public formula make_SSF()
{
if (this.is_PNF)
{
formula ssf = new formula();
if (this.top_operation is quantifier)
{
int all_quantors = 0;
int existance_quantors = -1;
ArrayList all_variables = new ArrayList();
ArrayList quantifiers = new ArrayList();
while (this.is_quantum_expression && top_operation is quantifier)
{
quantifier K = new quantifier((quantifier)this.top_operation);
if (K.is_universality)
{
all_quantors++;
quantifiers.Add(K);
this.logical_exp.RemoveAt(0);
all_variables.Add(K.variable);
}
else // if (K.is_existance)
{
existance_quantors++;
if (all_quantors == 0)
{
this.logical_exp.RemoveAt(0);
this.rename_variable(K.variable, "const");
}
else
{
this.logical_exp.RemoveAt(0);
function scolem = new function("s" + existance_quantors, all_variables);
ssf = this.change_variable(K.variable, scolem);
}
}
}
ssf.logical_exp.InsertRange(0, quantifiers);
}
else
{
return(ssf);
}
return(ssf);
}
else
{
MessageBox.Show("Для сколемизации формула должна быть в ПНФ!", "Ошибка");
return(this);
}
}
//взять связанную переменную из квантора
public string get_bounded_variable(operation this_operation)
{
string var = "";
if (this_operation is quantifier)
{
quantifier K = new quantifier((quantifier)this_operation);
var = K.variable;
}
else
{
throw new Exception("Нельзя взять связанную переменную, так как операция - не квантор");
}
return(var);
}
public formula get_basic()
{
if (this.is_basic)
{
return(this);
}
formula func = new formula();
//если вдруг импликация
if (top_operation is imp)
{
func = (~(first_operand.get_basic())).get_basic() | second_operand.get_basic();
}
else
{
if (top_operation.dimension == 1)
{
func = first_operand.get_basic();
func.logical_exp.Insert(0, top_operation);
}
else
{
if (top_operation is dis)
{
func = first_operand.get_basic() | second_operand.get_basic();
}
else
{
func = first_operand.get_basic() & second_operand.get_basic();
}
}
}
//отрицание перед скобками
if (top_operation is neg)
{
formula negation_trick = new formula(first_operand.logical_exp);
if (negation_trick.top_operation is neg)
{
negation_trick.logical_exp.RemoveAt(0); //убираем второе отрицание
}
if (negation_trick.top_operation is quantifier)
{
quantifier K = new quantifier((quantifier)negation_trick.top_operation);
K.change_quant();
negation_trick.logical_exp.RemoveAt(0);
negation_trick = (~negation_trick).get_basic();
negation_trick.logical_exp.Insert(0, K);
}
//применяем правила ДеМоргана:
if (negation_trick.top_operation is kon)
{
negation_trick = (~(negation_trick.first_operand.get_basic())).get_basic() | (~(negation_trick.second_operand.get_basic())).get_basic();
}
else if (negation_trick.top_operation is dis)
{
negation_trick = (~(negation_trick.first_operand.get_basic())).get_basic() & (~(negation_trick.second_operand.get_basic())).get_basic();
}
return(negation_trick);
}
return(func);
}
public formula make_PNF()
{
if (this.is_PNF)
{
return(this);
}
formula pnf = new formula();
if (top_operation is quantifier)
{
quantifier K1 = new quantifier((quantifier)top_operation);
//bounded_variables.Add(K1.variable);
pnf = first_operand.make_PNF();
pnf.logical_exp.Insert(0, top_operation);
return(pnf);
}
else
{
//1 правило вноса атомов под квантор
if (top_operation is dis)
{
if (first_operand.is_free_from_quntifiers && second_operand.is_free_from_quntifiers) //два атома => итак уже пнф
{
return(first_operand | second_operand);
}
else if (first_operand.is_free_from_quntifiers && second_operand.is_quantum_expression) //атом и кванторное выражение => записываем атом под квантор
{
pnf = first_operand | second_operand.first_operand.make_PNF();
pnf.logical_exp.Insert(0, second_operand.top_operation);
pnf = pnf.make_PNF();
}
else if (!first_operand.is_free_from_quntifiers && first_operand.top_operation is quantifier) //два кванторных выражения
{
string variable = get_bounded_variable(first_operand.top_operation);
if (second_operand.is_free_from(variable))
{
pnf = first_operand.first_operand.make_PNF() | second_operand.make_PNF();
pnf.logical_exp.Insert(0, first_operand.top_operation);
pnf = pnf.make_PNF();
}
}
else if (!second_operand.is_free_from_quntifiers && second_operand.top_operation is quantifier)
{
string variable = get_bounded_variable(second_operand.top_operation);
if (first_operand.is_free_from(variable))
{
pnf = first_operand.make_PNF() | second_operand.first_operand.make_PNF();
pnf.logical_exp.Insert(0, second_operand.top_operation);
pnf = pnf.make_PNF();
}
}
}
else if (top_operation is kon)
{
