/// <summary>Make proposiiton with operator, atom and two sub-proposition</summary>
/// <param name="op">Operator of proposition</param>
/// <param name="atom">Atom of proposition</param>
/// <param name="expr1">First sub-proposition of proposition</param>
/// <param name="expr2">Second sub-proposition of proposition</param>
public Proposition(Operator op, Atom atom, Proposition expr1, Proposition expr2)
{
this.left = expr1;
this.right = expr2;
this.atom = atom;
this.op = op;
}
/// <summary>Evaluate at given proposition</summary>
/// <param name="expr">Proposition to evaluate</param>
/// <returns>Result of evaluation</returns>
private bool Evaluate(Proposition expr)
{
switch (expr.op)
{
case Operator.Atom:
string s = expr.atom.Symbol;
if (s == ParseEngine.SYMBOL_T)
{
return(true);
}
else if (s == ParseEngine.SYMBOL_F)
{
return(false);
}
return(evalData[s]);
case Operator.Or:
return(Evaluate(expr.left) || Evaluate(expr.right));
case Operator.And:
return(Evaluate(expr.left) && Evaluate(expr.right));
case Operator.Not:
return(!Evaluate(expr.left));
case Operator.Imply:
return(!Evaluate(expr.left) || Evaluate(expr.right));
case Operator.IfOnlyIf:
return(!(Evaluate(expr.left) ^ Evaluate(expr.right)));
default:
return(false);
}
}
/// <summary>Parse from current position with given priority</summary>
/// <param name="prec">Priority</param>
/// <returns>Parsed proposition</returns>
private Proposition ParseWithPrec(int prec)
{
Proposition expr1, expr2;
expr1 = GetNextExpression();
backIndex = index;
while (index != input.Length)
{
string s = GetNextToken();
if (s == SYMBOL_RP)
{
index = backIndex;
return(expr1);
}
Operator op = GetOperator(s);
int pr = GetPrecedence(op);
if (pr > prec)
{
index = backIndex;
return(expr1);
}
else
{
expr2 = ParseWithPrec(pr);
expr1 = new Proposition(op, expr1, expr2);
}
}
return(expr1);
}
/// <summary>Check whether give proposition is contradiction</summary>
/// <param name="expr">Proposition to check</param>
/// <exception cref="InvaildPropositionException"></exception>
/// <returns>True if contradiction</returns>
public bool IsContradiction(Proposition expr)
{
if (expr == null || !expr.IsVaild())
{
throw new InvalidPropositionException("INVAILD");
}
return(GetTrueAssignmentList(expr).Count == 0);
}
/// <summary>Find assignment list which each assignment table make give proposition true</summary>
/// <param name="expr">Proposition to get true assignment list</param>
/// <exception cref="InvaildPropositionException"></exception>
/// <returns>Assignment list</returns>
public List <Dictionary <string, bool> > GetTrueAssignmentList(Proposition expr)
{
if (expr == null || !expr.IsVaild())
{
throw new InvalidPropositionException("INVAILD");
}
trueList = new List <Dictionary <string, bool> >();
GetTrueAssignmentListCore(expr, new Dictionary <string, bool>());
return(trueList);
}
/// <summary>Check whether give proposition is tautology</summary>
/// <param name="expr">Proposition to check</param>
/// <exception cref="InvaildPropositionException"></exception>
/// <returns>True if tautology</returns>
public bool IsTautology(Proposition expr)
{
if (expr == null || !expr.IsVaild())
{
throw new InvalidPropositionException("INVAILD");
}
if (!expr.IsCNF())
{
expr = ConvertToCNF(ConvertToNNF(expr));
}
return(IsTautologyCore(expr));
}
/// <summary>Convert given NNF proposition to CNF proposition</summary>
/// <param name="expr">NNF proposition to convert</param>
/// <exception cref="PropositionNotSupportException"></exception>
/// <returns>CNF proposition</returns>
public Proposition ConvertToCNF(Proposition expr)
