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)));
}
public object visitConnectedSentence(ConnectedSentence sentence, object arg)
{
// Distribute V over ^:
// This will cause flattening out of nested ^s and Vs
Sentence alpha = (Sentence)sentence.getFirst().accept(this, arg);
Sentence beta = (Sentence)sentence.getSecond().accept(this, arg);
// (alpha V (beta ^ gamma)) equivalent to
// ((alpha V beta) ^ (alpha V gamma))
if (Connectors.isOR(sentence.getConnector()) &&
beta is ConnectedSentence)
{
ConnectedSentence betaAndGamma = (ConnectedSentence)beta;
if (Connectors.isAND(betaAndGamma.getConnector()))
{
beta = betaAndGamma.getFirst();
Sentence gamma = betaAndGamma.getSecond();
return(new ConnectedSentence(Connectors.AND,
(Sentence)(new ConnectedSentence(Connectors.OR, alpha, beta)).accept(this, arg),
(Sentence)(new ConnectedSentence(Connectors.OR, alpha, gamma)).accept(this, arg)));
}
}
// ((alpha ^ gamma) V beta) equivalent to
// ((alpha V beta) ^ (gamma V beta))
if (Connectors.isOR(sentence.getConnector()) &&
alpha is ConnectedSentence)
{
ConnectedSentence alphaAndGamma = (ConnectedSentence)alpha;
if (Connectors.isAND(alphaAndGamma.getConnector()))
{
alpha = alphaAndGamma.getFirst();
Sentence gamma = alphaAndGamma.getSecond();
return(new ConnectedSentence(Connectors.AND,
(Sentence)(new ConnectedSentence(Connectors.OR, alpha,
beta)).accept(this, arg),
(Sentence)(new ConnectedSentence(Connectors.OR, gamma,
beta)).accept(this, arg)));
}
}
return(new ConnectedSentence(sentence.getConnector(), alpha, beta));
}