| public getAtomicSentence ( ) : AtomicSentence | ||
| return | AtomicSentence | |
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);
}
public Literal subst(Dictionary<Variable, Term> theta, Literal aLiteral)
{
return aLiteral.newInstance((AtomicSentence)aLiteral
.getAtomicSentence().accept(this, theta));
}
private String getFactKey(Literal l)
{
StringBuilder key = new StringBuilder();
if (l.isPositiveLiteral())
{
key.Append("+");
}
else
{
key.Append("-");
}
key.Append(l.getAtomicSentence().getSymbolicName());
return key.ToString();
}
// Note: see pg. 281
public bool isRenaming(Literal l, List<Literal> possibleMatches)
{
foreach (Literal q in possibleMatches)
{
if (l.isPositiveLiteral() != q.isPositiveLiteral())
{
continue;
}
Dictionary<Variable, Term> subst = unifier.unify(l.getAtomicSentence(), q
.getAtomicSentence());
if (null != subst)
{
int cntVarTerms = 0;
foreach (Term t in subst.Values)
{
if (t is Variable)
{
cntVarTerms++;
}
}
// If all the substitutions, even if none, map to Variables
// then this is a renaming
if (subst.Count == cntVarTerms)
{
return true;
}
}
}
return false;
}
// Note: pg 278, FETCH(q) concept.
public /* lock */ List<Dictionary<Variable, Term>> fetch(Literal l)
{
// Get all of the substitutions in the KB that p unifies with
List<Dictionary<Variable, Term>> allUnifiers = new List<Dictionary<Variable, Term>>();
List<Literal> matchingFacts = fetchMatchingFacts(l);
if (null != matchingFacts)
{
foreach (Literal fact in matchingFacts)
{
Dictionary<Variable, Term> substitution = unifier.unify(l
.getAtomicSentence(), fact.getAtomicSentence());
if (null != substitution)
{
allUnifiers.Add(substitution);
}
}
}
return allUnifiers;
}
//
// 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;
}
