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)︰2017/04/07
考试时限(分钟):90
试题 :
一、请建构适用的命题逻辑语言(提示:包括符号与形构规则两个部分)10%
(Construct a suitable language for propositional logic. Hint:two parts
involved, Alphabets and Formation Rules)
二、请判断下列句式哪些是合宜的句式?哪些是不合宜的句式?10%
(Please consider the following formulae and distinguish the well-formed
formulae from ill-formed ones.)
(a) P → ~Q → R (b) ~~H~
(c) ~~A ^ B (d) (L v M ^ N) → (M v M)
(e) (~G ^ D) v (D <-> ~G v D) (f) H ; ~M <-> N
(g) (D <-> (E ^ ~F)) <-> E (h) (K → ~L) ^ (M <-> L)) ^ ~K
(i) A ^ (C → ~B) (j) →HK
合宜的句式:____________________________
不合宜的句式:___________________________
三、请判断下列陈述的真假,并且分别以T与F代表“真”与“假”。10%
(Please judge the following statements which are true or false.)
_ 1. 结论为矛盾句的论证必定是无效论证。
_ 2. 对前提不为空集合所有论证而言,若该论证是无效论证,则其前提可能在某
个情况全部为真。
_ 3. 前提与结论都实际上为真的论证必定是有效论证。
_ 4. 前提实际上为真而且结论实际上为假的论证可能是有效论证。
_ 5. 前提不可能全部为真的论证必定是有效论证。
_ 6. 前提与结论都实际上为假的论证可能是有效论证
_ 7. 前提与结论皆为恒真句的论证必定是有效论证。
_ 8. 前提中有矛盾句的论证必定是有效论证。
_ 9. 结论实际上为真的论证都是有效论证。
_ 10. 前提与结论均为偶真句的论证可能是有效论证。
四、请判断下列句式哪些是恒真句、矛盾句或者是未定句。你可以使用任何学过的方法,
包含真值表法或简易真值表法,必须列出演算过程。15%
(Using some method (Truth Table or Short-Cut) shows that the following
are Tautologies, Contradictions, or Indeterminate Fomulae. Computational
process is required.)
(a) ((M → N) → M) → M
(b) (G v H) → (H ^ K)
(c) (D → D) → (E ^ ~E)
五、请写出真值表并判断下列个题中两个句式之间是蕴含或是等值关系。如果是蕴含关
系,以ρ╞ ψ表示;若为等值关系,则以╞ ρ<-> ψ表示,必须列出演算过程。15%
(show the Truth Tables of the following formulas and determine the
semantic relation between them. If the entailment relation holds then
show them of the form ρ╞ ψ. On the other hand, show them of the form
╞ ρ<-> ψ if they are equivalent. Computational process is required.)
(a) L → (M → N) ; (L ^ M) → N
(b) ~((P → Q) v ~Q) ; ~Q v (Q → P)
(c) ((A ^ B) → C) v (B → ~C) ; A → C
六、请写出等值于语句ψ的DNF及CNF。10%
(Find out the DNF and CNF each which is equivalent to the following
formulae ψ.)
(a) ┌─┬─┬─┬──┐ (b) ψ: L <-> (M <-> N)
│P │Q │R │ ψ │
├─┼─┼─┼──┤
│T │T │T │ T │
├─┼─┼─┼──┤
│T │T │F │ F │
├─┼─┼─┼──┤
│T │F │T │ T │
├─┼─┼─┼──┤
│T │F │F │ T │
├─┼─┼─┼──┤
│F │T │T │ T │
├─┼─┼─┼──┤
│F │T │F │ F │
├─┼─┼─┼──┤
│F │F │T │ T │
├─┼─┼─┼──┤
│F │F │F │ F │
└─┴─┴─┴──┘
七、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结
构。20%
(Please use Tableaux to prove whether each of the following argument is
valid. And specify a counterexample if it is invalid.)
(a) (R ^ ~S) <-> R ; ~S v T╞ ~T → R
(b) ~G ; ~H <-> G ; ~G → H╞ H ^ (G → H)
八、(a)在说明古典逻辑条件句的真值表时,许多人会觉得某些情况的真假值与直觉判断
似乎有所出入,请举列说明之。5%
(b)如果妳认为古典逻辑对条件句的赋值方式是合理的,请解释如何消弥上述的问题。
反之,如果妳认为古典逻辑是不合理的,请显示你认为能够反应条件句的真值表,
并尝试说明你的理由。5%
(a)Some logicians contend that the assignment of conditionals in classical
logic seems to be counterintuitive. Please illustrate it with some
instances.
(b)If you agree with the assignment of conditionals provided by classical
logic, then try to explain away the puzzle. Nevertheless. try to
construct a compelling one and provide your reason for it if you do not
agree.
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