public Sentence GetNegation()
{
Sentence negated = new Sentence();
for (int i = 0; i < Clauses.Count; i++)
{
Clause currentClause = Clauses[i];
if (Clauses.Count > 1)
{
for (int j = i + 1; j < Clauses.Count; j++)
{
Clause nextClause = Clauses[j];
foreach (Literal lit1 in currentClause.Literals)
{
foreach (Literal lit2 in nextClause.Literals)
{
Clause clause = new Clause();
clause.AddLiteral(lit1.GetNegation());
clause.AddLiteral(lit2.GetNegation());
negated.AddClause(clause);
}
}
}
}
else
{
negated = currentClause.GetNegation();
}
}
return negated;
}
public static bool PlResolution(Sentence premises, Sentence conclusion)
{
List<Clause> clauses = premises.Clauses.Union(conclusion.GetNegation().Clauses).ToList();
List<Clause> newc = new List<Clause>();
while (true)
{
foreach (Clause ci in clauses)
{
List<Clause> restClauses = new List<Clause>(clauses);
restClauses.Remove(ci);
foreach (Clause cj in restClauses)
{
List<Clause> resolvents = PlResolve(ci, cj);
if (resolvents.All(x => x.IsEmpty()))
{
return true;
}
newc.U(resolvents);
}
}
if (newc.IsSubsetOf(clauses))
return false;
clauses.U(newc);
}
}
public void SentenceNegationTest()
{
Clause a = new Clause();
a.AddLiteral(new Literal("~", "A"));
a.AddLiteral(new Literal("", "B"));
a.AddLiteral(new Literal("~", "C"));
Clause b = new Clause();
b.AddLiteral(new Literal("", "C"));
b.AddLiteral(new Literal("", "D"));
b.AddLiteral(new Literal("", "E"));
Sentence s = new Sentence();
s.AddClause(a);
s.AddClause(b);
/*
s is now ( ~A v B v ~C ) ^ ( C v D v E )
NEGATE IT ~ ( ( ~A v B v ~C ) ^ ( C v D v E ) )
DeMorgan's gives us ~ ( ~A v B v ~C ) v ~ ( C v D v E )
DeMorgan's again ( A ^ ~B ^ C ) v (~C ^ ~D ^ ~E )
Expected result is thus:
( A v ~C ) ^ ( A v ~D ) ^ ( A v ~E ) ^ ( ~B v ~C ) ^ ( ~B v ~D ) ^ ( ~B v ~E ) ^ ( C v ~C ) ^ ( C v ~D ) ^ ( C v ~E )
*/
string expected =
"( A v ~C ) ^ ( A v ~D ) ^ ( A v ~E ) ^ ( ~B v ~C ) ^ ( ~B v ~D ) ^ ( ~B v ~E ) ^ ( C v ~C ) ^ ( C v ~D ) ^ ( C v ~E )";
Assert.AreEqual(expected, s.GetNegation().ToString(), "Negation result is incorrect");
}
public Sentence GetNegation()
{
Sentence negation = new Sentence();
foreach (Literal literal in Literals)
{
Clause negClause = new Clause();
negClause.AddLiteral(literal.GetNegation());
negation.AddClause(negClause);
}
return negation;
}
public void PlResolutionTest2()
{
Sentence premises = new Sentence();
Clause tempClause = new Clause();
tempClause.AddLiteral(new Literal("","A"));
premises.AddClause(tempClause);
Sentence conclusion = new Sentence();
conclusion.AddClause(tempClause);
bool canResolve = TheoremProver.PlResolution(premises, conclusion);
Assert.AreEqual(true, canResolve, "Resolution should be possible");
}
public void SentenceListTest()
{
Sentence s = new Sentence();
Clause a = new Clause();
a.AddLiteral(new Literal("~", "A"));
a.AddLiteral(new Literal("", "B"));
Clause b = new Clause();
b.AddLiteral(new Literal("","C"));
b.AddLiteral(new Literal("","D"));
s.AddClause(a);
s.AddClause(b);
Assert.AreEqual(s.Clauses[0].ToString(), "( ~A v B )", "First Clause incorrect");
Assert.AreEqual(s.Clauses[1].ToString(), "( C v D )", "Second Clause incorrect");
}
public static Sentence ExtractSentence(string input)
{
Sentence result = new Sentence();
foreach (Clause clause in ExtractClauses(input))
{
result.AddClause(clause);
}
return result;
}
public static void resolutionTest2()
{
Console.WriteLine("******************** start resolutionTest2 ********************");
Sentence premises = new Sentence();
Clause tempClause = new Clause();
Literal tempLiteral = new Literal("", "A");
tempClause.AddLiteral(tempLiteral);
tempLiteral = new Literal("~", "B");
tempClause.AddLiteral(tempLiteral);
premises.AddClause(tempClause);
tempClause = new Clause();
tempLiteral = new Literal("", "B");
tempClause.AddLiteral(tempLiteral);
tempLiteral = new Literal("~", "D");
tempClause.AddLiteral(tempLiteral);
premises.AddClause(tempClause);
tempClause = new Clause();
tempLiteral = new Literal("", "E");
tempClause.AddLiteral(tempLiteral);
tempLiteral = new Literal("~", "F");
tempClause.AddLiteral(tempLiteral);
tempLiteral = new Literal("~", "A");
tempClause.AddLiteral(tempLiteral);
premises.AddClause(tempClause);
//Console.WriteLine("premises\n"+premises);
///////////////
////////////
/////////////////
Sentence conclusion = new Sentence();
tempClause = new Clause();
tempLiteral = new Literal("", "C");
tempClause.AddLiteral(tempLiteral);
