// 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 static FOLKnowledgeBase createKingsKnowledgeBase(
InferenceProcedure infp)
{
FOLKnowledgeBase kb = new FOLKnowledgeBase(DomainFactory.kingsDomain(),
infp);
kb.tell("((King(x) AND Greedy(x)) => Evil(x))");
kb.tell("King(John)");
kb.tell("King(Richard)");
kb.tell("Greedy(John)");
return kb;
}
public static FOLKnowledgeBase createKingsKnowledgeBase(
InferenceProcedure infp)
{
FOLKnowledgeBase kb = new FOLKnowledgeBase(DomainFactory.kingsDomain(),
infp);
kb.tell("((King(x) AND Greedy(x)) => Evil(x))");
kb.tell("King(John)");
kb.tell("King(Richard)");
kb.tell("Greedy(John)");
return(kb);
}
public static FOLKnowledgeBase createWeaponsKnowledgeBase(
InferenceProcedure infp)
{
FOLKnowledgeBase kb = new FOLKnowledgeBase(DomainFactory
.weaponsDomain(), infp);
kb
.tell("( (((American(x) AND Weapon(y)) AND Sells(x,y,z)) AND Hostile(z)) => Criminal(x))");
kb.tell(" Owns(Nono, M1)");
kb.tell(" Missile(M1)");
kb.tell("((Missile(x) AND Owns(Nono,x)) => Sells(West,x,Nono))");
kb.tell("(Missile(x) => Weapon(x))");
kb.tell("(Enemy(x,America) => Hostile(x))");
kb.tell("American(West)");
kb.tell("Enemy(Nono,America)");
return kb;
}
// 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 static FOLKnowledgeBase createWeaponsKnowledgeBase(
InferenceProcedure infp)
{
FOLKnowledgeBase kb = new FOLKnowledgeBase(DomainFactory
.weaponsDomain(), infp);
kb
.tell("( (((American(x) AND Weapon(y)) AND Sells(x,y,z)) AND Hostile(z)) => Criminal(x))");
kb.tell(" Owns(Nono, M1)");
kb.tell(" Missile(M1)");
kb.tell("((Missile(x) AND Owns(Nono,x)) => Sells(West,x,Nono))");
kb.tell("(Missile(x) => Weapon(x))");
kb.tell("(Enemy(x,America) => Hostile(x))");
kb.tell("American(West)");
kb.tell("Enemy(Nono,America)");
return(kb);
}
public static FOLKnowledgeBase createRingOfThievesKnowledgeBase(
InferenceProcedure infp)
{
FOLKnowledgeBase kb = new FOLKnowledgeBase(DomainFactory
.ringOfThievesDomain(), infp);
// s(x) => ~c(x) One who skis never gets caught
kb.tell("(Skis(x) => NOT(Caught(x)))");
// c(x) => ~s(x) Those who are caught don't ever ski
kb.tell("(Caught(x) => NOT(Skis(x)))");
// p(x,y) & c(y) => s(x) Jailbird parents have skiing kids
kb.tell("((Parent(x,y) AND Caught(y)) => Skis(x))");
// s(x) & f(x,y) => s(y) All friends ski together
kb.tell("(Skis(x) AND Friend(x,y) => Skis(y))");
// f(x,y) => f(y,x) Friendship is symmetric
kb.tell("(Friend(x,y) => Friend(y,x))");
// FACTS
// 1. { p(Mike,Joe) } Premise
kb.tell("Parent(Mike, Joe)");
// 2. { p(Janet,Joe) } Premise
kb.tell("Parent(Janet,Joe)");
// 3. { p(Nancy,Mike) } Premise
kb.tell("Parent(Nancy,Mike)");
// 4. { p(Ernie,Janet) } Premise
kb.tell("Parent(Ernie,Janet)");
// 5. { p(Bert,Nancy) } Premise
kb.tell("Parent(Bert,Nancy)");
// 6. { p(Red,Ernie) } Premise
kb.tell("Parent(Red,Ernie)");
// 7. { f(Red,Bert) } Premise
kb.tell("Friend(Red,Bert)");
// 8. { f(Drew,Nancy) } Premise
kb.tell("Friend(Drew,Nancy)");
// 9. { c(Mike) } Premise
kb.tell("Caught(Mike)");
// 10. { c(Ernie) } Premise
kb.tell("Caught(Ernie)");