{
if (expr == null || !expr.IsNNF())
{
throw new PropositionNotSupportedException("NOT_NNF");
}
if (expr.op == Operator.Atom)
{
return(expr);
}
else if (expr.op == Operator.And) // S(P&Q) => S(P)&S(Q)
{
return(new Proposition(Operator.And,
ConvertToCNF(expr.left),
ConvertToCNF(expr.right)));
}
else if (expr.op == Operator.Or) // S(P|Q) =>
{
Proposition c1 = ConvertToCNF(expr.left);
Proposition c2 = ConvertToCNF(expr.right);
if (c1.op != Operator.And && c2.op != Operator.And) // S(P|Q) => S(P)|S(Q)
{
return(new Proposition(Operator.Or, c1, c2));
}
if (c1.op != Operator.And)
{
Proposition tmp = c1; c1 = c2; c2 = tmp; // S((A&B)|C) => S(A|C)&S(B|C)
}
return(new Proposition(Operator.And,
ConvertToCNF(new Proposition(Operator.Or, c1.left, c2)),
ConvertToCNF(new Proposition(Operator.Or, c1.right, c2))));
}
else if (expr.op == Operator.Not) // S(P) => S(P)
{
if (expr.left.op == Operator.Atom) // Must Be Unit According to Def. of NNF
{
return(expr);
}
}
return(null);
}
/// <summary>Evaluate proposition with given data</summary>
/// <param name="value">Result of evaluation</param>
/// <param name="error">Error Message</param>
/// <param name="expr">Proposition to evaluate</param>
/// <param name="data">Assignment table</param>
/// <returns>True if successed evaluate</returns>
public bool TryEvaluate(out bool value, out string error, Proposition expr, Dictionary <string, bool> data)
{
value = false; error = "";
if (expr == null || !expr.IsVaild())
{
error = InvalidPropositionException.REASON_INVAILD;
return(false);
}
List <string> atomList = expr.GetAtomList();
List <string> keyList = data.Keys.ToList();
if (atomList.Intersect(keyList).Count() != atomList.Count)
{
error = "모든 atom에 대해 적절한 대입값이 없습니다.";
return(false);
}
evalData = data;
value = Evaluate(expr);
return(true);
}
/// <summary>Build all possible assignment and calculate</summary>
/// <param name="expr">Proposition to calculate</param>
/// <param name="dict">Assignment list</param>
private void GetTrueAssignmentListCore(Proposition expr, Dictionary <string, bool> dict)
{
if (expr.GetAtomList().Count == dict.Count)
{
bool value; string result;
calcEng.TryEvaluate(out value, out result, expr, dict);
if (value)
{
trueList.Add(dict.DeepCopy());
}
}
else
{
string target = expr.GetAtomList().Except(dict.Keys.ToList()).First();
Dictionary <string, bool> dict1 = dict.DeepCopy(), dict2 = dict.DeepCopy();
dict1.Add(target, false);
dict2.Add(target, true);
GetTrueAssignmentListCore(expr, dict1);
GetTrueAssignmentListCore(expr, dict2);
}
}
/// <summary>Parse string to proposition object</summary>
/// <param name="expr">Parsed proposition object</param>
/// <param name="result">Result of parsing</param>
/// <param name="str">String to parse</param>
/// <returns>True if success parsing</returns>
public bool TryParse(out Proposition expr, out string result, string str)
{
expr = null; result = "";
backIndex = 0;
index = 0;
try
{
input = Normalize(str).ToCharArray();
expr = ParseWithPrec(PREC_MAX);
}
catch (ParseException e)
{
result = e.Message;
return(false);
}
if (index != input.Length)
{
result = ParseException.REASON_NOT_READ_ALL; return(false);
}
return(true);
}
/// <summary>Find next proposition from current position</summary>
/// <returns>Proposition</returns>
private Proposition GetNextExpression()
{
string s = GetNextToken();
if (s == SYMBOL_LP)
{
Proposition expr = ParseWithPrec(PREC_MAX);
if (!MoveNext(SYMBOL_RP))
{
throw new ParseException("NOT_MATCH_PARN", index.ToString());
}
return(expr);
}
else if (s == SYMBOL_NOT)
{
Proposition expr = ParseWithPrec(PREC_NOT);
