public bool ttCheckAll(Sentence kbSentence, Sentence querySentence,
List<Symbol> symbols, Model model)
{
if (symbols.Count==0)
{
if (model.isTrue(kbSentence))
{
// System.Console.WriteLine("#");
return model.isTrue(querySentence);
}
else
{
// System.Console.WriteLine("0");
return true;
}
}
else
{
Symbol symbol = (Symbol)Util.first(symbols);
List<Symbol> rest = Util.rest(symbols);
Model trueModel = model.extend(new Symbol(symbol.getValue()), true);
Model falseModel = model.extend(new Symbol(symbol.getValue()),
false);
return (ttCheckAll(kbSentence, querySentence, rest, trueModel) && (ttCheckAll(
kbSentence, querySentence, rest, falseModel)));
}
}
private Symbol getSymbolWhoseFlipMaximisesSatisfiedClauses(
List<Sentence> clauses, List<Symbol> symbols, Model model)
{
if (symbols.Count > 0)
{
Symbol retVal = symbols[0];
int maxClausesSatisfied = 0;
for (int i = 0; i < symbols.Count; i++)
{
Symbol sym = symbols[i];
if (getNumberOfClausesSatisfiedIn(clauses, model.flip(sym)) > maxClausesSatisfied)
{
retVal = sym;
maxClausesSatisfied = getNumberOfClausesSatisfiedIn(
clauses, model.flip(sym));
}
}
return retVal;
}
else
{
return null;
}
}
public bool dpllSatisfiable(Sentence s, Model m)
{
List<Sentence> clauses = new CNFClauseGatherer()
.getClausesFrom(new CNFTransformer().transform(s));
List<Symbol> symbols = new SymbolCollector()
.getSymbolsIn(s);
// System.Console.WriteLine(" numberOfSymbols = " + symbols.Count);
return dpll(clauses, symbols, m);
}
public void testDPLLReturnsFalseWhenOneClauseFalseInModel()
{
Model model = new Model();
model = model.extend(new Symbol("A"), true).extend(new Symbol("B"),
false);
Sentence sentence = (Sentence)parser.parse("((A OR B) AND (A => B))");
bool satisfiable = dpll.dpllSatisfiable(sentence, model);
Assert.AreEqual(false, satisfiable);
}
public void testSentenceStatusWhenPFalseAndQFalse()
{
String p = "P";
String q = "Q";
m = m.extend(new Symbol(p), false);
m = m.extend(new Symbol(q), false);
Assert.AreEqual(true, m.isFalse(andSentence));
Assert.AreEqual(true, m.isFalse(orSentence));
Assert.AreEqual(true, m.isTrue(impliedSentence));
Assert.AreEqual(true, m.isTrue(biConditionalSentence));
}
public void setUp()
{
parser = new PEParser();
trueSentence = (Sentence)parser.parse("true");
falseSentence = (Sentence)parser.parse("false");
andSentence = (Sentence)parser.parse("(P AND Q)");
orSentence = (Sentence)parser.parse("(P OR Q)");
impliedSentence = (Sentence)parser.parse("(P => Q)");
biConditionalSentence = (Sentence)parser.parse("(P <=> Q)");
m = new Model();
}
public void testDPLLFilteringNonTrueClausesGivesNullWhenAllClausesAreKnown()
{
Model model = new Model();
model = model.extend(new Symbol("A"), true).extend(new Symbol("B"),
true).extend(new Symbol("C"), true);
Sentence sentence = (Sentence)parser
.parse("((A AND B) AND (B AND C))");
List<Sentence> clauseList = new CNFClauseGatherer()
.getClausesFrom(new CNFTransformer()
.transform(sentence));
List<Sentence> clausesWithNonTrueValues = dpll
.clausesWithNonTrueValues(clauseList, model);
Assert.AreEqual(0, clausesWithNonTrueValues.Count);
}
public void testDPLLFiltersClausesTheStatusOfWhichAreKnown()
{
Model model = new Model();
model = model.extend(new Symbol("A"), true).extend(new Symbol("B"),
