课程名称︰ 逻辑 课程性质︰ 通识 A4 课程教师︰ 傅皓政 开课学院： 开课系所︰ 考试日期（年月日）︰2019/06/17 考试时限（分钟）：90分钟 试题 : 一、建构初阶逻辑语言 (提示：包括符号与形构规则两个部分)。 (10%) Construct a suitable language for first-order (or predicate) logic. Hint: two parts should be involved, alphabets and formation rules. 二、请以亚里斯多德的方法证明下列三段论的论证是否为有效论证，如为无效论证请写出 具有说服力的反例。 (15%) Please use the Aristotle's method to prove whether the arguments of the following syllogisms are valid arguments. For the invalid arguments, please write a persuasive counterexample. (a) M A P (b) S E M (c) S A M M A S P E M M A P ------- ------- ------- S A P S E P S I P 三、请将下列日常语言的语句翻译为初阶逻辑语言的表达式。 (15%) Please translate the following ordinary language statements into expressions of the first-order logic language. Cx: x是市民(x is a citizen) ； Hxy: x帮助y (x will help y) (a) 没有市民会帮助任何一个市民。 No citizen will help any citizen. (b) 没有市民会帮助每个市民。 No citizen will help every citizen. (c) 每个市民都会帮助某些市民。 Every citizen will help some citizens 四、请以真值树法证明下列语法序列是否为有效论证，若为无效论证请显示其反例节构。 (20%) Please use the tableaux method to prove whether the following sequence is a valid arguments. If it is an invalid argument, please show its counter-example structure. (a) (∀x)(GxＶHx), (∀x)(Hx→Kx) ├ (∀x)GxＶ(∀x)Kx (b) (∃x)Lx→(∀x)(Kx→(∃y)Mxy), (∀x)(∀y)(Mxy→Nx) ├ (∀x)((LxΛKx)→(∃y)Ny) 五、请以实例说明下列谬误，并说明为什麽它是这类谬误。 (10%) Please exemplify the following fallacies and explain why it is such a fallacies. (a) 人身攻击的谬误 Argument against the person (b) 滑坡谬误 Slippery Slope Fallacy 六、请完成下列演算，作答时需连同题目写在答案卷上。 (20%) Please complete the following calculations, and write the answer sheet together with the diagram. (a) ├ ﹁(P↔﹁P) P↔﹁P P↔﹁P ------- ------- P P→﹁P ﹁P ﹁P→P -------------- ---------------- P ﹁P P ﹁P ----------------- ------------------- ⊥ ⊥ --------- ------- ﹁P P ----------------------------------------- ⊥ ------------- ﹁(P↔﹁P) (b) (∀x)(Lx→(∃y)(LyΛMxy)), (∃x)(LxΛ(∀y)((LyΛMxy)→Nxy)) ├ (∃x)(∃y)((LxΛLy)→Nxy) 1. (∀x)(Lx→(∃y)(LyΛMxy)) __Pr__ 2. (∃x)(LxΛ(∀y)((LyΛMxy)→Nxy)) __Pr__ 3. LaΛ(∀y)((LyΛMay)→Nay) ______ 4. La ______ 5. La→(∃y)(LyΛMay) ______ 6. (∃y)(LyΛMay) ______ 7. LbΛMab ______ 8. (∀y)((LyΛMay)→Nay) ______ 9. (LbΛMab)→Nab ______ 10. Nab ______ 11. NabＶ﹁La ______ 12. (NabＶ﹁La)Ｖ﹁Lb ______ 13. NabＶ(﹁LaＶ﹁Lb) ______ 14. NabＶ﹁(LaΛLb) ______ 15. ﹁(LaΛLb)ＶNab ______ 16. LaΛLb→Nab ______ 17. (∃y)((LaΛLy→Nay) ______ 18. (∃x)(∃y)((LxΛLy)→Nxy) ______ 七、请说明罗素确定描述词理论的内容及其重要性为何。 (10%) Please briefly explain the content and significance of Russell's theory of description. *题目後附推论规则 1. 树状自然演绎法推论规则(rules of inferences: tree-likely natural deduction) 2. 线性自然演绎法推论规则(rules of inferences: linearly natural deduction) --- --

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