private void calculateFactors(List <Clause> parentFactors)
{
nonTrivialFactors = new List <Clause>();
Dictionary <Variable, Term> theta = new Dictionary <Variable, Term>();
List <Literal> lits = new List <Literal>();
for (int i = 0; i < 2; i++)
{
lits.Clear();
if (i == 0)
{
// Look at the positive literals
lits.AddRange(positiveLiterals);
}
else
{
// Look at the negative literals
lits.AddRange(negativeLiterals);
}
for (int x = 0; x < lits.Count; x++)
{
for (int y = x + 1; y < lits.Count; y++)
{
Literal litX = lits[x];
Literal litY = lits[y];
theta.Clear();
Dictionary <Variable, Term> substitution = _unifier.unify(litX
.getAtomicSentence(), litY.getAtomicSentence(),
theta);
if (null != substitution)
{
List <Literal> posLits = new List <Literal>();
List <Literal> negLits = new List <Literal>();
if (i == 0)
{
posLits
.Add(_substVisitor
.subst(substitution, litX));
}
else
{
negLits
.Add(_substVisitor
.subst(substitution, litX));
}
foreach (Literal pl in positiveLiterals)
{
if (pl == litX || pl == litY)
{
continue;
}
posLits.Add(_substVisitor.subst(substitution, pl));
}
foreach (Literal nl in negativeLiterals)
{
if (nl == litX || nl == litY)
{
continue;
}
negLits.Add(_substVisitor.subst(substitution, nl));
}
// Ensure the non trivial factor is standardized apart
_standardizeApart.standardizeApart(posLits, negLits,
_saIndexical);
Clause c = new Clause(posLits, negLits);
c.setProofStep(new ProofStepClauseFactor(c, this));
if (isImmutable())
{
c.setImmutable();
}
if (!isStandardizedApartCheckRequired())
{
c.setStandardizedApartCheckNotRequired();
}
if (null == parentFactors)
{
c.calculateFactors(nonTrivialFactors);
nonTrivialFactors.AddRange(c.getFactors());
}
else
{
if (!parentFactors.Contains(c))
{
c.calculateFactors(nonTrivialFactors);
nonTrivialFactors.AddRange(c.getFactors());
}
}
}
}
}
}
factors = new List <Clause>();
// Need to add self, even though a non-trivial
// factor. See: slide 30
// http://logic.stanford.edu/classes/cs157/2008/lectures/lecture10.pdf
// for example of incompleteness when
// trivial factor not included.
factors.Add(this);
factors.AddRange(nonTrivialFactors);
}
private bool checkSubsumes(Clause othC,
Dictionary <String, List <Literal> > thisToTry,
Dictionary <String, List <Literal> > othCToTry)
{
bool subsumes = false;
List <Term> thisTerms = new List <Term>();
List <Term> othCTerms = new List <Term>();
// Want to track possible number of permuations
List <int> radixs = new List <int>();
foreach (String literalName in thisToTry.Keys)
{
int sizeT = thisToTry[literalName].Count;
int sizeO = othCToTry[literalName].Count;
if (sizeO > 1)
{
// The following is being used to
// track the number of permutations
// that can be mapped from the
// other clauses like literals to this
// clauses like literals.
// i.e. n!/(n-r)!
// where n=sizeO and r =sizeT
for (int i = 0; i < sizeT; i++)
{
int r = sizeO - i;
if (r > 1)
{
radixs.Add(r);
}
}
}
// Track the terms for this clause
foreach (Literal tl in thisToTry[literalName])
{
List <FOLNode> folNodes = tl.getAtomicSentence().getArgs();
foreach (FOLNode n in folNodes)
{
thisTerms.Add((Term)n);
}
}
}
MixedRadixNumber permutation = null;
long numPermutations = 1L;
if (radixs.Count > 0)
{
permutation = new MixedRadixNumber(0, radixs);
numPermutations = permutation.getMaxAllowedValue() + 1;
}
// Want to ensure none of the othCVariables are
// part of the key set of a unification as
// this indicates it is not a legal subsumption.
List <Variable> othCVariables = _variableCollector
.collectAllVariables(othC);
Dictionary <Variable, Term> theta = new Dictionary <Variable, Term>();
List <Literal> literalPermuations = new List <Literal>();
for (long l = 0L; l < numPermutations; l++)
{
// Track the other clause's terms for this
// permutation.
