Free choice and contextually permitted actions
This paper offers a solution to the paradox of free-choice permission, that \(Pp\to P (p\vee q)\). This is often resolved by distinguishing two permission operators, a `weak' permission, \(P_w\), which satisfies \(P_w (p\vee q) \equiv P_w p\vee P_w\) \(q\), and a `strong' permission, \(P_s\), which satisfies \(P_s (p\vee q) \equiv P_s p \& P_s q\). Free-choice permission is supposed to be the latter, and for it the above entailment does not hold. Nevertheless, \(P_s p \to P_s(p \& q)\) now holds instead, which is probably worse. This paper presents a more sophisticated notion of free-choice permission within the framework of a general logic of action statements that allows a limiting of the contexts in which an action is permitted and the introduction of an operator `only', so that one may assert that only \(\alpha\) is performed in a context. On this basis the strong permission operator seems more benign when one interprets ordinary language assertions that an act \(\alpha\) is performed as expressing that only \(\alpha\) is performed, for then the above entailment for strong permission seems unproblematic.
scientific article; zbMATH DE number 929968