conclusion.AddClause(tempClause);
tempClause = new Clause();
tempLiteral = new Literal("~", "X");
tempClause.AddLiteral(tempLiteral);
conclusion.AddClause(tempClause);
Console.WriteLine("**** premises " + premises);
Console.WriteLine("***** conclusion " + conclusion);
bool canResolve = TheoremProver.PlResolution(premises, conclusion);
Console.WriteLine("canResolve " + canResolve);
Console.WriteLine("******************** end resolutionTest2 ********************");
}
public static void basicTests()
{
Console.WriteLine("******************** start basicTests ********************");
Sentence theSentence = new Sentence();
Clause tempClause = new Clause();
Literal tempLiteral = new Literal("", "A");
Console.WriteLine("tempLiteral (should be 'A')\n" + tempLiteral);
tempClause.AddLiteral(tempLiteral);
tempLiteral = new Literal("~", "B");
Console.WriteLine("tempLiteral (should be '~B')\n" + tempLiteral);
tempClause.AddLiteral(tempLiteral);
Console.WriteLine("tempClause (should be '( A v ~B )')\n" + tempClause);
theSentence.AddClause(tempClause);
Console.WriteLine("theSentence (should be '( A v ~B )')\n" + theSentence);
tempClause = new Clause();
tempLiteral = new Literal("", "B");
tempClause.AddLiteral(tempLiteral);
tempLiteral = new Literal("~", "D");
tempClause.AddLiteral(tempLiteral);
theSentence.AddClause(tempClause);
Console.WriteLine("theSentence (should be '( A v ~B ) ^ ( B v ~D )'\n" + theSentence);
tempClause = new Clause();
tempLiteral = new Literal("", "E");
tempClause.AddLiteral(tempLiteral);
tempLiteral = new Literal("~", "F");
tempClause.AddLiteral(tempLiteral);
tempLiteral = new Literal("~", "A");
tempClause.AddLiteral(tempLiteral);
theSentence.AddClause(tempClause);
Console.WriteLine("theSentence (should be '( A v ~B ) ^ ( B v ~D ) ^ ( E v ~F v ~A )'\n" + theSentence);
tempLiteral = new Literal("", "A");
Console.WriteLine("tempLiteral (should be 'A')\n" + tempLiteral);
tempLiteral = tempLiteral.GetNegation();
Console.WriteLine("negation of tempLiteral (should be '~A')\n" + tempLiteral);
tempLiteral = tempLiteral.GetNegation();
Console.WriteLine("negation of negation of tempLiteral (should be 'A')\n" + tempLiteral);
tempClause = new Clause();
tempClause.AddLiteral(tempLiteral);
tempLiteral = new Literal("", "B");
tempClause.AddLiteral(tempLiteral);
Console.WriteLine("tempClause (should be '( A v B )'\n" + tempClause);
Sentence negatedTempClause = tempClause.GetNegation();
Console.WriteLine("negatedTempClause (should be '( ~A ) ^ ( ~B )'\n" + negatedTempClause);
Sentence negatedSentence = negatedTempClause.GetNegation();
Console.WriteLine("negatedSentence (should be '( A v B )'\n" + tempClause);
Console.WriteLine("=======");
Console.WriteLine("=======");
Sentence testerSentence = new Sentence();
tempClause = new Clause();
tempLiteral = new Literal("~", "A");
tempClause.AddLiteral(tempLiteral);
tempLiteral = new Literal("", "B");
tempClause.AddLiteral(tempLiteral);
tempLiteral = new Literal("~", "C");
tempClause.AddLiteral(tempLiteral);
Console.WriteLine("tempClause (should be '( ~A v B v ~C )'\n" + tempClause);
testerSentence.AddClause(tempClause);
Console.WriteLine("testerSentence (should be '( ~A v B v ~C )'\n" + testerSentence);
tempClause = new Clause();
tempLiteral = new Literal("", "C");
tempClause.AddLiteral(tempLiteral);
tempLiteral = new Literal("", "D");
tempClause.AddLiteral(tempLiteral);
tempLiteral = new Literal("", "E");
tempClause.AddLiteral(tempLiteral);
Console.WriteLine("tempClause (should be '( C v D v E )'\n" + tempClause);
testerSentence.AddClause(tempClause);
Console.WriteLine("testerSentence (should be '( ~A v B v ~C ) ^ ( C v D v E )'\n" + testerSentence);
//WE START WITH ( ~A v B v ~C ) ^ ( C v D v E )
//NEGATE IT ~ ( ( ~A v B v ~C ) ^ ( C v D v E ) )
//DeMorgan's gives us ~ ( ~A v B v ~C ) v ~ ( C v D v E )
//DeMorgan's again ( A ^ ~B ^ C ) v (~C ^ ~D ^ ~E )
//now do distribution to arrive at CNF
/// ( A v ~C) ^ ( A v ~D ) ^ ( A v ~E ) ^ ( ~B v ~C ) ^ ( ~B v ~D ) ^ ( ~B v ~E ) ^ ( C v ~C ) ^ ( C v ~D ) ^ ( C v ~E )
Sentence negatedTesterSentence = testerSentence.GetNegation();
Console.WriteLine("negatedTesterSentence (should be '( A v ~C ) ^ ( A v ~D ) ^ ( A v ~E ) ^ ( ~B v ~C ) ^ ( ~B v ~D ) ^ ( ~B v ~E ) ^ ( C v ~C ) ^ ( C v ~D ) ^ ( C v ~E ) \n" +
" '\n" + negatedTesterSentence);
Console.WriteLine("******************** end basicTests ********************");
}