return(new Proposition(Operator.Not, expr));
}
else
{
return(new Proposition(Operator.Atom, new Atom(s)));
}
}
/// <summary>Tautology core engine</summary>
/// <param name="expr">Proposition to check</param>
/// <returns>True if tautology</returns>
private bool IsTautologyCore(Proposition expr)
{
if (expr.op == Operator.Atom)
{
if (expr.atom.Symbol == "T")
{
return(true);
}
else
{
return(false);
}
}
else if (expr.op == Operator.Not)
{
if (expr.atom.Symbol == "F")
{
return(true);
}
else
{
return(false);
}
}
else if (expr.op == Operator.And)
{
return(IsTautologyCore(expr.left) && IsTautologyCore(expr.right));
}
else if (expr.op == Operator.Or)
{
return(expr.IsTautologyClause());
}
else
{
return(false);
}
}
/// <summary>Make proposiiton with operator and two sub-proposition</summary>
/// <param name="op">Operator of proposition</param>
/// <param name="expr1">First sub-proposition of proposition</param>
/// <param name="expr2">Second sub-proposition of proposition</param>
public Proposition(Operator op, Proposition expr1, Proposition expr2) : this(op, null, expr1, expr2)
{
}
/// <summary>Convert given proposition to negative normal form</summary>
/// <param name="expr">Proposition to convert</param>
/// <exception cref="InvaildPropositionException"></exception>
/// <returns>NNF proposition</returns>
public Proposition ConvertToNNF(Proposition expr)
{
if (expr == null || !expr.IsVaild())
{
throw new InvalidPropositionException("INVAILD");
}
if (expr.op == Operator.Atom)
{
return(expr);
}
else if (expr.op == Operator.Or) // S(P|Q) => S(P)|S(Q)
{
return(new Proposition(Operator.Or,
ConvertToNNF(expr.left),
ConvertToNNF(expr.right)));
}
else if (expr.op == Operator.And) // S(P&Q) => S(P)&S(Q)
{
return(new Proposition(Operator.And,
ConvertToNNF(expr.left),
ConvertToNNF(expr.right)));
}
else if (expr.op == Operator.Imply) // S(P->Q) => S(~P)|S(Q)
{
return(new Proposition(Operator.Or,
ConvertToNNF(new Proposition(Operator.Not, expr.left)),
ConvertToNNF(expr.right)));
}
else if (expr.op == Operator.IfOnlyIf) // S(P<->Q) => S(P->Q)&S(Q->P)
{
return(new Proposition(Operator.And,
ConvertToNNF(new Proposition(Operator.Imply, expr.left, expr.right)),
ConvertToNNF(new Proposition(Operator.Imply, expr.right, expr.left))));
}
else if (expr.op == Operator.Not) // S(~P) =>
{
Proposition nexpr = expr.left;
if (nexpr.op == Operator.Atom) // S(T) => F, S(F) => T, S(~P) => ~P
{
if (nexpr.atom.Symbol == "T")
{
return(new Proposition(Operator.Atom, new Atom("F")));
}
else if (nexpr.atom.Symbol == "F")
{
return(new Proposition(Operator.Atom, new Atom("T")));
}
else
{
return(expr);
}
}
if (nexpr.op == Operator.Imply) // S(P->Q) => S(~P)|S(Q)
{
nexpr = new Proposition(Operator.Or,
ConvertToNNF(new Proposition(Operator.Not, nexpr.left)),
ConvertToNNF(nexpr.right));
}
else if (nexpr.op == Operator.IfOnlyIf) // S(P<->Q) => S(P->Q)&S(Q->P)
{
nexpr = new Proposition(Operator.And,
ConvertToNNF(new Proposition(Operator.Imply, nexpr.left, nexpr.right)),
ConvertToNNF(new Proposition(Operator.Imply, nexpr.right, nexpr.left)));
}
if (nexpr.op == Operator.Or) // S(~(P|Q)) => ~S(P)&~S(Q)
{
return(new Proposition(Operator.And,
ConvertToNNF(new Proposition(Operator.Not, nexpr.left)),
ConvertToNNF(new Proposition(Operator.Not, nexpr.right))));
}
else if (nexpr.op == Operator.And) // S(~(P&Q)) => ~S(P)|~S(Q)
{
return(new Proposition(Operator.Or,
ConvertToNNF(new Proposition(Operator.Not, nexpr.left)),
ConvertToNNF(new Proposition(Operator.Not, nexpr.right))));
}
else if (nexpr.op == Operator.Not) // S(~(~P))) => S(P)
{
return(ConvertToNNF(nexpr.left));
}
}
return(null);
}
