---
title: 2024-2025学年上学期期末
---
## 2024-2025学年上学期期末(不全)

### 简答题

1. What is the definition of validity for a propositional logic formula?

2. Please explain how to determine whether a given propositional logic formula with CNF is valid.

3. Please illustrate the different treatment for free and bound variables in the semantical evaluation of a predicate logic formula.

4. Please state the key idea of program verification using model checking techniques.

### 计算题

1. Convert the following formula into CNF and draw its parse tree: $(p \vee q \rightarrow r ) \rightarrow r \vee s$

2. Translate the following statements into predicate logic formula:

3. model checking

### 证明题

1. Prove the following statement: $(p \wedge q) \rightarrow r \vdash (p \rightarrow r) \vee (q \rightarrow r)$

2. Prove the following sequent doesn't hold using semantical evaluation:
  $\forall x \exists y P(x,y) \models \exists y \forall x P(x,y)$

3. Prove the total correctness of the following hoare triplet: $\\{ x \geq 0 \wedge y > 0 \\} Div \\{ y=d*x+r \wedge r < y \\}$

```cpp
Div:
  {pre-condition}
  r = y;
  d = 0;
  while (r >= y) {
    r = r - y;
    d = d + 1;
  }
  {post-condition}
  ```