Qualitative action theory: A comparison of the semantics of alternating-time temporal logic and the Kutschera-Belnap approach to agency

Abstract

Qualitative action theory deals with purely qualitative descriptions and formal representations of agency, i.e., agents and their possibilities for intervening in the causal flow of events. This means that, contrary to game theory, qualitative action theory abstains from any metric evaluation of the outcomes of actions. In this paper we present and compare two qualitative approaches to action theory that have been discussed in the literature. The first one coming from philosophical action theory is the Kutschera-Belnap approach, which is the semantic basis of so-called Stit-logics. The second approach is the semantics of Alur, Henzinger, and Kupferman's Alternating-time Temporal Logic (ATL). In computer science, ATL has been introduced as an extension of Computational Tree Logic (CTL) to allow for modeling systems that interact with their environment. Surprisingly, although both approaches are very close in spirit, a systematic analysis of the mutual dependencies between these approaches does not exist. The paper aims at bringing together these two research streams, which seem to have been developed independently in philosophy and computer science. In particular, we will investigate the assumptions with which both approaches may be considered equivalent. Finally, further research on this topic promises interesting results that translate between the approaches presented here.