public Object visitQuantifiedSentence(QuantifiedSentence sentence,
Object arg)
{
Sentence quantified = sentence.getQuantified();
List <Variable> universalScope = (List <Variable>)arg;
// Skolemize: Skolemization is the process of removing existential
// quantifiers by elimination. This is done by introducing Skolem
// functions. The general rule is that the arguments of the Skolem
// function are all the universally quantified variables in whose
// scope the existential quantifier appears.
if (Quantifiers.isEXISTS(sentence.getQuantifier()))
{
Dictionary <Variable, Term> skolemSubst = new Dictionary <Variable, Term>();
foreach (Variable eVar in sentence.getVariables())
{
if (universalScope.Count > 0)
{
// Replace with a Skolem Function
String skolemFunctionName = parser.getFOLDomain()
.addSkolemFunction();
skolemSubst.Add(eVar, new Function(skolemFunctionName,
new List <Term>(universalScope)));
}
else
{
// Replace with a Skolem Constant
String skolemConstantName = parser.getFOLDomain()
.addSkolemConstant();
skolemSubst.Add(eVar, new Constant(skolemConstantName));
}
}
Sentence skolemized = substVisitor.subst(skolemSubst, quantified);
return(skolemized.accept(this, arg));
}
// Drop universal quantifiers.
if (Quantifiers.isFORALL(sentence.getQuantifier()))
{
// Add to the universal scope so that
// existential skolemization may be done correctly
universalScope.AddRange(sentence.getVariables());
Sentence droppedUniversal = (Sentence)quantified.accept(this, arg);
// Enusre my scope is removed before moving back up
// the call stack when returning
foreach (Variable s in sentence.getVariables())
{
universalScope.Remove(s);
}
return(droppedUniversal);
}
// Should not reach here as have already
// handled the two quantifiers.
throw new ApplicationException("Unhandled Quantifier:"
+ sentence.getQuantifier());
}
public Object visitNotSentence(NotSentence notSentence, Object arg)
{
// CNF requires NOT (~) to appear only in literals, so we 'move ~
// inwards' by repeated application of the following equivalences:
Sentence negated = notSentence.getNegated();
// ~(~alpha) equivalent to alpha (double negation elimination)
if (negated is NotSentence)
{
return(((NotSentence)negated).getNegated().accept(this, arg));
}
if (negated is ConnectedSentence)
{
ConnectedSentence negConnected = (ConnectedSentence)negated;
Sentence alpha = negConnected.getFirst();
Sentence beta = negConnected.getSecond();
// ~(alpha ^ beta) equivalent to (~alpha V ~beta) (De Morgan)
if (Connectors.isAND(negConnected.getConnector()))
{
// I need to ensure the ~s are moved in deeper
Sentence notAlpha = (Sentence)(new NotSentence(alpha)).accept(
this, arg);
Sentence notBeta = (Sentence)(new NotSentence(beta)).accept(
this, arg);
return(new ConnectedSentence(Connectors.OR, notAlpha, notBeta));
}
// ~(alpha V beta) equivalent to (~alpha ^ ~beta) (De Morgan)
if (Connectors.isOR(negConnected.getConnector()))
{
// I need to ensure the ~s are moved in deeper
Sentence notAlpha = (Sentence)(new NotSentence(alpha)).accept(
this, arg);
Sentence notBeta = (Sentence)(new NotSentence(beta)).accept(
this, arg);
return(new ConnectedSentence(Connectors.AND, notAlpha, notBeta));
}
}
// in addition, rules for negated quantifiers:
if (negated is QuantifiedSentence)
{
QuantifiedSentence negQuantified = (QuantifiedSentence)negated;
// I need to ensure the ~ is moved in deeper
Sentence notP = (Sentence)(new NotSentence(negQuantified
.getQuantified())).accept(this, arg);
// ~FORALL x p becomes EXISTS x ~p
if (Quantifiers.isFORALL(negQuantified.getQuantifier()))
{
return(new QuantifiedSentence(Quantifiers.EXISTS, negQuantified
.getVariables(), notP));
}
// ~EXISTS x p becomes FORALL x ~p
if (Quantifiers.isEXISTS(negQuantified.getQuantifier()))
{
return(new QuantifiedSentence(Quantifiers.FORALL, negQuantified
.getVariables(), notP));
}
}
return(new NotSentence((Sentence)negated.accept(this, arg)));
}