return kb;
}
public static FOLKnowledgeBase createLovesAnimalKnowledgeBase(
InferenceProcedure infp)
{
FOLKnowledgeBase kb = new FOLKnowledgeBase(DomainFactory
.lovesAnimalDomain(), infp);
kb
.tell("FORALL x (FORALL y (Animal(y) => Loves(x, y)) => EXISTS y Loves(y, x))");
kb
.tell("FORALL x (EXISTS y (Animal(y) AND Kills(x, y)) => FORALL z NOT(Loves(z, x)))");
kb.tell("FORALL x (Animal(x) => Loves(Jack, x))");
kb.tell("(Kills(Jack, Tuna) OR Kills(Curiosity, Tuna))");
kb.tell("Cat(Tuna)");
kb.tell("FORALL x (Cat(x) => Animal(x))");
return kb;
}
public static FOLKnowledgeBase createLovesAnimalKnowledgeBase(
InferenceProcedure infp)
{
FOLKnowledgeBase kb = new FOLKnowledgeBase(DomainFactory
.lovesAnimalDomain(), infp);
kb
.tell("FORALL x (FORALL y (Animal(y) => Loves(x, y)) => EXISTS y Loves(y, x))");
kb
.tell("FORALL x (EXISTS y (Animal(y) AND Kills(x, y)) => FORALL z NOT(Loves(z, x)))");
kb.tell("FORALL x (Animal(x) => Loves(Jack, x))");
kb.tell("(Kills(Jack, Tuna) OR Kills(Curiosity, Tuna))");
kb.tell("Cat(Tuna)");
kb.tell("FORALL x (Cat(x) => Animal(x))");
return(kb);
}
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);
}
// 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;
}
// 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 static FOLKnowledgeBase createRingOfThievesKnowledgeBase(
InferenceProcedure infp)
{
FOLKnowledgeBase kb = new FOLKnowledgeBase(DomainFactory
.ringOfThievesDomain(), infp);
// s(x) => ~c(x) One who skis never gets caught
kb.tell("(Skis(x) => NOT(Caught(x)))");
// c(x) => ~s(x) Those who are caught don't ever ski
kb.tell("(Caught(x) => NOT(Skis(x)))");
// p(x,y) & c(y) => s(x) Jailbird parents have skiing kids
kb.tell("((Parent(x,y) AND Caught(y)) => Skis(x))");
// s(x) & f(x,y) => s(y) All friends ski together
kb.tell("(Skis(x) AND Friend(x,y) => Skis(y))");
// f(x,y) => f(y,x) Friendship is symmetric
kb.tell("(Friend(x,y) => Friend(y,x))");
// FACTS
// 1. { p(Mike,Joe) } Premise
kb.tell("Parent(Mike, Joe)");
// 2. { p(Janet,Joe) } Premise
kb.tell("Parent(Janet,Joe)");
// 3. { p(Nancy,Mike) } Premise
kb.tell("Parent(Nancy,Mike)");
// 4. { p(Ernie,Janet) } Premise
kb.tell("Parent(Ernie,Janet)");
// 5. { p(Bert,Nancy) } Premise
kb.tell("Parent(Bert,Nancy)");
// 6. { p(Red,Ernie) } Premise
kb.tell("Parent(Red,Ernie)");
// 7. { f(Red,Bert) } Premise
kb.tell("Friend(Red,Bert)");
// 8. { f(Drew,Nancy) } Premise
kb.tell("Friend(Drew,Nancy)");
// 9. { c(Mike) } Premise
kb.tell("Caught(Mike)");
// 10. { c(Ernie) } Premise
kb.tell("Caught(Ernie)");
return(kb);
}
//
// START-InferenceProcedure
/**
* <code>
* 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
* </code>
*/
public InferenceResult ask(FOLKnowledgeBase KB, Sentence query)
{
// Assertions on the type of queries this Inference procedure
// supports
if (!(query is AtomicSentence))
{
throw new ArgumentException(
"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<Literal> newSentences = new List<Literal>();
// Ensure query is not already a know fact before
// attempting forward chaining.