true);
Sentence sentence = (Sentence)parser
.parse("((A AND B) AND (B AND C))");
List<Sentence> clauseList = new CNFClauseGatherer()
.getClausesFrom(new CNFTransformer()
.transform(sentence));
List<Sentence> clausesWithNonTrueValues = dpll
.clausesWithNonTrueValues(clauseList, model);
Assert.AreEqual(1, clausesWithNonTrueValues.Count);
Sentence nonTrueClause = (Sentence)parser.parse("(B AND C)");
clausesWithNonTrueValues.Contains(nonTrueClause);
}
public Model findModelFor(String logicalSentence, int numberOfFlips,
double probabilityOfRandomWalk)
{
myModel = new Model();
Sentence s = (Sentence)new PEParser().parse(logicalSentence);
CNFTransformer transformer = new CNFTransformer();
CNFClauseGatherer clauseGatherer = new CNFClauseGatherer();
SymbolCollector sc = new SymbolCollector();
List<Symbol> symbols = sc.getSymbolsIn(s);
Random r = new Random();
for (int i = 0; i < symbols.Count; i++)
{
Symbol sym = (Symbol)symbols[i];
myModel = myModel.extend(sym, Util.randombool());
}
List<Sentence> clauses = clauseGatherer.getClausesFrom(transformer
.transform(s));
for (int i = 0; i < numberOfFlips; i++)
{
if (getNumberOfClausesSatisfiedIn(clauses, myModel) == clauses.Count)
{
return myModel;
}
Sentence clause = clauses[random.Next(clauses.Count)];
List<Symbol> symbolsInClause = sc
.getSymbolsIn(clause);
if (random.NextDouble() >= probabilityOfRandomWalk)
{
Symbol randomSymbol = symbolsInClause[random
.Next(symbolsInClause.Count)];
myModel = myModel.flip(randomSymbol);
}
else
{
Symbol symbolToFlip = getSymbolWhoseFlipMaximisesSatisfiedClauses(
clauses,
symbolsInClause, myModel);
myModel = myModel.flip(symbolToFlip);
}
}
return null;
}
public List<Sentence> clausesWithNonTrueValues(List<Sentence> clauseList,
Model model)
{
List<Sentence> clausesWithNonTrueValues = new List<Sentence>();
for (int i = 0; i < clauseList.Count; i++)
{
Sentence clause = clauseList[i];
if (!(isClauseTrueInModel(clause, model)))
{
if (!(clausesWithNonTrueValues.Contains(clause)))
{// defensive
// programming not really necessary
clausesWithNonTrueValues.Add(clause);
}
}
}
return clausesWithNonTrueValues;
}
private SymbolValuePair findUnitClause(List<Sentence> clauseList, Model model,
List<Symbol> symbols)
{
for (int i = 0; i < clauseList.Count; i++)
{
Sentence clause = (Sentence)clauseList[i];
if ((clause is Symbol)
&& (!(model.getAssignedSymbols().Contains(clause))))
{
// System.Console.WriteLine("found unit clause - assigning");
return new SymbolValuePair(new Symbol(((Symbol)clause)
.getValue()), true);
}
if (clause is UnarySentence)
{
UnarySentence sentence = (UnarySentence)clause;
Sentence negated = sentence.getNegated();
if ((negated is Symbol)
&& (!(model.getAssignedSymbols().Contains(negated))))
{
// System.Console.WriteLine("found unit clause type 2 -
// assigning");
return new SymbolValuePair(new Symbol(((Symbol)negated)
.getValue()), false);
}
}
}
return new SymbolValuePair();// failed to find any unit clause;
}
private bool isClauseTrueInModel(Sentence clause, Model model)
{
List<Symbol> positiveSymbols = new SymbolClassifier().getPositiveSymbolsIn(clause);
List<Symbol> negativeSymbols = new SymbolClassifier().getNegativeSymbolsIn(clause);
foreach (Symbol symbol in positiveSymbols)
