Temporal Logics of Agency

Time is the grand stage where human activities take place (rational or otherwise). And the view of a branching temporal universe, or tree of possible events, with our actual history linearly advancing through it, is a widely shared cultural idea, not confined to Academia (cf. Borges brilliant 1941 essay El Jard́ın de senderos que se bifurcan). Even though logic is often considered a study of timeless propositions, temporal languages and logics over tree structures have a long tradition. Philosophers have studied temporal structure and temporal reasoning since the 1950s, from the ‘tense logic’ of Prior [23] to the ‘STIT’ system of Belnap et al. [1]. Moreover, starting from the 1970s, computer scientists have joined in, and developed many further flavours of temporal logic, with major strands such as Pnueli on program correctness [18], Emerson and Clark on process specification and verification [5,6], Reiter on the situation calculus in AI [25], and Thomas on the automata-theoretic foundations of computing [26]. In addition, the pure firstand second-order logic of tree-like structures, starting from the Rabin’s classic decidability result [24], provides deeper background (cf. [12]). The chapter by Hodkinson and Reynolds on ‘Temporal Logic’ in the Handbook of Modal Logic [15] brings together many of these trends in one mathematical narrative. But the field of reasoning in, and about, time can be mapped out in many further ways: Van Benthems chapter Temporal Logic in the Handbook of Logic in Artificial Intelligence and Logic Programming [27] also includes issues in natural language semantics, discourse representation, and the duality between interval and point ontologies. Nowadays, temporal logics play an important role in theories of agency, an area where philosophy and computer science meet with other disciplines, such as game theory. Over the last decades, various paradigms have emerged for studying agents that process information and acquire knowledge while acting over time. In computer science, Interpreted Systems [8] and Epistemic Temporal Logic [21,22] are major examples,