public void Test3()
{
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> twoConst = new IndividualConstant <int>(2);
var xSqr = new FunctionTerm(Functions.Pow, x, twoConst);
var pr3 = new PredicateFormula(Predicates.MoreZero, xSqr);
var pr4 = new PredicateFormula(Predicates.EqualZero, x);
var f3 = new PropositionalConnectiveFormula(Disjunction.GetInstance(), pr3, pr4);
var f4 = new QuantifierFormula(UniversalQuantifier.GetInstance(), x, f3);
var f = new PropositionalConnectiveFormula(Conjunction.GetInstance(), f2, f4);
var actual = SimpleTarskiAlgorithm.QuantifiersElimination(f);
Formula expected = new PredicateFormula(True.GetInstance());
Assert.AreEqual(expected, actual);
}
public void Constructor_CreateUniversalQuantifierNoReplacementVariablesPresent_GammaRuleShouldNotBeAppliedNoChildrenGenerated()
{
// Arrange
char boundVariable = PropositionGenerator.GenerateBoundVariable();
List <char> boundVariables = new List <char>()
{
boundVariable
};
Predicate predicate = new Predicate(PropositionGenerator.GetRandomVariableLetter(), boundVariables);
UniversalQuantifier universalQuantifier = new UniversalQuantifier(boundVariable);
universalQuantifier.LeftSuccessor = predicate;
HashSet <Proposition> propositions = new HashSet <Proposition>()
{
universalQuantifier
};
// Act
SemanticTableauxElement semanticTableauxElement = new SemanticTableauxElement(propositions);
bool isReplaced = predicate.IsReplaced(boundVariable);
// Assert
isReplaced.Should().BeFalse("Because no replacement variables are available");
semanticTableauxElement.LeftChild.Should().BeNull("Because no replacement variables are available and thus no child was created");
}
private static Symbol SpecialSymbol(string str, ref int index)
{
++index;
if (index >= str.Length)
{
throw new ArgumentException(
$"a tag was expected, but there is no tag before the symbol \\ with the number {index - 1}");
}
var tag = GetTag(str, ref index);
if (tag.Length == 0)
{
throw new ArgumentException(
$"a tag was expected, but there is no tag before the symbol \\ with the number {index - 1}");
}
return(tag switch
{
"lnot" => Negation.GetInstance(),
"lor" => Disjunction.GetInstance(),
"land" => Conjunction.GetInstance(),
"to" => Implication.GetInstance(),
"forall" => UniversalQuantifier.GetInstance(),
"exists" => ExistentialQuantifier.GetInstance(),
"over" => Division.GetInstance(),
"func" => GetFunction(str, ref index), // \func{name arity}
"pr" => GetPredicate(str, ref index), // \pr{name arity}
_ => throw new ArgumentException($"unknown tag {tag} before the symbol with the number {index}")
});
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 Constructor_CreateNegatedUniversalQuantifier_DeltaRuleShouldBeAppliedChildShouldBePredicateAndVariableShouldBeIntroduced()
{
// Arrange
char boundVariable = PropositionGenerator.GenerateBoundVariable();
List <char> boundVariables = new List <char>()
{
boundVariable
};
Predicate predicate = new Predicate(PropositionGenerator.GetRandomVariableLetter(), boundVariables);
UniversalQuantifier universalQuantifier = new UniversalQuantifier(boundVariable);
universalQuantifier.LeftSuccessor = predicate;
Negation negatedUniversalQuantifier = new Negation();
negatedUniversalQuantifier.LeftSuccessor = universalQuantifier;
HashSet <Proposition> propositions = new HashSet <Proposition>()
{
negatedUniversalQuantifier
};
// Act
SemanticTableauxElement semanticTableauxElement = new SemanticTableauxElement(propositions);
List <char> replacementVariables = semanticTableauxElement.LeftChild.ReplacementVariables.ToList();
int expectedNumberOfReplacementVariables = 1;
int actualNumberOfReplacementVariables = replacementVariables.Count;
// Assert
actualNumberOfReplacementVariables.Should().Be(expectedNumberOfReplacementVariables, "Because the only bound variable should be replaced based on the rules");
foreach (Proposition proposition in semanticTableauxElement.LeftChild.Propositions)
{
if (proposition is Predicate)
{
predicate = (Predicate)proposition;
bool isReplaced = predicate.IsReplaced(boundVariable);
isReplaced.Should().BeTrue("Because after applying a delta rule, the only bound variable in the predicate should be replaced");
}
}
}
public void Constructor_CreateUniversalQuantifierWithReplacementVariablePresent_GammaRuleShouldBeAppliedAndNewChildrenCreated()
{
// Arrange
char boundVariable = PropositionGenerator.GenerateBoundVariable();
List <char> boundVariables = new List <char>()
{
boundVariable
};
Predicate predicate = new Predicate(PropositionGenerator.GetRandomVariableLetter(), boundVariables);
UniversalQuantifier universalQuantifier = new UniversalQuantifier(boundVariable);
universalQuantifier.LeftSuccessor = predicate;
HashSet <Proposition> propositions = new HashSet <Proposition>()
{
universalQuantifier
};
// Act
char availableReplacementVariable = 'd';
SemanticTableauxElement semanticTableauxElement = new SemanticTableauxElement(propositions, new HashSet <char>()
{
availableReplacementVariable
});
// Assert
semanticTableauxElement.LeftChild.Should().NotBeNull("Because children should be created now that a replacement variable is present");
foreach (Proposition proposition in semanticTableauxElement.LeftChild.Propositions)
{
if (proposition is Predicate)
{
Predicate pred = (Predicate)proposition;
bool isReplaced = pred.IsReplaced(boundVariable);
isReplaced.Should().BeTrue($"Because the replacement variable {availableReplacementVariable} is available");
}
}
}
