// 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 testCascadedOccursCheck()
{
FOLDomain domain = new FOLDomain();
domain.addPredicate("P");
domain.addFunction("F");
domain.addFunction("SF0");
domain.addFunction("SF1");
FOLParser parser = new FOLParser(domain);
Sentence s1 = parser.parse("P(SF1(v2),v2)");
Sentence s2 = parser.parse("P(v3,SF0(v3))");
IMap <Variable, Term> result = unifier.unify(s1, s2);
Assert.IsNull(result);
s1 = parser.parse("P(v1,SF0(v1),SF0(v1),SF0(v1),SF0(v1))");
s2 = parser.parse("P(v2,SF0(v2),v2, v3, v2)");
result = unifier.unify(s1, s2);
Assert.IsNull(result);
s1 = parser
.parse("P(v1, F(v2),F(v2),F(v2),v1, F(F(v1)),F(F(F(v1))),v2)");
s2 = parser
.parse("P(F(v3),v4, v5, v6, F(F(v5)),v4, F(v3), F(F(v5)))");
result = unifier.unify(s1, s2);
Assert.IsNull(result);
}
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 setUp()
{
FOLDomain domain = DomainFactory.crusadesDomain();
lexer = new FOLLexer(domain);
parser = new FOLParser(lexer);
}
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 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 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 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 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 void testImplicationsAndExtendedAndsOrs()
{
FOLDomain domain = new FOLDomain();
domain.addPredicate("Cheat");
domain.addPredicate("Extra");
domain.addPredicate("Knows");
domain.addPredicate("Diff");
domain.addPredicate("F");
domain.addPredicate("A");
domain.addPredicate("Probation");
domain.addPredicate("Award");
FOLParser parser = new FOLParser(domain);
CNFConverter cnfConv = new CNFConverter(parser);
// cheat(x,y) => f(x,y)
Sentence def1 = parser.parse("(Cheat(x,y) => F(x,y))");
CNF cnfDef1 = cnfConv.convertToCNF(def1);
Assert.AreEqual("[~Cheat(x,y), F(x,y)]", cnfDef1.ToString());
// extra(x,y) | knows(x) => a(x,y)
Sentence def2 = parser.parse("((Extra(x,y) OR Knows(x)) => A(x,y))");
CNF cnfDef2 = cnfConv.convertToCNF(def2);
Assert.AreEqual("[~Extra(x,y), A(x,y)],[~Knows(x), A(x,y)]",
cnfDef2.ToString());
// f(x,y) & f(x,z) & diff(y,z) <=> probation(x)
Sentence def3 = parser
.parse("(((NOT(((F(x,y) AND F(x,z)) AND Diff(y,z)))) OR Probation(x)) AND (((F(x,y) AND F(x,z)) AND Diff(y,z)) OR NOT(Probation(x))))");
CNF cnfDef3 = cnfConv.convertToCNF(def3);
Assert
.AreEqual(
"[~Diff(y,z), ~F(x,y), ~F(x,z), Probation(x)],[~Probation(x), F(x,y)],[~Probation(x), F(x,z)],[~Probation(x), Diff(y,z)]",
cnfDef3.ToString());
// a(x,y) & a(x,z) & diff(y,z) <=> award(x)
Sentence def4 = parser
.parse("(((NOT(((A(x,y) AND A(x,z)) AND Diff(y,z)))) OR Award(x)) AND (((A(x,y) AND A(x,z)) AND Diff(y,z)) OR NOT(Award(x))))");
CNF cnfDef4 = cnfConv.convertToCNF(def4);
Assert
.AreEqual(
"[~A(x,y), ~A(x,z), ~Diff(y,z), Award(x)],[~Award(x), A(x,y)],[~Award(x), A(x,z)],[~Award(x), Diff(y,z)]",
cnfDef4.ToString());
// f(x,y) <=> ~a(x,y)
Sentence def5 = parser
.parse("( ( NOT(F(x,y)) OR NOT(A(x,y))) AND ( F(x,y) OR NOT(NOT(A(x,y))) ) )");
CNF cnfDef5 = cnfConv.convertToCNF(def5);
Assert.AreEqual("[~A(x,y), ~F(x,y)],[A(x,y), F(x,y)]", cnfDef5
.ToString());
}
public void testNestedExistsAndOrs()
{
FOLDomain domain = new FOLDomain();
domain.addPredicate("P");
domain.addPredicate("R");
domain.addPredicate("Q");
FOLParser parser = new FOLParser(domain);
Sentence origSentence = parser
.parse("EXISTS w (FORALL x ( (EXISTS z (Q(w, z))) => (EXISTS y (NOT(P(x, y)) AND R(y))) ) )");
CNFConverter cnfConv = new CNFConverter(parser);
CNF cnf = cnfConv.convertToCNF(origSentence);
Assert.AreEqual("[~P(x,SF0(x)), ~Q(SC0,z)],[~Q(SC0,z), R(SF0(x))]",
cnf.ToString());
// Ax.Ay.(p(x,y) => Ez.(q(x,y,z)))
origSentence = parser
.parse("FORALL x1 (FORALL y1 (P(x1, y1) => EXISTS z1 (Q(x1, y1, z1))))");
cnf = cnfConv.convertToCNF(origSentence);
Assert.AreEqual("[~P(x1,y1), Q(x1,y1,SF1(x1,y1))]", cnf.ToString());
// Ex.Ay.Az.(r(y,z) <=> q(x,y,z))
origSentence = parser
.parse("EXISTS x2 (FORALL y2 (FORALL z2 (R(y2, z2) <=> Q(x2, y2, z2))))");
cnf = cnfConv.convertToCNF(origSentence);
Assert.AreEqual(
"[~R(y2,z2), Q(SC1,y2,z2)],[~Q(SC1,y2,z2), R(y2,z2)]", cnf
