Prawitz (1971) conjectured that proof-theoretic validity offers a semantics for intuitionistic logic. This conjecture has recently been proven false by Piecha and Schroeder-Heister (2019). This article resolves one of the questions left open by this recent result by showing the extensional alignment of proof-theoretic validity and general inquisitive logic. General inquisitive logic is a generalisation of inquisitive semantics, a uniform semantics for questions and assertions. The paper further defines a notion of quasi-proof-theoretic validity by restricting proof-theoretic validity to allow double negation elimination for atomic formulas and proves the extensional alignment of quasi-proof-theoretic validity and inquisitive logic.

Prawitz (1971) 推测证明理论有效性为直觉逻辑提供了语义。Piecha 和 Schroeder-Heister（2019）最近证明了这一猜想是错误的。本文通过展示证明理论有效性和一般探究逻辑的外延一致性，解决了这一最近结果留下的一个问题。一般探究逻辑是探究语义的概括，是问题和断言的统一语义。本文进一步定义了准证明理论有效性的概念，通过限制证明理论有效性来允许原子公式的双重否定消除，并证明了准证明理论有效性和好奇逻辑的外延对齐。