- 实验目的和要求
实验目的：理解命题逻辑相关运算，增强逻辑推理能力
实验要求：
(1).从键盘输入命题常元的真值求他们的合取、析取、求反、异或、单条件、 双条件以及命题表达式的真值。
(2).求任意一个给定命题表达式的真值表，并根据真值表给出主范式。
思路：对于求合取、析取、求反、异或、单条件（蕴含）、 双条件（等价）这些基础逻辑运算比较容易实现，对于常元与（2）的变元表达式，可以使用双栈结构（类似双栈计算器），借助栈的“先进后出”特性来解析表达式子；注意表达式的输入格式。
2. 实验环境和工具
开发环境：Visual Studio 2019
3. 实验结果
3.1 程序流程图
3.2 程序代码 （仅供参考，水平有限，有错请指出）
#include#include #include #include #include using namespace std; void show() { cout << "******************************" << endl; cout << "***********逻辑运算***********" << endl; cout << " 1——逻辑与运算" << endl; cout << " 2——逻辑或运算" << endl; cout << " 3——逻辑非运算" << endl; cout << " 4——逻辑异或运算" << endl; cout << " 5——逻辑单条件运算" << endl; cout << " 6——逻辑双条件运算" << endl; cout << " 7——逻辑常元表达式运算" << endl; cout << " 8——逻辑变元表达式运算" << endl; cout << " 0——程序退出" << endl; cout << "******************************" << endl; cout << endl; } void menu1() { cout << "----------------使用说明----------------" << endl; cout << "========================================" << endl; cout << "== true用'1' false用'0' ==" << endl; cout << "== 命题变元字母不能重复且数量小于8 ==" << endl; cout << "== 逻辑变元用单个字母表示 ==" << endl; cout << "== 与逻辑用'*' 或逻辑用'+' ==" << endl; cout << "== 非逻辑用'!' 异或逻辑用'^' ==" << endl; cout << "== 单条件用'>' 双条件用'=' ==" << endl; cout << "=======================================" << endl; } void menu2() { cout << "----------------使用说明----------------" << endl; cout << "========================================" << endl; cout << "== 命题变元所用字母不能重复 ==" << endl; cout << "== 且变元个数不能超过8个 ==" << endl; cout << "== 逻辑变元用单个字母表示 ==" << endl; cout << "== 与逻辑用'*' 或逻辑用'+' ==" << endl; cout << "== 非逻辑用'!' 异或逻辑用'^' ==" << endl; cout << "== 单条件用'>' 双条件用'=' ==" << endl; cout << "========================================" << endl; } stack opr; stack opr1; stack cal; bool calculate() { bool a = 0, b = 0; char c = '0'; c = cal.top(); cal.pop(); if (c != '!') { b = opr.top(); opr.pop(); } a = opr.top(); opr.pop(); switch (c) { case '!': return !a; case'*': return a && b; case'+': return a || b; case'>': { if (a == 1 && b == 0) return 0; else return 1; } case'=': return a == b; } } int priority(const char ch)//符号优先级判断 { //¬, ∧, ∨, →, ↔ switch (ch) { case'(': return 0; case'^': return 1; case'=': return 2; case'>': return 3; case'+': return 4; case'*': return 5; case'!': return 6; case')': return 7; } } bool pack(string str1) { char ch = '0'; int lv1 = 0, lv2 = 0; bool r = 0, result = 1; int i = 0, len = str1.size() - 1;//读到最后一个 while (i < len)//扫描式子 { if (str1[i] == '0' || str1[i] == '1') { if (str1[i] == '0') { r = 0; opr.push(r); } else { r = 1; opr.push(r); } i++; } else { if (cal.empty()) { cal.push(str1[i]); i++; continue; } else { ch = cal.top(); lv1 = priority(ch); lv2 = priority(str1[i]); if (lv2 == 0) { cal.push(str1[i]); i++; } else if (lv2 == 7) { ch = cal.top(); while (ch != '(') { result = calculate(); opr.push(result); ch = cal.top(); } cal.pop();//弹出左括号 i++; } else { while (!cal.empty() && lv2 <= lv1) { result = calculate(); opr.push(result); if (!cal.empty()) { ch = cal.top(); lv1 = priority(ch); } } cal.push(str1[i]); i++; } } } } while (!cal.empty())//当把式子读完且操作符栈仍非空时 { result = calculate();//计算 opr.push(result); } if (cal.empty()) return result; } void case1(bool P, bool Q, bool result) { cout << "请输入真值value1和value2："; cin >> P >> Q; result = P && Q; cout << "逻辑与结果为：" << result << endl; cout << endl; } void case2(bool P, bool Q, bool result) { cout << "请输入真值value1和value2："; cin >> P >> Q; result = P || Q; cout << "逻辑或结果为：" << result << endl; cout << endl; } void case3(bool P, bool result) { cout << "请输入真值value1："; cin >> P; result = !P; cout << "逻辑非结果为：" << result << endl; cout << endl; } void case4(bool P, bool Q, bool