othCTerms.Clear();
int radixIdx = 0;
foreach (String literalName in thisToTry.Keys)
{
int sizeT = thisToTry[literalName].Count;
literalPermuations.Clear();
literalPermuations.AddRange(othCToTry[literalName]);
int sizeO = literalPermuations.Count;
if (sizeO > 1)
{
for (int i = 0; i < sizeT; i++)
{
int r = sizeO - i;
if (r > 1)
{
// If not a 1 to 1 mapping then you need
// to use the correct permuation
int numPos = permutation
.getCurrentNumeralValue(radixIdx);
Literal lit = literalPermuations[numPos];
literalPermuations.Remove(lit);
foreach (FOLNode arg in lit.getAtomicSentence().getArgs())
{
othCTerms.Add((Term)arg);
}
radixIdx++;
}
else
{
// is the last mapping, therefore
// won't be on the radix
foreach (FOLNode arg in literalPermuations[0].getAtomicSentence().getArgs())
{
othCTerms.Add((Term)arg);
}
}
}
}
else
{
// a 1 to 1 mapping
foreach (FOLNode arg in literalPermuations[0].getAtomicSentence().getArgs())
{
othCTerms.Add((Term)arg);
}
}
}
// Note: on unifier
// unifier.unify(P(w, x), P(y, z)))={w=y, x=z}
// unifier.unify(P(y, z), P(w, x)))={y=w, z=x}
// Therefore want this clause to be the first
// so can do the othCVariables check for an invalid
// subsumes.
theta.Clear();
List <FOLNode> termNodes = new List <FOLNode>();
foreach (Term t in thisTerms)
{
termNodes.Add((FOLNode)t);
}
List <FOLNode> othCNodes = new List <FOLNode>();
foreach (Term t in othCTerms)
{
othCNodes.Add((FOLNode)t);
}
if (null != _unifier.unify(termNodes, othCNodes, theta))
{
bool containsAny = false;
foreach (Variable v in theta.Keys)
{
if (othCVariables.Contains(v))
{
containsAny = true;
break;
}
}
if (!containsAny)
{
subsumes = true;
break;
}
}
// If there is more than 1 mapping
// keep track of where I am in the
// possible number of mapping permutations.
if (null != permutation)
{
permutation.increment();
}
}
return(subsumes);
}
// Note: Applies binary resolution rule and factoring
// Note: returns a set with an empty clause if both clauses
// are empty, otherwise returns a set of binary resolvents.
public List <Clause> binaryResolvents(Clause othC)
{
List <Clause> resolvents = new List <Clause>();
// Resolving two empty clauses
// gives you an empty clause
if (isEmpty() && othC.isEmpty())
{
resolvents.Add(new Clause());
return(resolvents);
}
// Ensure Standardized Apart
// Before attempting binary resolution
othC = saIfRequired(othC);
List <Literal> allPosLits = new List <Literal>();
List <Literal> allNegLits = new List <Literal>();
allPosLits.AddRange(this.positiveLiterals);
allPosLits.AddRange(othC.positiveLiterals);
allNegLits.AddRange(this.negativeLiterals);
allNegLits.AddRange(othC.negativeLiterals);
List <Literal> trPosLits = new List <Literal>();
List <Literal> trNegLits = new List <Literal>();
List <Literal> copyRPosLits = new List <Literal>();
List <Literal> copyRNegLits = new List <Literal>();
for (int i = 0; i < 2; i++)
{
trPosLits.Clear();
trNegLits.Clear();
if (i == 0)
{
// See if this clauses positives
// unify with the other clauses
// negatives
trPosLits.AddRange(this.positiveLiterals);
trNegLits.AddRange(othC.negativeLiterals);
}
else
{
// Try the other way round now
trPosLits.AddRange(othC.positiveLiterals);
trNegLits.AddRange(this.negativeLiterals);
}
// Now check to see if they resolve
Dictionary <Variable, Term> copyRBindings = new Dictionary <Variable, Term>();
foreach (Literal pl in trPosLits)
{
foreach (Literal nl in trNegLits)
{
copyRBindings.Clear();
if (null != _unifier.unify(pl.getAtomicSentence(), nl
.getAtomicSentence(), copyRBindings))
{
copyRPosLits.Clear();
copyRNegLits.Clear();
bool found = false;
foreach (Literal l in allPosLits)
{
if (!found && pl.Equals(l))
{
found = true;
continue;
}
copyRPosLits.Add(_substVisitor.subst(copyRBindings,
l));
}
found = false;
foreach (Literal l in allNegLits)
{
if (!found && nl.Equals(l))
{
found = true;
continue;
}
copyRNegLits.Add(_substVisitor.subst(copyRBindings,
l));
}
// Ensure the resolvents are standardized apart
Dictionary <Variable, Term> renameSubstitituon = _standardizeApart
.standardizeApart(copyRPosLits, copyRNegLits,
_saIndexical);
Clause c = new Clause(copyRPosLits, copyRNegLits);
c.setProofStep(new ProofStepClauseBinaryResolvent(c,
this, othC, copyRBindings, renameSubstitituon));
if (isImmutable())
{
c.setImmutable();
}
if (!isStandardizedApartCheckRequired())
{
c.setStandardizedApartCheckNotRequired();
}
resolvents.Add(c);
}
}
}
}
return(resolvents);
}