if (first_operand.is_free_from_quntifiers && second_operand.is_free_from_quntifiers) //два атома => итак уже пнф
{
return(first_operand & second_operand);
}
else if (first_operand.is_free_from_quntifiers && second_operand.is_quantum_expression) //атом и кванторное выражение => записываем атом под квантор
{
pnf = first_operand & second_operand.first_operand.make_PNF();
pnf.logical_exp.Insert(0, second_operand.top_operation);
pnf = pnf.make_PNF();
}
else if (second_operand.is_free_from_quntifiers && first_operand.is_quantum_expression) //кванторное выражение и атом
{
pnf = first_operand.first_operand.make_PNF() & second_operand;
pnf.logical_exp.Insert(0, first_operand.top_operation);
pnf = pnf.make_PNF();
}
if (first_operand.is_quantum_expression && first_operand.top_operation is quantifier)
{
string variable = get_bounded_variable(first_operand.top_operation);
bounded_variables.Add(variable);
if (second_operand.is_free_from(variable))
{
pnf = first_operand.first_operand.make_PNF() & second_operand.make_PNF();
pnf.logical_exp.Insert(0, first_operand.top_operation);
pnf = pnf.make_PNF();
}
}
else if (second_operand.is_quantum_expression && second_operand.top_operation is quantifier)
{
string variable = get_bounded_variable(second_operand.top_operation);
//bounded_variables.Add(variable);
if (first_operand.is_free_from(variable))
{
pnf = first_operand.make_PNF() & second_operand.first_operand.make_PNF();
pnf.logical_exp.Insert(0, second_operand.top_operation);
pnf = pnf.make_PNF();
}
}
}
//2 - правила объединения кванторов
//2.1 - всеобщность
if (top_operation is kon)
{
if (first_operand.is_quantum_expression && second_operand.is_quantum_expression)
{
if (first_operand.top_operation is quantifier && second_operand.top_operation is quantifier)
{
quantifier K1 = new quantifier((quantifier)first_operand.top_operation);
//bounded_variables.Add(K1.variable);
quantifier K2 = new quantifier((quantifier)second_operand.top_operation);
if (K1.is_universality && K2.is_universality && K1.variable == K2.variable)
{
pnf = first_operand.first_operand & second_operand.first_operand;
pnf.logical_exp.Insert(0, first_operand.top_operation);
}
}
}
}
//2.2 - существование
if (top_operation is dis)
{
if (first_operand.is_quantum_expression && second_operand.is_quantum_expression)
{
if (first_operand.top_operation is quantifier && second_operand.top_operation is quantifier)
{
quantifier K1 = new quantifier((quantifier)first_operand.top_operation);
//bounded_variables.Add(K1.variable);
quantifier K2 = new quantifier((quantifier)second_operand.top_operation);
if (K1.is_existance && K2.is_existance && K1.variable == K2.variable)
{
pnf = first_operand.first_operand | second_operand.first_operand;
pnf.logical_exp.Insert(0, first_operand.top_operation);
}
}
}
}
//3 - правило выноса квантора за скобки (с переименованием связанных переменных)
if (top_operation is dis)
{
if (first_operand.is_quantum_expression && second_operand.is_quantum_expression)
{
quantifier K1 = new quantifier((quantifier)first_operand.top_operation);
//bounded_variables.Add(K1.variable);
quantifier K2 = new quantifier((quantifier)second_operand.top_operation);
if (K1.variable == K2.variable && bounded_variables.Contains(K2.variable))
{
pnf = first_operand.first_operand | second_operand.first_operand.rename_variable(K2.variable, K2.variable + "_renamed");
K2.variable = K2.variable + "1";
pnf.logical_exp.Insert(0, K2);
pnf.logical_exp.Insert(0, K1);
}
else if (!second_operand.is_free_from(K1.variable))
{
pnf = first_operand.first_operand | second_operand.first_operand.rename_variable(K1.variable, K1.variable + "_renamed");
pnf.logical_exp.Insert(0, K2);
pnf.logical_exp.Insert(0, K1);
}
else
{
pnf = first_operand.first_operand | second_operand.first_operand;
pnf.logical_exp.Insert(0, K2);
pnf.logical_exp.Insert(0, K1);
}
}
}
else if (top_operation is kon)
{
if (first_operand.is_quantum_expression && second_operand.is_quantum_expression)
{
quantifier K1 = new quantifier((quantifier)first_operand.top_operation);
quantifier K2 = new quantifier((quantifier)second_operand.top_operation);
if (K1.variable == K2.variable)
{
pnf = first_operand.first_operand & second_operand.first_operand.rename_variable(K2.variable, K2.variable + "_renamed");
K2.variable = K2.variable + "1";
pnf.logical_exp.Insert(0, K2);
pnf.logical_exp.Insert(0, K1);
}
}
}
return(pnf);
}
}
//конструктор копирования:
public quantifier(quantifier copy)
{
_quant = copy._quant;
_var = copy._var;
}