{
if ((model.isTrue(symbol)))
{
return true;
}
}
foreach (Symbol symbol in negativeSymbols)
{
if ((model.isFalse(symbol)))
{
return true;
}
}
return false;
}
private bool areAllClausesTrue(Model model, List<Sentence> clauseList)
{
for (int i = 0; i < clauseList.Count; i++)
{
Sentence clause = (Sentence)clauseList[i];
// System.Console.WriteLine("evaluating " + clause.ToString());
if (!isClauseTrueInModel(clause, model))
{ // ie if false or
// UNKNOWN
// System.Console.WriteLine(clause.ToString()+ " is not true");
return false;
}
}
return true;
}
private bool isEvenOneClauseFalse(Model model, List<Sentence> clauseList)
{
for (int i = 0; i < clauseList.Count; i++)
{
Sentence clause = (Sentence)clauseList[i];
if (model.isFalse(clause))
{
// System.Console.WriteLine(clause.ToString() + " is false");
return true;
}
}
return false;
}
public Model extend(Symbol symbol, bool b) {
Model m = new Model();
m.h = this.h;
m.h.Add(symbol, b);
return m;
}
public void testDPLLFindsPurePositiveSymbolsWhenTheyExist()
{
Model model = new Model();
model = model.extend(new Symbol("A"), true).extend(new Symbol("B"),
true);
Sentence sentence = (Sentence)parser
.parse("((A AND B) AND (B AND C))");
List<Sentence> clauseList = new CNFClauseGatherer()
.getClausesFrom(new CNFTransformer()
.transform(sentence));
List<Symbol> symbolList = new SymbolCollector().getSymbolsIn(sentence);
DPLL.SymbolValuePair sv = dpll.findPureSymbolValuePair(clauseList,
model, symbolList);
Assert.IsNotNull(sv);
Assert.AreEqual(new Symbol("C"), sv.symbol);
Assert.AreEqual(true, sv.value);
}
public void testExtendModel()
{
String p = "P";
m = m.extend(new Symbol(p), true);
Assert.AreEqual(true, m.getStatus(new Symbol("P")));
}
public void testComplexSentence()
{
String p = "P";
String q = "Q";
m = m.extend(new Symbol(p), true);
m = m.extend(new Symbol(q), false);
Sentence sent = (Sentence)parser.parse("((P OR Q) AND (P => Q))");
Assert.IsFalse(m.isTrue(sent));
Assert.IsTrue(m.isFalse(sent));
Sentence sent2 = (Sentence)parser.parse("((P OR Q) AND (Q))");
Assert.IsFalse(m.isTrue(sent2));
Assert.IsTrue(m.isFalse(sent2));
}
private int getNumberOfClausesSatisfiedIn(List<Sentence> clauses, Model model)
{
int retVal = 0;
foreach(Sentence s in clauses)
{
if (model.isTrue(s))
{
retVal += 1;
}
}
return retVal;
}
public SymbolValuePair findPureSymbolValuePair(List<Sentence> clauseList,
Model model, List<Symbol> symbols)
{
List<Sentence> _clausesWithNonTrueValues = clausesWithNonTrueValues(clauseList,
model);
Sentence nonTrueClauses = LogicUtils.chainWith("AND",
_clausesWithNonTrueValues);
// System.Console.WriteLine("Unsatisfied clauses = "
// + clausesWithNonTrueValues.Count);
List<Symbol> symbolsAlreadyAssigned = new List<Symbol>( model.getAssignedSymbols());
// debug
// List symList = asList(symbolsAlreadyAssigned);
//
// System.Console.WriteLine(" assignedSymbols = " + symList.Count);
// if (symList.Count == 52) {
// System.Console.WriteLine("untrue clauses = " + clausesWithNonTrueValues);
// System.Console.WriteLine("model= " + model);
// }
// debug
List<Symbol> purePositiveSymbols = SetOps
.difference(new SymbolClassifier()
.getPurePositiveSymbolsIn(nonTrueClauses),
symbolsAlreadyAssigned);
List<Symbol> pureNegativeSymbols = SetOps