List<Dictionary<Variable, Term>> answers = KB.fetch(alpha);
if (answers.Count > 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)
foreach (Clause impl in KB.getAllDefiniteClauseImplications())
{
Clause impl2 = 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
foreach (Dictionary<Variable, Term> theta in KB.fetch(invert(new List<Literal>(impl2
.getNegativeLiterals()))))
{
// q' <- SUBST(theta, q)
Literal qPrime = KB.subst(theta, impl.getPositiveLiterals()
[0]);
// if q' does not unify with some sentence already in KB or
// new then do
if (!KB.isRenaming(qPrime)
&& !KB.isRenaming(qPrime, newSentences))
{
// add q' to new
newSentences.Add(qPrime);
ansHandler.addProofStep(impl, qPrime, theta);
// theta <- UNIFY(q', alpha)
Dictionary<Variable, Term> theta2 = KB.unify(qPrime.getAtomicSentence(), alpha
.getAtomicSentence());
// if theta is not fail then return theta
if (null != theta2)
{
foreach (Literal l in 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
foreach (Literal l in newSentences)
{
Sentence s = null;
if (l.isPositiveLiteral())
{
s = l.getAtomicSentence();
}
else
{
s = new NotSentence(l.getAtomicSentence());
}
KB.tell(s);
}
} while (newSentences.Count > 0);
// return false
return ansHandler;
}
public void testBinaryResolventsOrderDoesNotMatter()
{
// This is a regression test, to ensure
// the ordering of resolvents does not matter.
// If the order ends up mattering, then likely
// a problem was introduced in the Clause class
// unifier, or related class.
// Set up the initial set of clauses based on the
// loves animal domain as it contains functions
// new clauses will always be created (i.e. is an
// infinite universe of discourse).
FOLKnowledgeBase kb = new FOLKnowledgeBase(DomainFactory
.lovesAnimalDomain());
kb
.tell("FORALL x (FORALL y (Animal(y) => Loves(x, y)) => EXISTS y Loves(y, x))");
kb
.tell("FORALL x (EXISTS y (Animal(y) AND Kills(x, y)) => FORALL z NOT(Loves(z, x)))");
kb.tell("FORALL x (Animal(x) => Loves(Jack, x))");
kb.tell("(Kills(Jack, Tuna) OR Kills(Curiosity, Tuna))");
kb.tell("Cat(Tuna)");
kb.tell("FORALL x (Cat(x) => Animal(x))");
List<Clause> clauses = new List<Clause>();
clauses.AddRange(kb.getAllClauses());
List<Clause> newClauses = new List<Clause>();
long maxRunTime = 30 * 1000; // 30 seconds
long finishTime = System.DateTime.UtcNow.Ticks + maxRunTime;
do
{
clauses.AddRange(newClauses);
newClauses.Clear();
Clause[] clausesA = new Clause[clauses.Count];
clauses.CopyTo(clausesA);
for (int i = 0; i < clausesA.Length; i++)
{
Clause cI = clausesA[i];
for (int j = 0; j < clausesA.Length; j++)
{
Clause cJ = clausesA[j];
newClauses.AddRange(cI.getFactors());
newClauses.AddRange(cJ.getFactors());
List<Clause> cIresolvents = cI.binaryResolvents(cJ);
List<Clause> cJresolvents = cJ.binaryResolvents(cI);
if (!cIresolvents.Equals(cJresolvents))
{
System.Console.WriteLine("cI=" + cI);
System.Console.WriteLine("cJ=" + cJ);
System.Console.WriteLine("cIR=" + cIresolvents);
System.Console.WriteLine("cJR=" + cJresolvents);
Assert
.Fail("Ordering of binary resolvents has become usingant, which should not be the case");
}
foreach (Clause r in cIresolvents)
{
newClauses.AddRange(r.getFactors());
}
if (System.DateTime.UtcNow.Ticks > finishTime)
{
break;
}
}
if (System.DateTime.UtcNow.Ticks > finishTime)
{
break;
}
}
} while (System.DateTime.UtcNow.Ticks < finishTime);
}
