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

Abstract

Spatial constraint systems are algebraic structures from concurrent constraint programming to specify spatial and epistemic behavior in multi-agent systems. In this paper spatial constraint systems are used 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, a necessary and sufficient condition for the existence of right inverses is identified and the abstract notion of normality is shown to correspond to the preservation of finite suprema. Furthermore, a taxonomy of normal right inverses is provided, identifying the greatest normal right inverse as well as the complete family of minimal right inverses. These results are applied to existing modal languages such $ This work has been partially supported by the Colciencias project 125171250031 CLASSIC, STIC Am-Sud 17-STIC-04 project EPIC, and COFINPRO2016 project 4473 CREATE.

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].…”

A Rewriting Logic Approach to Stochastic and Spatial Constraint System Specification and Verification

“…The authors of [29] extended the notion of CS to account for distributed and multi-agent scenarios where agents have their own space for local information and computation. In [19,22,23,25,21] CS are further extended to model mobile behaviour and reason about beliefs, lies, and group epistemic behaviour inspired by social networks.…”

“…M. Guzman et al [20] develop the theory of spatial constraint systems to provide a mechanism for specifying the mobility of information or processes from one space to another. In [24], spatial constraint systems are used as an abstract representation of modal logics. This is useful to characterize the notion of normality for self-maps in a constraint system.…”