// 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());
}
