private void SimplifyChild(STElement left)
{
if (!leftNode.ExistsContradiction())
{
leftNode.Simplify();
}
}
private bool ApplyNegationRule()
{
string rule = "Negation rule";
foreach (Node n in propositions)
{
if (n is NegationSign)
{
if (((NegationSign)n).ReturnChildNode() is NegationSign)
{
HashSet <Node> props = new HashSet <Node>(propositions);
props.Remove(n);
HashSet <Node> nodes = new HashSet <Node> {
((NegationSign)((NegationSign)n).ReturnChildNode()).ReturnChildNode()
};
props.UnionWith(nodes);
leftNode = new STElement(props, ActiveVariables, rule);
SimplifyChild(leftNode);
return(true);
}
else
{
continue;
}
}
}
return(false);
}
public ST(Node proposition)
{
Root = new STElement(new HashSet <Node> {
new NegationSign(proposition)
}, new List <char>(), "");
Root.Simplify();
IsTautology = Root.IsClosed();
}
private bool ApplyGammaRules()
{
string rule = "Gamma rule";
HashSet <Node> nodes = new HashSet <Node>();
foreach (Node n in propositions)
{
if (n is UniversalQuantifier)
{
UniversalQuantifier quantifier = (UniversalQuantifier)n;
//add predicates for existing variables
foreach (char var in ActiveVariables)
{
try
{
UniversalQuantifier newQuantifier = (UniversalQuantifier)quantifier.Copy().ReplaceObjectVariableNewNode(quantifier.Variable, var);
if (quantifier != null)
{
nodes.Add(newQuantifier.Proposition);
}
}
catch (Exception ex) { DirectMessage.ShowError(ex.Message); }
}
}
else if (n is NegationSign && ((NegationSign)n).ReturnChildNode() is ExistentialQuantifier)
{
ExistentialQuantifier quantifier = (ExistentialQuantifier)((NegationSign)n).ReturnChildNode();
//add predicates for existing variables
foreach (char var in ActiveVariables)
{
try
{
ExistentialQuantifier newQuantifier = (ExistentialQuantifier)quantifier.Copy().ReplaceObjectVariableNewNode(quantifier.Variable, var);
if (quantifier != null)
{
nodes.Add(new NegationSign(newQuantifier.Proposition));
}
}
catch (Exception ex) { DirectMessage.ShowError(ex.Message); }
}
}
else
{
continue;
}
}
if (nodes.Count > 0 && !nodes.IsSubsetOf(propositions))
{
nodes.UnionWith(propositions);
leftNode = new STElement(nodes, ActiveVariables, rule);
SimplifyChild(leftNode);
return(true);
}
return(false);
}
private void SimplifyChilds(STElement left, STElement right)
{
if (!leftNode.ExistsContradiction())
{
leftNode.Simplify();
}
if (!rightNode.ExistsContradiction())
{
rightNode.Simplify();
}
}
private bool ApplyDeltaRules()
{
string rule = "Delta rule";
foreach (Node n in propositions)
{
if (n is ExistentialQuantifier)
{
HashSet <Node> props = new HashSet <Node>(propositions);
props.Remove(n);
//change variable
List <char> newVariables = AddNewVariable();
try
{
ExistentialQuantifier quantifier = (ExistentialQuantifier)n.Copy();
quantifier.ReplaceObjectVariable(quantifier.Variable, newVariables[newVariables.Count - 1]);
HashSet <Node> nodes = new HashSet <Node> {
quantifier.Proposition
};
props.UnionWith(nodes);
leftNode = new STElement(props, newVariables, rule);
SimplifyChild(leftNode);
return(true);
}
catch (Exception ex) { DirectMessage.ShowError(ex.Message); }
}
else if (n is NegationSign && ((NegationSign)n).ReturnChildNode() is UniversalQuantifier)
{
HashSet <Node> props = new HashSet <Node>(propositions);
props.Remove(n);
//change variable
