Workshop on Formal Theories of Group Agency

Abstract: In this talk, I will show how to obtain better-behaved fragments of STIT-like logics via borrowing techniques from cylindric algebras. On the first glance, the connection between cylindric algebras and logics of group agency is accidental. I will use this case as an example to ruminate over why we use modal logic and other formalisms to come up with philosophical arguments.

Abstract: TBA

We argue that an important part of the practice of logic in philosophy and in computer science is best understood as an exercise in mathematical modeling, akin, for instance, to modeling in economics. Viewed this way, past and current debates in epistemic and deontic logic, for instance, can be reformulated as raising questions of the nature of idealizations, and the epistemic potential of logical models. The practice of logical modelling, we suggest, is best understood as the construction and the study of so-called minimal and toy models. In philosophy, such models typically function as exploratory models aimed at learning about the structure of a target theory. In computer science and AI, they function as engineering models, intended to enable reliable and tractable reasoning over a phenomenon rather than to learn about it. Taken together, these roles show that viewing logic as a mathematical modelling practice is, contra to what has been suggested in the literature, far from a trivial observation, and that it gives a unifying perspective how logic is used in philosophy, in computer science and in AI. Time permitting, we will also discuss how viewing logic as an (economic) model sheds light on questions of logical pluralism and anti-exceptionalism. 

Consider multi-agent systems represented by multi-player concurrent games, where coalitions of agents aim to achieve coalitional goals by following a joint “winning strategy” consisting of their individual strategies. Usually, a coalition may have several joint winning strategies, and then the agents in that coalition need to coordinate on one such joint strategy. When the agents in the coalition cannot communicate before or during the play of the game, their coordination becomes a non-trivial problem which does not always have a guaranteed solution. A well-know simple example for that is the  “Coordinated attack problem”. 

In this talk I will present an ongoing work which proposes an approach for solving the coordination problem described above by employing the theory of “pure win-lose coordination games” (WLC games) developed in a series of recent papers by Goranko, Kuusisto, and Rönnholm. I will present and discuss an example on which I will illustrate the coordination problem and the proposed methodology for solving it by reduction to solving WLC games. I will then outline and discuss a modified semantics for the coalitional strategic operators featuring in Coalition logic (CL) and Alternating time temporal logic (ATL) that imposes the stronger requirement of existence of a joint winning strategy on which the agents in the coalition can coordinate with certainty, by applying suitable principles of rational coordination in WLC games.