(F(G(A)), x, F(H(z,z)), H(y, G(w)))"); s2 = parser.parse("P(y, G(z), F(v ), H(F(w), x ))"); result = unifier.unify(s1, s2); Assert.AreEqual( "[[y, F(G(A))], [x, G(G(A))], [v, H(G(A),G(A))], [w, G(A)], [z, G(A)]]", result.ToString()); }
public void testAdditionalVariableMixtures() { FOLDomain domain = new FOLDomain(); domain.addConstant("A"); domain.addConstant("B"); domain.addFunction("F"); domain.addFunction("G"); domain.addFunction("H"); domain.addPredicate("P"); FOLParser parser = new FOLParser(domain); // Test Cascade Substitutions handled correctly Sentence s1 = parser.parse("P(z, x)"); Sentence s2 = parser.parse("P(x, a)"); Dictionary <Variable, Term> result = unifier.unify(s1, s2); Assert.AreEqual("{z=a, x=a}", result.ToString()); s1 = parser.parse("P(x, z)"); s2 = parser.parse("P(a, x)"); result = unifier.unify(s1, s2); Assert.AreEqual("{x=a, z=a}", result.ToString()); s1 = parser.parse("P(w, w, w)"); s2 = parser.parse("P(x, y, z)"); result = unifier.unify(s1, s2); Assert.AreEqual("{w=z, x=z, y=z}", result.ToString()); s1 = parser.parse("P(x, y, z)"); s2 = parser.parse("P(w, w, w)"); result = unifier.unify(s1, s2); Assert.AreEqual("{x=w, y=w, z=w}", result.ToString()); s1 = parser.parse("P(x, B, F(y))"); s2 = parser.parse("P(A, y, F(z))"); result = unifier.unify(s1, s2); Assert.AreEqual("{x=A, y=B, z=B}", result.ToString()); s1 = parser.parse("P(F(x,B), G(y), F(z,A))"); s2 = parser.parse("P(y, G(F(G(w),w)), F(w,z))"); result = unifier.unify(s1, s2); Assert.IsNull(result); s1 = parser.parse("P(F(G(A)), x, F(H(z,z)), H(y, G(w)))"); s2 = parser.parse("P(y, G(z), F(v ), H(F(w), x ))"); result = unifier.unify(s1, s2); Assert.AreEqual( "{y=F(G(A)), x=G(G(A)), v=H(G(A),G(A)), w=G(A), z=G(A)}", result.ToString()); }
public static FOLDomain kingsDomain() { FOLDomain domain = new FOLDomain(); domain.addConstant("John"); domain.addConstant("Richard"); domain.addPredicate("King"); domain.addPredicate("Greedy"); domain.addPredicate("Evil"); return(domain); }
public static FOLDomain knowsDomain() { FOLDomain domain = new FOLDomain(); domain.addConstant("John"); domain.addConstant("Jane"); domain.addConstant("Bill"); domain.addConstant("Elizabeth"); domain.addFunction("Mother"); domain.addPredicate("Knows"); return(domain); }
public static FOLDomain lovesAnimalDomain() { FOLDomain domain = new FOLDomain(); domain.addPredicate("Animal"); domain.addPredicate("Loves"); domain.addPredicate("Kills"); domain.addPredicate("Cat"); domain.addConstant("Jack"); domain.addConstant("Tuna"); domain.addConstant("Curiosity"); return(domain); }
public void testInductionAxiomSchema() { FOLDomain domain = new FOLDomain(); domain.addPredicate("Equal"); domain.addFunction("Plus"); domain.addConstant("A"); domain.addConstant("B"); domain.addConstant("N"); domain.addConstant("ONE"); domain.addConstant("ZERO"); FOLParser parser = new FOLParser(domain); CNFConverter cnfConv = new CNFConverter(parser); // Base Case: Sentence sent = parser .parse("NOT(FORALL x (FORALL y (Equal(Plus(Plus(x,y),ZERO), Plus(x,Plus(y,ZERO))))))"); CNF cnf = cnfConv.convertToCNF(sent); Assert.AreEqual( "[~Equal(Plus(Plus(SC0,SC1),ZERO),Plus(SC0,Plus(SC1,ZERO)))]", cnf.ToString()); // Instance of Induction Axion Scmema sent = parser .parse("((" + "Equal(Plus(Plus(A,B),ZERO), Plus(A,Plus(B,ZERO)))" + " AND " + "(FORALL x (FORALL y (FORALL z(" + "Equal(Plus(Plus(x,y),z), Plus(x,Plus(y,z)))" + " => " + "Equal(Plus(Plus(x,y),Plus(z,ONE)), Plus(x,Plus(y,Plus(z,ONE))))" + "))))" + ")" + " => " + "FORALL x (FORALL y (FORALL z(" + "Equal(Plus(Plus(x,y),z), Plus(x,Plus(y,z)))" + "))))"); cnf = cnfConv.convertToCNF(sent); Assert .AreEqual( "[~Equal(Plus(Plus(A,B),ZERO),Plus(A,Plus(B,ZERO))), Equal(Plus(Plus(q0,q1),q2),Plus(q0,Plus(q1,q2))), Equal(Plus(Plus(SC2,SC3),SC4),Plus(SC2,Plus(SC3,SC4)))],[~Equal(Plus(Plus(A,B),ZERO),Plus(A,Plus(B,ZERO))), ~Equal(Plus(Plus(SC2,SC3),Plus(SC4,ONE)),Plus(SC2,Plus(SC3,Plus(SC4,ONE)))), Equal(Plus(Plus(q0,q1),q2),Plus(q0,Plus(q1,q2)))]", cnf.ToString()); // Goal sent = parser .parse("NOT(FORALL x (FORALL y (FORALL z (Equal(Plus(Plus(x,y),z), Plus(x,Plus(y,z)))))))"); cnf = cnfConv.convertToCNF(sent); Assert.AreEqual( "[~Equal(Plus(Plus(SC5,SC6),SC7),Plus(SC5,Plus(SC6,SC7)))]", cnf.ToString()); }
public void setUp() { FOLDomain domain = new FOLDomain(); domain.addConstant("P"); domain.addConstant("John"); domain.addConstant("Saladin"); domain.addFunction("LeftLeg"); domain.addFunction("BrotherOf"); domain.addFunction("EnemyOf"); domain.addPredicate("HasColor"); domain.addPredicate("King"); lexer = new FOLLexer(domain); }
public static FOLDomain crusadesDomain() { FOLDomain domain = new FOLDomain(); domain.addConstant("John"); domain.addConstant("Richard"); domain.addConstant("England"); domain.addConstant("Saladin"); domain.addConstant("Crown"); domain.addFunction("LeftLegOf"); domain.addFunction("BrotherOf"); domain.addFunction("EnemyOf"); domain.addFunction("LegsOf"); domain.addPredicate("King"); return(domain); }
public void testExhaustsSearchSpace() { // Taken from AIMA pg 679 FOLDomain domain = new FOLDomain(); domain.addPredicate("alternate"); domain.addPredicate("bar"); domain.addPredicate("fri_sat"); domain.addPredicate("hungry"); domain.addPredicate("patrons"); domain.addPredicate("price"); domain.addPredicate("raining"); domain.addPredicate("reservation"); domain.addPredicate("type"); domain.addPredicate("wait_estimate"); domain.addPredicate("will_wait"); domain.addConstant("Some"); domain.addConstant("Full"); domain.addConstant("French"); domain.addConstant("Thai"); domain.addConstant("Burger"); domain.addConstant("$"); domain.addConstant("_30_60"); domain.addConstant("X0"); FOLParser parser = new FOLParser(domain); // The hypothesis String c1 = "patrons(v,Some)"; String c2 = "patrons(v,Full) AND (hungry(v) AND type(v,French))"; String c3 = "patrons(v,Full) AND (hungry(v) AND (type(v,Thai) AND fri_sat(v)))"; String c4 = "patrons(v,Full) AND (hungry(v) AND type(v,Burger))"; String sh = "FORALL v (will_wait(v) <=> (" + c1 + " OR (" + c2 + " OR (" + c3 + " OR (" + c4 + ")))))"; Sentence hypothesis = parser.parse(sh); Sentence desc = parser .parse("(((((((((alternate(X0) AND NOT(bar(X0))) AND NOT(fri_sat(X0))) AND hungry(X0)) AND patrons(X0,Full)) AND price(X0,$)) AND NOT(raining(X0))) AND NOT(reservation(X0))) AND type(X0,Thai)) AND wait_estimate(X0,_30_60))"); Sentence classification = parser.parse("will_wait(X0)"); FOLKnowledgeBase kb = new FOLKnowledgeBase(domain, new FOLOTTERLikeTheoremProver(false)); kb.tell(hypothesis); kb.tell(desc); InferenceResult ir = kb.ask(classification); Assert.IsFalse(ir.isTrue()); Assert.IsTrue(ir.isPossiblyFalse()); Assert.IsFalse(ir.isUnknownDueToTimeout()); Assert.IsFalse(ir.isPartialResultDueToTimeout()); Assert.AreEqual(0, ir.getProofs().Count); }
public static FOLDomain weaponsDomain() { FOLDomain domain = new FOLDomain(); domain.addConstant("West"); domain.addConstant("America"); domain.addConstant("M1"); domain.addConstant("Nono"); domain.addPredicate("American"); domain.addPredicate("Weapon"); domain.addPredicate("Sells"); domain.addPredicate("Hostile"); domain.addPredicate("Criminal"); domain.addPredicate("Missile"); domain.addPredicate("Owns"); domain.addPredicate("Enemy"); return(domain); }
public void testSimpleClauseExamples() { FOLDomain domain = new FOLDomain(); domain.addConstant("A"); domain.addConstant("B"); domain.addConstant("C"); domain.addConstant("D"); domain.addConstant("E"); domain.addPredicate("P"); domain.addPredicate("Q"); domain.addPredicate("W"); domain.addFunction("F"); domain.addFunction("G"); domain.addFunction("H"); domain.addFunction("J"); FOLParser parser = new FOLParser(domain); List <Literal> lits = new List <Literal>(); Predicate p1 = (Predicate)parser.parse("Q(z, G(D,B))"); Predicate p2 = (Predicate)parser.parse("P(x, G(A,C))"); Predicate p3 = (Predicate)parser.parse("W(z,x,u,w,y)"); lits.Add(new Literal(p1)); lits.Add(new Literal(p2)); lits.Add(new Literal(p3)); Clause clExpression = new Clause(lits); TermEquality assertion = (TermEquality)parser.parse("G(x,y) = x"); Clause altClExpression = demodulation.apply(assertion, clExpression); Assert.AreEqual("[P(x,G(A,C)), Q(z,D), W(z,x,u,w,y)]", altClExpression.ToString()); altClExpression = demodulation.apply(assertion, altClExpression); Assert.AreEqual("[P(x,A), Q(z,D), W(z,x,u,w,y)]", altClExpression .ToString()); }
public void testSimpleAtomicExamples() { FOLDomain domain = new FOLDomain(); domain.addConstant("A"); domain.addConstant("B"); domain.addConstant("C"); domain.addConstant("D"); domain.addConstant("E"); domain.addPredicate("P"); domain.addFunction("F"); domain.addFunction("G"); domain.addFunction("H"); domain.addFunction("J"); FOLParser parser = new FOLParser(domain); Predicate expression = (Predicate)parser .parse("P(A,F(B,G(A,H(B)),C),D)"); TermEquality assertion = (TermEquality)parser.parse("B = E"); Predicate altExpression = (Predicate)demodulation.apply(assertion, expression); Assert.IsFalse(expression.Equals(altExpression)); Assert .AreEqual("P(A,F(E,G(A,H(B)),C),D)", altExpression .ToString()); altExpression = (Predicate)demodulation .apply(assertion, altExpression); Assert .AreEqual("P(A,F(E,G(A,H(E)),C),D)", altExpression .ToString()); assertion = (TermEquality)parser.parse("G(x,y) = J(x)"); altExpression = (Predicate)demodulation.apply(assertion, expression); Assert.AreEqual("P(A,F(B,J(A),C),D)", altExpression.ToString()); }