.ToString());
// Ax.Ey.(~p(x,y) => Az.(q(x,y,z)))
origSentence = parser
.parse("FORALL x3 (EXISTS y3 (NOT(P(x3, y3)) => FORALL z3 (Q(x3, y3, z3))))");
cnf = cnfConv.convertToCNF(origSentence);
Assert
.AreEqual("[P(x3,SF2(x3)), Q(x3,SF2(x3),z3)]", cnf
.ToString());
// Ew.Ex.Ey.Ez.(r(x,y) & q(x,w,z))
origSentence = parser
.parse("NOT(EXISTS w4 (EXISTS x4 (EXISTS y4 ( EXISTS z4 (R(x4, y4) AND Q(x4, w4, z4))))))");
cnf = cnfConv.convertToCNF(origSentence);
Assert.AreEqual("[~Q(x4,w4,z4), ~R(x4,y4)]", cnf.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 FOLKnowledgeBase(FOLDomain domain, InferenceProcedure inferenceProcedure, Unifier unifier)
{
this.parser = new FOLParser(new FOLDomain(domain));
this.inferenceProcedure = inferenceProcedure;
this.unifier = unifier;
//
this.substVisitor = new SubstVisitor();
this.variableCollector = new VariableCollector();
this._standardizeApart = new StandardizeApart(variableCollector, substVisitor);
this.cnfConverter = new CNFConverter(parser);
}
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 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 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 FOLLexer(FOLDomain domain)
{
this.domain = domain;
connectors = new HashSet <String>();
connectors.Add(Connectors.NOT);
connectors.Add(Connectors.AND);
connectors.Add(Connectors.OR);
connectors.Add(Connectors.IMPLIES);
connectors.Add(Connectors.BICOND);
quantifiers = new HashSet <String>();
quantifiers.Add(Quantifiers.FORALL);
quantifiers.Add(Quantifiers.EXISTS);
}
public FOLLexer(FOLDomain domain)
{
this.domain = domain;
connectors = CollectionFactory.CreateSet <string>();
connectors.Add(Connectors.NOT);
connectors.Add(Connectors.AND);
connectors.Add(Connectors.OR);
connectors.Add(Connectors.IMPLIES);
connectors.Add(Connectors.BICOND);
quantifiers = CollectionFactory.CreateSet <string>();
quantifiers.Add(Quantifiers.FORALL);
quantifiers.Add(Quantifiers.EXISTS);
}
public FOLLexer(FOLDomain domain)
{
this.Domain = domain;
connectors = new HashedSet <string>();
connectors.Add(Connectors.Not);
connectors.Add(Connectors.And);
connectors.Add(Connectors.Or);
connectors.Add(Connectors.Implies);
connectors.Add(Connectors.BiCond);
quantifiers = new HashedSet <string>();
quantifiers.Add(Quantifiers.ForAll);
quantifiers.Add(Quantifiers.Exists);
}
public void testExamplePg295AIMA2e()
{
FOLDomain domain = DomainFactory.weaponsDomain();
FOLParser parser = new FOLParser(domain);
Sentence origSentence = parser
.parse("FORALL x ((((American(x) AND Weapon(y)) AND Sells(x, y, z)) AND Hostile(z)) => Criminal(x))");
CNFConverter cnfConv = new CNFConverter(parser);
CNF cnf = cnfConv.convertToCNF(origSentence);
Assert.AreEqual(
"[~American(x), ~Hostile(z), ~Sells(x,y,z), ~Weapon(y), Criminal(x)]",
cnf.ToString());
}
public void testExamplePg296AIMA2e()
{
FOLDomain domain = DomainFactory.lovesAnimalDomain();
FOLParser parser = new FOLParser(domain);
Sentence origSentence = parser
.parse("FORALL x (FORALL y (Animal(y) => Loves(x, y)) => EXISTS y Loves(y, x))");
CNFConverter cnfConv = new CNFConverter(parser);
CNF cnf = cnfConv.convertToCNF(origSentence);
Assert.AreEqual(
"[Animal(SF0(x)), Loves(SF1(x),x)],[~Loves(x,SF0(x)), Loves(SF1(x),x)]",
cnf.ToString());
}
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 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);
}
static void fOL_CNFConversion()
{
System.Console.WriteLine("-------------------------------------------------");
System.Console.WriteLine("Conjuctive Normal Form for First Order Logic Demo");
System.Console.WriteLine("-------------------------------------------------");
FOLDomain domain = DomainFactory.lovesAnimalDomain();
FOLParser parser = new FOLParser(domain);
Sentence origSentence = parser.parse("FORALL x (FORALL y (Animal(y) => Loves(x, y)) => EXISTS y Loves(y, x))");
CNFConverter cnfConv = new CNFConverter(parser);
CNF cnf = cnfConv.convertToCNF(origSentence);
System.Console.WriteLine("Convert '" + origSentence + "' to CNF.");
System.Console.WriteLine("CNF=" + cnf.ToString());
System.Console.WriteLine("");
}