List <char> newVariables = AddNewVariable();
try
{
UniversalQuantifier quantifier = (UniversalQuantifier)((NegationSign)n).ReturnChildNode().Copy();
quantifier.ReplaceObjectVariable(quantifier.Variable, newVariables[newVariables.Count - 1]);
HashSet <Node> nodes = new HashSet <Node> {
new NegationSign(quantifier.Proposition)
};
props.UnionWith(nodes);
leftNode = new STElement(props, newVariables, rule);
SimplifyChild(leftNode);
return(true);
}
catch (Exception ex) { DirectMessage.ShowError(ex.Message); }
}
else
{
continue;
}
}
return(false);
}
private bool ApplyBetaRules()
{
string rule = "Beta rule";
foreach (Node n in propositions)
{
if (n is NegationSign && ((NegationSign)n).ReturnChildNode() is ConjunctionSign)
{
HashSet <Node> props = new HashSet <Node>(propositions);
props.Remove(n);
HashSet <Node> propsb = new HashSet <Node>(props);
ConjunctionSign negationSignChild = (ConjunctionSign)((NegationSign)n).ReturnChildNode();
HashSet <Node> nodes = new HashSet <Node> {
new NegationSign(negationSignChild.ReturnLeftNode())
};
HashSet <Node> nodeb = new HashSet <Node> {
new NegationSign(negationSignChild.ReturnRightNode())
};
props.UnionWith(nodes);
propsb.UnionWith(nodeb);
leftNode = new STElement(props, ActiveVariables, rule);
rightNode = new STElement(propsb, ActiveVariables, rule);
SimplifyChilds(leftNode, rightNode);
return(true);
}
else if (n is NegationSign && ((NegationSign)n).ReturnChildNode() is NANDSign)
{
HashSet <Node> props = new HashSet <Node>(propositions);
props.Remove(n);
HashSet <Node> propsb = new HashSet <Node>(props);
NANDSign NANDSign = (NANDSign)((NegationSign)n).ReturnChildNode();
HashSet <Node> nodes = new HashSet <Node> {
NANDSign.ReturnLeftNode()
};
HashSet <Node> nodeb = new HashSet <Node> {
NANDSign.ReturnRightNode()
};
props.UnionWith(nodes);
propsb.UnionWith(nodeb);
leftNode = new STElement(props, ActiveVariables, rule);
rightNode = new STElement(propsb, ActiveVariables, rule);
SimplifyChilds(leftNode, rightNode);
return(true);
}
else if (n is NANDSign)
{
HashSet <Node> props = new HashSet <Node>(propositions);
props.Remove(n);
HashSet <Node> propsb = new HashSet <Node>(props);
NANDSign NANDSign = (NANDSign)n;
HashSet <Node> nodes = new HashSet <Node> {
new NegationSign(NANDSign.ReturnLeftNode())
};
HashSet <Node> nodeb = new HashSet <Node> {
new NegationSign(NANDSign.ReturnRightNode())
};
props.UnionWith(nodes);
propsb.UnionWith(nodeb);
leftNode = new STElement(props, ActiveVariables, rule);
rightNode = new STElement(propsb, ActiveVariables, rule);
SimplifyChilds(leftNode, rightNode);
return(true);
}
else if (n is DisjunctionSign)
{
HashSet <Node> props = new HashSet <Node>(propositions);
props.Remove(n);
HashSet <Node> propsb = new HashSet <Node>(props);
HashSet <Node> nodes = new HashSet <Node> {
((DisjunctionSign)n).ReturnLeftNode()
};
HashSet <Node> nodeb = new HashSet <Node> {
((DisjunctionSign)n).ReturnRightNode()
};
props.UnionWith(nodes);
propsb.UnionWith(nodeb);
leftNode = new STElement(props, ActiveVariables, rule);
rightNode = new STElement(propsb, ActiveVariables, rule);
SimplifyChilds(leftNode, rightNode);
return(true);
}
else if (n is ImplicationSign)
{
HashSet <Node> props = new HashSet <Node>(propositions);
props.Remove(n);
HashSet <Node> propsb = new HashSet <Node>(props);
