/**
* 章衡量词消去公式五 2 succ(_Y,_Z) -> ((theta(_X,_Z) | t(_X,_Z)) -> t(_X,_Y))
* @param originalFml 一阶语句
* @return
*/
Formula HengZhang::createFormula_5_2(const Formula& _originalFml) {
//1 _succ(_Y,_Z)
_term* term_y_z = Utils::combineTerms(m_vTermsY, m_vTermsZ);
_formula* succ_y_z = Utils::compositeToAtom(m_nSymbolSucc, term_y_z);
//2 T(_X,_Y)
_term* term_x_y = Utils::combineTerms(m_vTermsX, m_vTermsY);
_formula* t_x_y = Utils::compositeToAtom(m_nSymbolT, term_x_y);
//3 theta(_X,_Z)
Formula copyOriginalFml = _originalFml;
copyOriginalFml.replaceTerms(m_vTermsY, m_vTermsZ);
_formula* theta_x_z = Utils::copyFormula(copyOriginalFml.getFormula());
//4 T(_X,_Z)
_term* term_x_z = Utils::combineTerms(m_vTermsX, m_vTermsZ);
_formula* t_x_z = Utils::compositeToAtom(m_nSymbolT, term_x_z);
//create structure
_formula* left = succ_y_z;
_formula* rl = Utils::compositeByConnective(DISJ, theta_x_z, t_x_z);
_formula* right = Utils::compositeByConnective(IMPL, rl, t_x_y);
_formula* F = Utils::compositeByConnective(IMPL, left, right);
Formula fml = Formula(F, false);
return fml;
}
/**
* 章衡量词消去公式三 t(_X,_MIN) | theta(_X,_MIN)
* @param originalFml 一阶语句
* @return
*/
Formula HengZhang::createFormula_3(const Formula& _originalFml) {
//create left sub-formula t(_X,_MIN)
_term* term_x_min = Utils::combineTerms(m_vTermsX, m_vTermsMIN);
_formula* t_x_min = Utils::compositeToAtom(m_nSymbolT, term_x_min);
//create right sub-formula theta(_X,_MIN)
Formula copyOriginalFml = _originalFml;
copyOriginalFml.replaceTerms(m_vTermsY, m_vTermsMIN);
_formula* theta_x_min = Utils::copyFormula(copyOriginalFml.getFormula());
//create structure
_formula* F = Utils::compositeByConnective(DISJ, t_x_min, theta_x_min);
Formula fml = Formula(F, false);
return fml;
}
