public static bool ValidateTautology(TableuxNode tree)
{
if (tree == null)
{
throw new ArgumentNullException();
}
int leafsCounter = 0;
int truthsCounter = 0;
void IterateOverLeafs(TableuxNode node)
{
if (node == null)
{
return;
}
if (node.Left == null && node.Right == null)
{
// we are in a leaf
leafsCounter++;
truthsCounter += TableuxNode.IsTautology(node.ListOfNodes) ? 1 : 0;
}
else
{
IterateOverLeafs(node.Left);
IterateOverLeafs(node.Right);
}
}
IterateOverLeafs(tree);
return(leafsCounter == truthsCounter);
}
public static int CountLeaves(TableuxNode tree)
{
int leafsCounter = 0;
void IterateOverLeafs(TableuxNode node)
{
if (node == null)
{
return;
}
if (node.Left == null && node.Right == null)
{
// we are in a leaf
leafsCounter++;
}
else
{
IterateOverLeafs(node.Left);
IterateOverLeafs(node.Right);
}
}
IterateOverLeafs(tree);
return(leafsCounter);
}
/// <summary>
/// Inserts a new TableuxNode into the current one
/// </summary>
/// <param name="toInsert"></param>
/// <returns></returns>
private bool Insert(TableuxNode toInsert)
{
if (Left == null)
{
Left = toInsert;
return(true);
}
if (Right == null)
{
Right = toInsert;
return(true);
}
return(false);
}
public Tableux(Node root, bool containsQuantifiers = false)
{
GlobalCounter.nrOfBetaRules = 1;
GlobalCounter.nrOfGammaRules = 0;
GlobalCounter.nrOfGammaRules = 0;
GlobalCounter.tautologyBeenIdentified = false;
GlobalCounter.nrOfTruthsReturnedByQuantifiers = 0;
GlobalCounter.nrOfTruthsReturnedNotByQuantifiers = 0;
this.containsQuantifiers = containsQuantifiers;
_root = Functions.NegateTree(root);
List <Node> passIN = new List <Node>(1);
passIN.Add(_root);
tree = new TableuxNode(passIN);
treeHasQuantifiers = HasQuantifiers(root);
BuildTableux(tree);
}
private void BuildTableux(TableuxNode root)
{
void ResetVariable()
{
isTautology = false;
treeHasQuantifiers = HasQuantifiers(_root);
truthsCounterForQuantifiers = 0;
GlobalCounter.nrOfBetaRules = 1;
GlobalCounter.nrOfGammaRules = 0;
GlobalCounter.tautologyBeenIdentified = false;
GlobalCounter.nrOfTruthsReturnedByQuantifiers = 0;
GlobalCounter.nrOfTruthsReturnedNotByQuantifiers = 0;
}
if (!root.TableuxIsSimplifiable())
{
return;
}
ResetVariable();
root.Generate();
}
public void Generate()
{
if (GlobalCounter.tautologyBeenIdentified || GlobalCounter.nrOfGammaRules > 250)
{
return;
}
if (!TableuxIsSimplifiable())
{
return;
}
/* get the most important tree to work on (NotNode based trees come first always) */
var(priorityTree, position) = GetPriorityTree();
/* get id of all biimplications or nands if there are any */
Functions.GetRidOfBiImplicationAndNand(ref priorityTree);
/* create a list that contains all previous elements but the one that you're gonna apply alpha/beta rules to */
var newList = GetListWithoutPriorityTree(position); // everything except for a tree that we're going to apply rules onto
bool betaRuleWorked = false;
if (IsBetaRule(priorityTree))
{
GlobalCounter.nrOfBetaRules++;
var(leftBranchList, rightBranchList) = ApplyBetaRules(priorityTree);
leftBranchList.AddRange(newList);
rightBranchList.AddRange(newList);
TableuxNode newLeftNodeToInsert = new TableuxNode(leftBranchList);
TableuxNode newRightNodeToInsert = new TableuxNode(rightBranchList);
// insert two new nodes
if (!(Insert(newLeftNodeToInsert) && Insert(newRightNodeToInsert)))
{
MessageBox.Show("Problems detected");
}
else
{
betaRuleWorked = true;
}
}
else if (IsDeltaRule(priorityTree))
{
newList.AddRange(ApplyDeltaRules(priorityTree));
}
else if (IsGammaRule(priorityTree))
{
newList.AddRange(ApplyGammaRules(priorityTree));
GlobalCounter.nrOfGammaRules++;
if (GlobalCounter.nrOfGammaRules > 250)
{
MessageBox.Show(
"Have done 250 iterations... didn't find anything. So it's probably not a tautology");
return;
}
}
else
{
newList.AddRange(ApplyAlphaRules(priorityTree));
}
// check if beta rule has been applied, if so, then do nothing and proceed to work on left and right branches
// if beta rule wasn't applied, then insert alpha-rule
if (!betaRuleWorked)
{
TableuxNode newNodeToInsert = new TableuxNode(newList);
var insertionResult = Insert(newNodeToInsert);
if (!insertionResult)
{
throw new Exception("Problems detected");
}
}
if (Tableux.treeHasQuantifiers)
{
var isItTautologyNow = IsTautologyQuantifiers(listOfNodes);
if (isItTautologyNow)
{
GlobalCounter.nrOfTruthsReturnedByQuantifiers++;
}
if (GlobalCounter.nrOfTruthsReturnedByQuantifiers == GlobalCounter.nrOfBetaRules)
{
MessageBox.Show("It's a tautology!");
GlobalCounter.tautologyBeenIdentified = true;
return;
}
}
else
{
var isTautologyNow = IsTautology(listOfNodes);
if (isTautologyNow)
{
GlobalCounter.nrOfTruthsReturnedNotByQuantifiers++;
}
if (GlobalCounter.nrOfTruthsReturnedNotByQuantifiers == GlobalCounter.nrOfBetaRules)
{
GlobalCounter.tautologyBeenIdentified = true;
return;
}
}
/* recursively do it all over again until there's no more work that needs to be done */
Left?.Generate();
Right?.Generate();
}