HashSet <Node> nodes = new HashSet <Node> {
new NegationSign(((ImplicationSign)n).ReturnLeftNode())
};
HashSet <Node> nodeb = new HashSet <Node> {
((ImplicationSign)n).ReturnRightNode()
};
props.UnionWith(nodes);
propsb.UnionWith(nodeb);
leftNode = new STElement(props, ActiveVariables, rule);
rightNode = new STElement(propsb, ActiveVariables, rule);
SimplifyChilds(leftNode, rightNode);
return(true);
}
else if (n is NegationSign && ((NegationSign)n).ReturnChildNode() is BiImplicationSign)
{
BiImplicationSign biImplicationSign = (BiImplicationSign)((NegationSign)n).ReturnChildNode();
HashSet <Node> props = new HashSet <Node>(propositions);
props.Remove(n);
HashSet <Node> propsb = new HashSet <Node>(props);
HashSet <Node> nodes = new HashSet <Node> {
new NegationSign(new ImplicationSign(
biImplicationSign.ReturnLeftNode(), biImplicationSign.ReturnRightNode()))
};
HashSet <Node> nodeb = new HashSet <Node> {
new NegationSign(new ImplicationSign(
biImplicationSign.ReturnRightNode(), biImplicationSign.ReturnLeftNode()))
};
props.UnionWith(nodes);
propsb.UnionWith(nodeb);
leftNode = new STElement(props, ActiveVariables, rule);
rightNode = new STElement(propsb, ActiveVariables, rule);
SimplifyChilds(leftNode, rightNode);
return(true);
}
else
{
continue;
}
}
return(false);
}
private bool ApplyAlfaRules()
{
string rule = "Alfa rule";
foreach (Node n in propositions)
{
if (n is ConjunctionSign)
{
HashSet <Node> props = new HashSet <Node>(propositions);
props.Remove(n);
HashSet <Node> nodes = new HashSet <Node> {
((ConjunctionSign)n).ReturnLeftNode(), ((ConjunctionSign)n).ReturnRightNode()
};
props.UnionWith(nodes);
leftNode = new STElement(props, ActiveVariables, rule);
SimplifyChild(leftNode);
return(true);
}
else if (n is BiImplicationSign)
{
HashSet <Node> props = new HashSet <Node>(propositions);
props.Remove(n);
HashSet <Node> nodes = new HashSet <Node> {
new ImplicationSign(((BiImplicationSign)n).ReturnLeftNode(), ((BiImplicationSign)n).ReturnRightNode()),
new ImplicationSign(((BiImplicationSign)n).ReturnRightNode(), ((BiImplicationSign)n).ReturnLeftNode()),
};
props.UnionWith(nodes);
leftNode = new STElement(props, ActiveVariables, rule);
SimplifyChild(leftNode);
return(true);
}
else if (n is NegationSign)
{
if (((NegationSign)n).ReturnChildNode() is DisjunctionSign)
{
HashSet <Node> props = new HashSet <Node>(propositions);
props.Remove(n);
DisjunctionSign disjunctionSign = (DisjunctionSign)((NegationSign)n).ReturnChildNode();
HashSet <Node> nodes = new HashSet <Node> {
new NegationSign(disjunctionSign.ReturnLeftNode()),
new NegationSign(disjunctionSign.ReturnRightNode())
};
props.UnionWith(nodes);
leftNode = new STElement(props, ActiveVariables, rule);
SimplifyChild(leftNode);
return(true);
}
else if (((NegationSign)n).ReturnChildNode() is ImplicationSign)
{
HashSet <Node> props = new HashSet <Node>(propositions);
props.Remove(n);
ImplicationSign implicationSign = (ImplicationSign)((NegationSign)n).ReturnChildNode();
HashSet <Node> nodes = new HashSet <Node> {
implicationSign.ReturnLeftNode(),
new NegationSign(implicationSign.ReturnRightNode())
};
props.UnionWith(nodes);
leftNode = new STElement(props, ActiveVariables, rule);
SimplifyChild(leftNode);
return(true);
}
else
{
continue;
}
}
else
{
continue;
}
}
return(false);
}