Algebraic Structures from Concurrent Constraint Programming Calculi for Distributed Information in Multi-Agent Systems

TL;DR

This paper develops algebraic and semantic structures called spatial constraint systems to analyze distributed information in multi-agent systems, with applications in mathematical morphology and infinite group reasoning.

Contribution

It introduces a novel algebraic framework for reasoning about distributed information using spatial constraint systems and characterizes their properties for infinite groups.

Findings

Distributed information is characterized as the infimum of join-preserving functions.

For completely distributive lattices, distributed information is the greatest information below all combinations.

Conditions are provided for finite groups to replicate infinite group information.

Abstract

Spatial constraint systems (scs) are semantic structures for reasoning about spatial and epistemic information in concurrent systems. We develop the theory of scs to reason about the distributed information of potentially infinite groups. We characterize the notion of distributed information of a group of agents as the infimum of the set of join-preserving functions that represent the spaces of the agents in the group. We provide an alternative characterization of this notion as the greatest family of join-preserving functions that satisfy certain basic properties. For completely distributive lattices, we establish that distributed information of a group is the greatest information below all possible combinations of information in the spaces of the agents in the group that derive a given piece of information. We show compositionality results for these characterizations and conditions under which information that can be obtained by an infinite group can also be obtained by a finite group. Finally, we provide an application on mathematical morphology where dilations, one of its fundamental operations, define an scs on a powerset lattice. We show that distributed information represents a particular dilation in such scs.