.difference(new SymbolClassifier()
.getPureNegativeSymbolsIn(nonTrueClauses),
symbolsAlreadyAssigned);
// if none found return "not found
if ((purePositiveSymbols.Count == 0)
&& (pureNegativeSymbols.Count == 0))
{
return new SymbolValuePair();// automatically set to null values
}
else
{
if (purePositiveSymbols.Count > 0)
{
Symbol symbol =purePositiveSymbols[0];
if (pureNegativeSymbols.Contains(symbol))
{
throw new ApplicationException("Symbol " + symbol.getValue()
+ "misclassified");
}
return new SymbolValuePair(symbol, true);
}
else
{
Symbol symbol = new Symbol((pureNegativeSymbols[0])
.getValue());
if (purePositiveSymbols.Contains(symbol))
{
throw new ApplicationException("Symbol " + symbol.getValue()
+ "misclassified");
}
return new SymbolValuePair(symbol, false);
}
}
}
public void testModelEvaluation()
{
kb.tell("(NOT P11)");
kb.tell("(B11 <=> (P12 OR P21))");
kb.tell("(B21 <=> ((P11 OR P22) OR P31))");
kb.tell("(NOT B11)");
kb.tell("(B21)");
Model model = new Model();
model = model.extend(new Symbol("B11"), false);
model = model.extend(new Symbol("B21"), true);
model = model.extend(new Symbol("P11"), false);
model = model.extend(new Symbol("P12"), false);
model = model.extend(new Symbol("P21"), false);
model = model.extend(new Symbol("P22"), false);
model = model.extend(new Symbol("P31"), true);
Sentence kbs = kb.asSentence();
Assert.AreEqual(true, model.isTrue(kbs));
}
//
// PRIVATE METHODS
//
private bool dpll(List<Sentence> clauses, List<Symbol> symbols, Model model)
{
// List<Sentence> clauseList = asList(clauses);
List<Sentence> clauseList = clauses;
// System.Console.WriteLine("clauses are " + clauses.ToString());
// if all clauses are true return true;
if (areAllClausesTrue(model, clauseList))
{
// System.Console.WriteLine(model.ToString());
return true;
}
// if even one clause is false return false
if (isEvenOneClauseFalse(model, clauseList))
{
// System.Console.WriteLine(model.ToString());
return false;
}
// System.Console.WriteLine("At least one clause is unknown");
// try to find a unit clause
SymbolValuePair svp = findPureSymbolValuePair(clauseList, model,
symbols);
if (svp.notNull())
{
Symbol[] copy = new Symbol[symbols.Count];
symbols.CopyTo(copy);
List<Symbol> newSymbols = new List<Symbol>(copy);
newSymbols.Remove(new Symbol(svp.symbol.getValue()));
Model newModel = model.extend(new Symbol(svp.symbol.getValue()),
svp.value);
return dpll(clauses, newSymbols, newModel);
}
SymbolValuePair svp2 = findUnitClause(clauseList, model, symbols);
if (svp2.notNull())
{
Symbol[] copy = new Symbol[symbols.Count];
symbols.CopyTo(copy);
List<Symbol> newSymbols = new List<Symbol>(copy);
newSymbols.Remove(new Symbol(svp2.symbol.getValue()));
Model newModel = model.extend(new Symbol(svp2.symbol.getValue()),
svp2.value);
return dpll(clauses, newSymbols, newModel);
}
Symbol symbol = (Symbol)symbols[0];
// System.Console.WriteLine("default behaviour selecting " + symbol);
Symbol[] symbolsArr = new Symbol[symbols.Count];
symbols.CopyTo(symbolsArr);
List<Symbol> newSymbols2 = symbolsArr.ToList<Symbol>();
newSymbols2.RemoveAt(0);
return (dpll(clauses, newSymbols2, model.extend(symbol, true)) || dpll(
clauses, newSymbols2, model.extend(symbol, false)));
}