static void fOL_Paramodulation() { System.Console.WriteLine("-------------------"); System.Console.WriteLine("Paramodulation Demo"); System.Console.WriteLine("-------------------"); FOLDomain domain = new FOLDomain(); domain.addConstant("A"); domain.addConstant("B"); domain.addPredicate("P"); domain.addPredicate("Q"); domain.addPredicate("R"); domain.addFunction("F"); FOLParser parser = new FOLParser(domain); ICollection <Literal> lits = CollectionFactory.CreateQueue <Literal>(); AtomicSentence a1 = (AtomicSentence)parser.parse("P(F(x,B),x)"); AtomicSentence a2 = (AtomicSentence)parser.parse("Q(x)"); lits.Add(new Literal(a1)); lits.Add(new Literal(a2)); Clause c1 = new Clause(lits); lits.Clear(); a1 = (AtomicSentence)parser.parse("F(A,y) = y"); a2 = (AtomicSentence)parser.parse("R(y)"); lits.Add(new Literal(a1)); lits.Add(new Literal(a2)); Clause c2 = new Clause(lits); Paramodulation paramodulation = new Paramodulation(); ISet <Clause> paras = paramodulation.apply(c1, c2); System.Console.WriteLine("Paramodulate '" + c1 + "' with '" + c2 + "' to give"); System.Console.WriteLine(paras.ToString()); System.Console.WriteLine(""); }
public void testSimpleExample() { FOLDomain domain = new FOLDomain(); domain.addConstant("A"); domain.addConstant("B"); domain.addPredicate("P"); domain.addPredicate("Q"); domain.addPredicate("R"); domain.addFunction("F"); FOLParser parser = new FOLParser(domain); List <Literal> lits = new List <Literal>(); AtomicSentence a1 = (AtomicSentence)parser.parse("P(F(x,B),x)"); AtomicSentence a2 = (AtomicSentence)parser.parse("Q(x)"); lits.Add(new Literal(a1)); lits.Add(new Literal(a2)); Clause c1 = new Clause(lits); lits.Clear(); a1 = (AtomicSentence)parser.parse("F(A,y) = y"); a2 = (AtomicSentence)parser.parse("R(y)"); lits.Add(new Literal(a1)); lits.Add(new Literal(a2)); Clause c2 = new Clause(lits); List <Clause> paras = paramodulation.apply(c1, c2); Assert.AreEqual(2, paras.Count); foreach (Clause c in paras) { Assert.AreEqual("[P(B,A), Q(A), R(B)]", c.ToString()); Assert.AreEqual("[P(F(A,F(x,B)),x), Q(x), R(F(x,B))]", c .ToString()); } }
public void testSimpleExample() { FOLDomain domain = new FOLDomain(); domain.addConstant("A"); domain.addConstant("B"); domain.addPredicate("P"); domain.addPredicate("Q"); domain.addPredicate("R"); domain.addFunction("F"); FOLParser parser = new FOLParser(domain); ICollection <Literal> lits = CollectionFactory.CreateQueue <Literal>(); AtomicSentence a1 = (AtomicSentence)parser.parse("P(F(x,B),x)"); AtomicSentence a2 = (AtomicSentence)parser.parse("Q(x)"); lits.Add(new Literal(a1)); lits.Add(new Literal(a2)); Clause c1 = new Clause(lits); lits.Clear(); a1 = (AtomicSentence)parser.parse("F(A,y) = y"); a2 = (AtomicSentence)parser.parse("R(y)"); lits.Add(new Literal(a1)); lits.Add(new Literal(a2)); Clause c2 = new Clause(lits); ISet <Clause> paras = paramodulation.apply(c1, c2); Assert.AreEqual(2, paras.Size()); Assert.AreEqual("[P(B,A), Q(A), R(B)]", Util.first(paras).ToString()); paras.Remove(Util.first(paras)); Assert.AreEqual("[P(F(A,F(x,B)),x), Q(x), R(F(x,B))]", Util.first(paras).ToString()); }
