3.4.7. (a) In some systems of logic (mostly constructive systems where ‘true’ is taken to mean ‘provable’) there is a rule if (Γ |- (φ ∨ ψ)) is a correct sequent then at least one of (Γ |- φ) and (Γ |- ψ) is also correct. By giving a counterexample to a particular instance, show that this is unacceptable as a rule for LP. [Start by giving counterexamples for both the sequents (|- p0) and (|- (¬p0)).]


(b) Aristotle (Greece, fourth century bc), who invented logic, once said ‘It is not possible to deduce a true conclusion from contradictory premises’ (Prior Analytics 64b7). He must have meant something subtler, but his statement looks like the following sequent rule: if ({φ} |- ψ) and ({(¬φ)} |- ψ) are correct sequents, then so is the sequent ( |-(¬ψ)). By giving a counterexample to a particular instance, show that this is unacceptable as a rule for LP.


위 2문제 입니다.


(a), (b) 모두 어떤 Sequent Rule의 counterexample을 찾으라는 문제입니다.


그런데 제가 이해하기론 []안에 있는 hint도 그렇고 true이면서 동시에 false로 interpreted 되는 propositional symbol이 있어야 답이 나오는 느낌이라서요.


답을 도저히 모르겠네요.


출처: Chiswell, I., & Hodges, W. (2013). Mathematical logic (p. 61). Oxford: Oxford University Press.