ALX, an action logic for agents with bounded rationality

Abstract

We propose a modal action logic that combines ideas from H.A. Simon's bounded rationality, S. Kripke's possible world semantics, G.H. von Wright's preference logic, Pratt's dynamic logic, Stalnaker's minimal change and more recent approaches to update semantics. ALX (the xth action logic) is sound, complete and decidable, making it the first complete logic for two-place preference operators. ALX avoids important drawbacks of other action logics, especially the counterintuitive necessitation rule for goals (every theorem must be a goal) and the equally counterintuitive closure of goals under logical implication.