Colloquium: Agency and Time. Putting them together.

ABSTRACT: Time seems to play an important role in addressing a proper conceptual framework for agency: we make choices and then we act accordingly, we are responsible for a given course of events after we acted to the effect that such a course holds, and so on. Some prominent logics of agency – e.g. Coalition Logic (CL) and Alternating-Time Temporal Logic (ATL) – deal with agency without taking time into account. By contrast, Stit Logic (STIT) takes time into account, but cannot express temporal distinctions (“once in the past”, “once in the future”) within its language. In the present talk, I offer conceptual and technical reasons to endorse a logic that takes both agency and temporal distinction into account. Then, I introduce a mono-agent tempo-modal logic for discrete branching-time, called BTC, and I show that: 1) BTC expresses a discrete version of mono-agent STIT; 2) BTC is complete. These results are of great importance in the fields of time and agency. The first shows that BTC is a bridge between tempo-modal logics and the logics of agency. The second shows that the results also open interesting research perspectives. First, if completeness is paired with decidability, BTC can in principle be computed by a program. Second, recent results in the literature have shown that CL and ATL can be unravelled and expressed in some discrete version of STIT (say, turned into a fragment of some discrete STIT). Since mono-agent discrete STIT is expressed in BTC, it is probable that some multi-agent STIT are expressed in a version of BTC with many-agents. If the conjecture holds, BTC represents an interesting candidate to unify many logics of agency.