소요의 철학 아카이브

2023-2 Modal Logic (Segment 3) Q) Describe in some detail the different approaches to understanding possible worlds—e.g., out in Lycan’s discussion in “The Trouble with Possible Worlds”. What is the problem of how we know we are actual”? What are some main difficulties of and attempt at a combinatorial approach to possible worlds? What sense of “possible” seems more amenable to a combinatorial a..

2023-2 Modal Logic (Segment 2) Q) Evaluate the following wffs in the B-semantics + inclusion requirement and determine in what systems, K, T, S4, β, S5 (if any) they are valid. 1. (∃y)LM(ϕy ⊃ (∀x)ϕx) 2. L(∃x)(Lϕx ∨ ψy) ⊃ (∃x)L(Lϕx ∨ ψy) 3. L(M(∃x)ϕx ⊃ (∃x)Mϕx) 4. L(∃x)ϕx ⊃ (∃x)Lϕx

2023-2 Modal Logic (Segment 3) Q) Use the tableau method (which involves non-normal world idea) to determine whether the following are valid in Lewis’ systems S2, S3:1. Lp ⊃ LLp2. L( M(p ∧ q) ⊃ Mp)3. L(L(p ⊃ q ) ⊃ L(Lp ⊃ Lq))

2023-2 Modal Logic (Segment 3) Q) How might one use relevant logic to interpret C. I. Lewis’ strict implication as relevant entailment where we have:Give proofs of the wffs K and T in Lewis’s S1, i.e., prove:1. L(p ⊃ q) : ⊃: Lp ⊃ Lq2. Lp ⊃ p

2023-2 Modal Logic (Segment 3) Q) Routley-Meyer Semantics for Relevant Logic has this: Prove (using the semantics) the following:1. A & B .–▶. A v B 2. ¬¬A ◀– –▶ A 3. ¬(A & B) ◀– –▶.  ¬A v ¬B 4. ¬A –▶ B .–▶. ¬B –▶ A

2023-2 Modal Logic (Segment 3) Q) Explain why that (∀x)Roox yields (∀x)Roxo and collapses Relevent logic into classical logic. If is sufficient (for the present purposes) to just prove something that doesn’t hold in Relevant Logic, e.g., ¬A ∧ (A ∨ B) .–Ȝ. B. Why does it seem not to be viable to take relevant logic to be a universal logic (a logic that can capture all others?) #2) Generally speak..

2023-2 Modal Logic (Segment 1)① Determine whether the following valid in the systems indicated by the semantic tableauL(Lp ⊃ Lq) ∨ L(Lq ⊃ Lp)ML(p ⊃ LMp)② Determine which of the following are valid in K, D, T, S4, S5, B by tableaux.L(p ∨ Lq) .⊃. Lq ∨ LpM(p⊃p)Mp ⊃ LMMpLp ∧ M(q ⊃ r) :⊃: L(p⊃q) ⊃ M(p ∧ r)

2023-2 Modal Logic (Segment 1) Q) Prove the following by Translation into quantification theory (you may use conditional proof). Trans(R) & Symm(R) ├ Mp ∧ Mq .⊃. M(p ∧ Mq) Trans(R)├ M(Lp ⊃ Mq) ⊃ M(p ⊃ q) Symm(R) ├ p ⊃ LMp

양상 연산자(Modal operator) L(□)과 M(◇)의 중요한 특징 중 하나는 그것들이 '모든(∀)'과 '어떤(∃)'의 개념을 포함하고 있다는 점이다. 즉, (세계 w에서 성립하는) 명제 Lp는 w가 볼 수 있는 모든 세계에서 p가 성립함을 뜻한다는 점에서 '모든'의 개념을 포함한다. 마찬가지로, Mp는 w가 볼 수 있는 어떤(최소한 하나 이상의) 세계에서 p가 성립함을 의미한다는 점에서 '어떤'의 개념을 포함한다. 따라서 우리는 양상 연산자가 쓰인 모든 문장을 양화 이론(quantification theory)으로 번역할 수 있다. ① (Lp)ʷ와 (Mp)ʷ 우선 Lp와 Mp에 대한 정의는 다음과 같다: 여기에서 (Lp)ʷ가 의미하는 바는 w가 볼 수 있는 모든 세계 α에서 p가 성립한다는 것이..

G.E. Hughes & M.J. Cresswell, A New Introduction to Modal Logic, London and New York: Routledge, 1996, pp. 62-64. (8) The Brouwerian System ① B p ⊃ LMp B (or S5 (8)) p ⊃ LMp ② Translation into quantification theory ③ S5 (9) MLp ⊃ p S5 (9) MLp ⊃ p ④ Neither of these theorems is in S4. Indeed, if we were to add either as an extra axiom to S4 we should obtain a system at least as strong as S5. (In ..