Deriving Inverse Operators for Modal Logic

Abstract

International audienceSpatial constraint systems are algebraic structures from concurrent constraint programming to specify spatial and epistemic behavior in multi-agent systems. We shall use spatial constraint systems to give an abstract characterization of the notion of normality in modal logic and to derive right inverse/reverse operators for modal languages. In particular, we shall identify the weakest condition for the existence of right inverses and show that the abstract notion of normality corresponds to the preservation of finite suprema. We shall apply our results to existing modal languages such as the weakest normal modal logic, Hennessy-Milner logic, and linear-time temporal logic. We shall discuss our results in the context of modal concepts such as bisimilarity and inconsistency invariance

Semantic Structures for Spatially-Distributed Multi-Agent Systems

“…In [8,12] we developed the theory of spatial constraint systems (scs) with extrusion to specify information and processes moving from a space to another. In [11,10] scs with extrusion are used to give a novel algebraic characterization of the notion of normality in modal logic and to derive right inverse/reverse operators for modal languages. These results were applied to derive new expressiveness results for bisimilarity and well-established modal languages such as Hennessy-Milner logic, and lineartime temporal logic.…”

“…In [8,10,11,12] scs are used to reason about beliefs, lies and other epistemic utterances but also restricted to a finite number of agents and individual, rather than group, behaviour of agents.…”

“…These structures single out the notions we previously discussed: Namely, space, beliefs, and distributed information of potentially infinite groups. In this paper we will describe the theory of scs and highlight its main results from [8,10,11,12,9].…”

Characterizing right inverses for spatial constraint systems with applications to modal logic

“…This submission is the extended and revised version of [16] for the special issue of selected papers from ICTAC 2016. In this version we have included all proofs as well as new material in Section 5 corresponding to the derivation of all minimal normal right inverses.…”

“…In this version we have included all proofs as well as new material in Section 5 corresponding to the derivation of all minimal normal right inverses. The work in [16] does not study minimal right inverses. This submission thus offers a complete taxonomy of normal right inverses.…”