Title: Two-Sorted Social Friendly Coalition Logic

Speaker: Yuanzhe Yang (Peking University)

Time: 2025/4/1 (Tuesday) 15:10-18:00

Location: Room 215, Natural ​Sciences Teaching Building (理教), Peking University

Abstract:

Coalition Logic (initiated by Pauly (2001, 2002)) is a kind of modal logic that studies the actions of coalitions of agents under a multi-agent setting. Recently, Goranko and Enqvist (2018) proposed a new kind of coalition logic called "social friendly coalition logic (SFCL)", which employs operators that resembles the operators of instantial neighborhood modal logic (INL) proposed by van Benthem et al. (2017). In this talk, inspired by the two-sorted language for INL proposed in Wang and Yu (2024), we consider a two-sorted language for SFCL, in which one sort of formulas describes properties of states, and the other describes properties of joint actions. We offer a complete axiomatization for the two-agent case, and show that the satisfiability problem is decidable in this case. We also show that when we have three or more agents, the same axiomatization is actually incomplete; but when we restrict our language to a well-structured set of coalitions, completeness can again be achieved. Then, we introduce a stronger kind of two-sorted language, which merges SFCL and the "group protecting coalition logic (GPCL)" proposed in Goranko and Enqvist (2018), and offer a complete axiomatization for this logic in the language of restricted coalitions. We also show that the satisfiability problem is decidable in this case.