public void testNOTSentence() { FOLDomain domain = new FOLDomain(); domain.addConstant("A"); domain.addConstant("B"); domain.addConstant("C"); domain.addFunction("Plus"); domain.addPredicate("P"); FOLParser parser = new FOLParser(domain); Sentence s1 = parser.parse("NOT(P(A))"); Sentence s2 = parser.parse("NOT(P(A))"); IMap <Variable, Term> result = unifier.unify(s1, s2); Assert.IsNotNull(result); Assert.AreEqual(0, result.Size()); s1 = parser.parse("NOT(P(A))"); s2 = parser.parse("NOT(P(B))"); result = unifier.unify(s1, s2); Assert.IsNull(result); s1 = parser.parse("NOT(P(A))"); s2 = parser.parse("NOT(P(x))"); result = unifier.unify(s1, s2); Assert.IsNotNull(result); Assert.AreEqual(1, result.Size()); Assert.AreEqual(new Constant("A"), result.Get(new Variable("x"))); }
public void testEqualityBinaryResolvents() { FOLDomain domain = new FOLDomain(); domain.addConstant("A"); domain.addConstant("B"); FOLParser parser = new FOLParser(domain); // B = A Clause c1 = new Clause(); c1.addPositiveLiteral((AtomicSentence)parser.parse("B = A")); Clause c2 = new Clause(); c2.addNegativeLiteral((AtomicSentence)parser.parse("B = A")); c2.addPositiveLiteral((AtomicSentence)parser.parse("B = A")); ISet <Clause> resolvents = c1.binaryResolvents(c2); Assert.AreEqual(1, resolvents.Size()); Assert.AreEqual("[[B = A]]", resolvents.ToString()); }
public static FOLDomain ringOfThievesDomain() { FOLDomain domain = new FOLDomain(); domain.addPredicate("Parent"); domain.addPredicate("Caught"); domain.addPredicate("Friend"); domain.addPredicate("Skis"); domain.addConstant("Mike"); domain.addConstant("Joe"); domain.addConstant("Janet"); domain.addConstant("Nancy"); domain.addConstant("Ernie"); domain.addConstant("Bert"); domain.addConstant("Red"); domain.addConstant("Drew"); return(domain); }
public void testNegationsAndNestedImplications() { FOLDomain domain = new FOLDomain(); domain.addPredicate("P"); domain.addPredicate("Q"); domain.addPredicate("R"); domain.addConstant("A"); FOLParser parser = new FOLParser(domain); CNFConverter cnfConv = new CNFConverter(parser); // ~(((~p or ~q) => ~(p or q)) => r) Sentence sent = parser .parse("NOT(((((NOT(P(A)) OR NOT(Q(A)))) => NOT((P(A) OR Q(A)))) => R(A)))"); CNF cnf = cnfConv.convertToCNF(sent); Assert.AreEqual( "[~P(A), P(A)],[~P(A), Q(A)],[~Q(A), P(A)],[~Q(A), Q(A)],[~R(A)]", cnf.ToString()); }
public void testIsTautology() { FOLDomain domain = new FOLDomain(); domain.addConstant("A"); domain.addPredicate("P"); domain.addPredicate("Q"); domain.addPredicate("R"); domain.addFunction("F"); FOLParser parser = new FOLParser(domain); // {p(f(a)),~p(f(a))} Clause c = new Clause(); c.addPositiveLiteral((Predicate)parser.parse("P(F(A))")); Assert.IsFalse(c.isTautology()); c.addNegativeLiteral((Predicate)parser.parse("P(F(A))")); Assert.IsTrue(c.isTautology()); // {p(x),q(y),~q(y),r(z)} c = new Clause(); c.addPositiveLiteral((Predicate)parser.parse("P(x)")); Assert.IsFalse(c.isTautology()); c.addPositiveLiteral((Predicate)parser.parse("Q(y)")); Assert.IsFalse(c.isTautology()); c.addNegativeLiteral((Predicate)parser.parse("Q(y)")); Assert.IsTrue(c.isTautology()); c.addPositiveLiteral((Predicate)parser.parse("R(z)")); Assert.IsTrue(c.isTautology()); // {~p(a),p(x)} c = new Clause(); c.addNegativeLiteral((Predicate)parser.parse("P(A)")); Assert.IsFalse(c.isTautology()); c.addPositiveLiteral((Predicate)parser.parse("P(x)")); Assert.IsFalse(c.isTautology()); }
public void testTermEquality() { FOLDomain domain = new FOLDomain(); domain.addPredicate("P"); domain.addPredicate("Q"); domain.addPredicate("R"); domain.addConstant("A"); domain.addConstant("B"); domain.addConstant("C"); domain.addConstant("D"); domain.addFunction("Plus"); domain.addConstant("ONE"); domain.addConstant("ZERO"); FOLParser parser = new FOLParser(domain); CNFConverter cnfConv = new CNFConverter(parser); // x=y Sentence sent = parser.parse("x = y"); CNF cnf = cnfConv.convertToCNF(sent); Assert.AreEqual("[x = y]", cnf.ToString()); // x!=y sent = parser.parse("NOT(x = y)"); cnf = cnfConv.convertToCNF(sent); Assert.AreEqual("[~x = y]", cnf.ToString()); // A=B sent = parser.parse("A = B"); cnf = cnfConv.convertToCNF(sent); Assert.AreEqual("[A = B]", cnf.ToString()); // A!=B sent = parser.parse("NOT(A = B)"); cnf = cnfConv.convertToCNF(sent); Assert.AreEqual("[~A = B]", cnf.ToString()); // ~(((~A=B or ~D=C) => ~(A=B or D=C)) => A=D) sent = parser .parse("NOT(((((NOT(A = B) OR NOT(D = C))) => NOT((A = B OR D = C))) => A = D))"); cnf = cnfConv.convertToCNF(sent); Assert.AreEqual( "[~A = B, A = B],[~A = B, D = C],[~D = C, A = B],[~D = C, D = C],[~A = D]", cnf.ToString()); // // Induction Axiom Schema using Term Equality // Base Case: sent = parser .parse("NOT(FORALL x (FORALL y (Plus(Plus(x,y),ZERO) = Plus(x,Plus(y,ZERO)))))"); cnf = cnfConv.convertToCNF(sent); Assert.AreEqual( "[~Plus(Plus(SC0,SC1),ZERO) = Plus(SC0,Plus(SC1,ZERO))]", cnf.ToString()); // Instance of Induction Axion Scmema sent = parser.parse("((" + "Plus(Plus(A,B),ZERO) = Plus(A,Plus(B,ZERO))" + " AND " + "(FORALL x (FORALL y (FORALL z(" + "Plus(Plus(x,y),z) = Plus(x,Plus(y,z))" + " => " + "Plus(Plus(x,y),Plus(z,ONE)) = Plus(x,Plus(y,Plus(z,ONE)))" + "))))" + ")" + " => " + "FORALL x (FORALL y (FORALL z(" + "Plus(Plus(x,y),z) = Plus(x,Plus(y,z))" + "))))"); cnf = cnfConv.convertToCNF(sent); Assert.AreEqual( "[~Plus(Plus(A,B),ZERO) = Plus(A,Plus(B,ZERO)), Plus(Plus(q0,q1),q2) = Plus(q0,Plus(q1,q2)), Plus(Plus(SC2,SC3),SC4) = Plus(SC2,Plus(SC3,SC4))],[~Plus(Plus(A,B),ZERO) = Plus(A,Plus(B,ZERO)), ~Plus(Plus(SC2,SC3),Plus(SC4,ONE)) = Plus(SC2,Plus(SC3,Plus(SC4,ONE))), Plus(Plus(q0,q1),q2) = Plus(q0,Plus(q1,q2))]", cnf.ToString()); // Goal sent = parser .parse("NOT(FORALL x (FORALL y (FORALL z (Plus(Plus(x,y),z) = Plus(x,Plus(y,z))))))"); cnf = cnfConv.convertToCNF(sent); Assert.AreEqual( "[~Plus(Plus(SC5,SC6),SC7) = Plus(SC5,Plus(SC6,SC7))]", cnf.ToString()); }