/// <summary>
/// a<=>b into (a=>b)&(b=>a) into ((~a||b)&(a||~b)) (Prioritize CNF over DNF)
/// Warning: This method is one directional, do not use this to convert a logic block into <=>
/// </summary>
/// <param name="logicBlock"></param>
/// <returns>The block passed to this method</returns>
public override Block Translate()
{
if (FirstBlock == null || SecondBlock == null)
{
ThrowErrorOnFirstCheck();
}
if (!Logic.IsBiconditional)
{
return(ConcatStoredBlocks());
}
Block cloneFirstBlock = new Block(FirstBlock.GetContent(true).ToString(), FirstBlock.IsNegated),
cloneSecondBlock = new Block(SecondBlock.GetContent(true).ToString(), SecondBlock.IsNegated);
// (~a||b)
FirstBlock.SetNegation(!FirstBlock.IsNegated)
.InsertBack(new Block(PropositionalLogic.Disjunction))
.InsertBack(SecondBlock);
// (a||~b)
cloneFirstBlock
.InsertBack(new Block(PropositionalLogic.Disjunction))
.InsertBack(cloneSecondBlock.SetNegation(!cloneFirstBlock.IsNegated));
// ((~a||b)&(a||~b))
var nested = new Block(FirstBlock);
nested.InsertBack(new Block(PropositionalLogic.Conjunction))
.InsertBack(new Block(cloneFirstBlock));
return(nested);
}
/// <summary>
/// a->b <=> (~a||b)
/// </summary>
/// <param name="logicBlock"></param>
/// <returns>The block passed to this method</returns>
public override Block Translate()
{
if (FirstBlock == null || SecondBlock == null)
{
ThrowErrorOnFirstCheck();
}
// elimination
if (Logic.IsImplication)
{
FirstBlock.SetNegation(!FirstBlock.IsNegated)
.InsertBack(new Block(PropositionalLogic.Disjunction))
.InsertBack(SecondBlock);
return(FirstBlock);
}
// reverse elimination
// ~a||b into a=>b and a||~b into b=>a
// accepting either one of them is negated, not both true or both false => XOR is the best choice
if (Logic.IsDisjunction && (FirstBlock.IsNegated ^ SecondBlock.IsNegated))
{
FirstBlock = FirstBlock.IsNegated ? FirstBlock : SecondBlock;
SecondBlock = FirstBlock.IsNegated ? SecondBlock : FirstBlock;
FirstBlock.SetNegation(!FirstBlock.IsNegated)
.InsertBack(new Block(PropositionalLogic.Implication))
.InsertBack(SecondBlock);
return(FirstBlock);
}
return(ConcatStoredBlocks());
}