result) { cout << "请输入真值value1和value2："; cin >> P >> Q; result = P ^ Q; cout << "逻辑异或结果为：" << result << endl; cout << endl; } void case5(bool P, bool Q, bool result) { cout << "请输入真值value1和value2："; cin >> P >> Q; if (P == 1 && Q == 0) result = 0; cout << "逻辑单条件结果为：" << result << endl; cout << endl; } void case6(bool P, bool Q, bool result) { cout << "请输入真值value1和value2："; cin >> P >> Q; if (P != Q) result = 0; cout << "逻辑双条件结果为：" << result << endl; cout << endl; } void case7() { string str1; cout << "请输入表达式<以#键结束>："; cin >> str1; cout << "运算结果为：" << pack(str1) << endl; cout << endl; } void case8() { string s; cout << "请输入表达式<以#键结束>："; cin >> s; s.pop_back(); vector letter, disjunctive, conjunctive; //letter存放字母 for (int i = 0; i < s.size(); i++) { if ((s[i] > 64 && s[i] < 91) || (s[i] > 96 && s[i] < 123)) {//大小写26个字母 letter.push_back(s[i]); } } //真值表 cout << "真值表为：" << endl; cout << "————————————————————" << endl; for (int i = 0; i < letter.size(); i++) cout << letter[i] << " "; cout << s << endl; cout << "————————————————————" << endl; vector letters = letter; int d; stack stk; for (int i = 0; i < pow(2, letter.size()); i++) { int t = i; string s1 = s; for (int j = 0; j < letter.size(); j++) { d = t % 2; t = t / 2; stk.push(d); } for (int k = 0; k < letter.size(); k++) { int top = stk.top(); cout << top << " "; s1[s1.find(letter[k])] = top + 48;//转成char型的0和1 stk.pop(); } s1.push_back('#'); bool c = pack(s1); cout << c << endl; //主析取范式 if (c == true) { int num = 0; disjunctive.push_back('('); for (int i = 0; i < s1.size(); i++) { if (s1[i] == 48) //真值为0，加! { disjunctive.push_back('!'); disjunctive.push_back(letters[num]); disjunctive.push_back('*'); num++; } else if (s1[i] == 49) //真值为1 { disjunctive.push_back(letters[num]); disjunctive.push_back('*'); num++; } else if (s1[i] == '#') break; else continue; } disjunctive.pop_back(); disjunctive.push_back(')'); disjunctive.push_back('+'); } //主合取范式 else { int num = 0; conjunctive.push_back('('); for (int i = 0; i < s1.size(); i++) { if (s1[i] == 49) {//真值为1，加! conjunctive.push_back('!'); conjunctive.push_back(letters[num]); conjunctive.push_back('+'); num++; } else if (s1[i] == 48) {//真值为0 conjunctive.push_back(letters[num]); conjunctive.push_back('+'); num++; } else if (s1[i] == '#') break; else continue; } conjunctive.pop_back(); conjunctive.push_back(')'); conjunctive.push_back('*'); } } disjunctive.pop_back(); conjunctive.pop_back(); cout << "————————————————————" << endl; cout << "主析取范式为："; for (int i = 0; i < disjunctive.size(); i++) { cout << disjunctive[i]; } cout << endl << "主合取范式为："; for (int i = 0; i < conjunctive.size(); i++) { cout << conjunctive[i]; } cout << endl; cout << endl; } int main() { int choice = 0; bool p = 0, q = 0, r = 0, result = 1; show(); while (true) { cout << "请输入您要进行逻辑运算的符号："; cin >> choice; switch (choice) { case 1: menu1(); case1(p, q, result); break; case 2: menu1(); case2(p, q, result); break; case 3: menu1(); case3(p, result); break; case 4: menu1(); case4(p, q, result); break; case 5: menu1(); case5(p, q, result); break; case 6: menu1(); case6(p, q, result); break; case 7: case7(); break; case 8: menu2(); case8(); break; case 0: exit(0); break; default: cout << "输入错误请重新输入!" << endl; break; } } return 0; }
3.3 运行结果
（1）逻辑与运算
（2）逻辑或运算：
（3）逻辑非运算：
（4）逻辑异或运算：
（5）逻辑单条件运算：
（6）逻辑双条件运算：
（7）命题常元表达式运算：
（8）命题变元表达式运算：
其他实验：合肥工业大学2021离散数学上机实验四https://blog.csdn.net/qq_52791068/article/details/122656507合肥工业大学2021离散数学上机实验六https://blog.csdn.net/qq_52791068/article/details/122656801
合肥工业大学2021离散数学上机实验八https://mp.csdn.net/mp_blog/creation/editor/122663212
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