public Sequent Apply(Sequent sequent)
{
QuantifierFormula implicationFormula = (QuantifierFormula)sequent.RightHandSide.Formulas.Where
(
x => x is QuantifierFormula formula && formula.Quantifier == QuantifierConnective.ForAll
).FirstOrDefault();
if (implicationFormula == null)
{
return(null);
}
var formula = implicationFormula.Formula.Clone();
Terminal a;
if (implicationFormula.FreeVariables.Count == 0 && implicationFormula.WorldIndex.IsGround)
{
a = termNamer.GetNewConstant();
}
else
{
var skolemVariables = new List <Terminal>(formula.WorldIndex.Symbols.Select(x => x.ToTerminal()));
skolemVariables.AddRange(implicationFormula.FreeVariables);
a = termNamer.GetNewFunction(skolemVariables);
}
formula.ApplySubstitution(new Substitution(implicationFormula.Variable, a));
sequent.RightHandSide.Formulas.Remove(implicationFormula);
sequent.RightHandSide.Formulas.Add(formula);
sequent.Justification = "R9 (" + sequent.Name + ")";
return(sequent);
}
public void Test4()
{
ObjectVariableTerm x = new ObjectVariable('x');
IndividualConstantTerm <RationalNumber> half =
(IndividualConstant <RationalNumber>)(new RationalNumber(1, 2));
IndividualConstantTerm <RationalNumber>
one = (IndividualConstant <RationalNumber>)(new RationalNumber(1, 1));
var pr1 = new PredicateFormula(Predicates.More, x, half);
var pr2 = new PredicateFormula(Predicates.Less, x, one);
var f1 = new PropositionalConnectiveFormula(Conjunction.GetInstance(), pr1, pr2);
var f2 = new QuantifierFormula(ExistentialQuantifier.GetInstance(), x, f1);
IndividualConstantTerm <int> two = new IndividualConstant <int>(2);
var xSqr = new FunctionTerm(Functions.Pow, x, two);
var pr3 = new PredicateFormula(Predicates.MoreZero, xSqr);
var pr4 = new PredicateFormula(Predicates.EqualZero, x);
var f3 = new PropositionalConnectiveFormula(Disjunction.GetInstance(), pr3, pr4);
var f = new PropositionalConnectiveFormula(Conjunction.GetInstance(), f2, f3);
var actual = SimpleTarskiAlgorithm.QuantifiersElimination(f);
Formula expected = f3;
Formula expected1 = new PropositionalConnectiveFormula(Disjunction.GetInstance(), pr4, pr3);
Assert.IsTrue(expected.Equals(actual) || expected1.Equals(actual));
}
public void ZeroEqualZero()
{
ObjectVariableTerm x = new ObjectVariable('x');
IndividualConstantTerm <int> zero = (IndividualConstant <int>) 0;
var pr = new PredicateFormula(Predicates.Equal, zero, zero);
var f = new QuantifierFormula(UniversalQuantifier.GetInstance(), x, pr);
var actual = SimpleTarskiAlgorithm.QuantifiersElimination(f);
var expected = new PredicateFormula(True.GetInstance());
Assert.AreEqual(expected, actual);
}
public void Test1()
{
ObjectVariableTerm x = new ObjectVariable('x');
IndividualConstantTerm <RationalNumber> half =
(IndividualConstant <RationalNumber>)(new RationalNumber(1, 2));
var formula1 = new PredicateFormula(Predicates.More, x, half);
var formula2 = new QuantifierFormula(ExistentialQuantifier.GetInstance(), x, formula1);
var res = SimpleTarskiAlgorithm.QuantifiersElimination(formula2);
var expected = new PredicateFormula(True.GetInstance());
Assert.AreEqual(expected, res);
}
private static void CalcQuantifier(Quantifier quantifier, Stack <object> stack)
{
if (stack.Count < 2)
{
throw new ArgumentException("incorrect quantifier formula");
}
try
{
var formula = (Formula)stack.Pop();
var objectVar = (ObjectVariableTerm)stack.Pop();
var newFormula = new QuantifierFormula(quantifier, objectVar, formula);
stack.Push(newFormula);
}
catch (Exception)
{
throw new ArgumentException("incorrect quantifier formula");
}
}
public Sequent Apply(Sequent sequent)
{
QuantifierFormula implicationFormula = (QuantifierFormula)sequent.LeftHandSide.Formulas.Where
(
x => x is QuantifierFormula formula && formula.Quantifier == QuantifierConnective.ForAll
).FirstOrDefault();
if (implicationFormula == null)
{
return(null);
}
var formula = implicationFormula.Formula.Clone();
formula.ApplySubstitution(new Substitution(implicationFormula.Variable, LogicSolver.TermNamer.GetNewVariable()));
sequent.LeftHandSide.Formulas.Remove(implicationFormula);
sequent.LeftHandSide.Formulas.Add(formula);
sequent.Justification = "R10 (" + sequent.Name + ")";
return(sequent);
}
public void Test2()
{
ObjectVariableTerm x = new ObjectVariable('x');
IndividualConstantTerm <RationalNumber> half =
(IndividualConstant <RationalNumber>)(new RationalNumber(1, 2));
IndividualConstantTerm <RationalNumber> one = (IndividualConstant <RationalNumber>) new RationalNumber(1, 1);
var pr1 = new PredicateFormula(Predicates.More, x, half);
var pr2 = new PredicateFormula(Predicates.Less, x, one);
var f1 = new PropositionalConnectiveFormula(Conjunction.GetInstance(), pr1, pr2);
var f2 = new QuantifierFormula(ExistentialQuantifier.GetInstance(), x, f1);
var actual = SimpleTarskiAlgorithm.QuantifiersElimination(f2);
var expected = new PredicateFormula(True.GetInstance());
Assert.AreEqual(expected, actual);
}
