Two variable fragment of Term Modal Logic

Term modal logics (TML) are modal logics with unboundedly many modalities, with quantification over modal indices, so that we can have formulas of the form Exists y Forall x (Box_x P(x,y) implies Diamond_y P(y,x)). Like First order modal logic, TML is also "notoriously" undecidable, in the sense that even very simple fragments are undecidable. In this paper, we show the decidability of one interesting fragment, that of two variable TML. This is in contrast to two-variable First order modal logic, which is undecidable

Epistemic Logics of Structured Intensional Groups

Epistemic logics of intensional groups lift the assumption that membership in a group of agents is common knowledge. Instead of being represented directly as a set of agents, intensional groups are represented by a property that may change its extension from world to world. Several authors have considered versions of the intensional group framework where group-specifying properties are articulated using structured terms of a language, such as the language of Boolean algebras or of description logic. In this paper we formulate a general semantic framework for epistemic logics of structured intensional groups, develop the basic theory leading to completeness-via-canonicity results, and show that several frameworks presented in the literature correspond to special cases of the general framework.Comment: In Proceedings TARK 2023, arXiv:2307.0400