A many-sorted epistemic logic for chromatic hypergraphs

TL;DR

This paper introduces a many-sorted modal logic for multi-agent systems, enabling reasoning about local and global knowledge properties within chromatic hypergraph semantics, extending existing epistemic frameworks.

Contribution

It presents a novel many-sorted epistemic logic with semantics based on chromatic hypergraphs, unifying local and global knowledge reasoning in distributed systems.

Findings

Logic is sound and complete with respect to chromatic hypergraph semantics.

Connects chromatic hypergraphs with neighborhood frames.

Extends standard epistemic logic to multi-sorted, environment-aware reasoning.

Abstract

We propose a many-sorted modal logic for reasoning about knowledge in multi-agent systems. Our logic introduces a clear distinction between participating agents and the environment. This allows to express local properties of agents and global properties of worlds in a uniform way, as well as to talk about the presence or absence of agents in a world. The logic subsumes the standard epistemic logic and is a conservative extension of it. The semantics is given in chromatic hypergraphs, a generalization of chromatic simplicial complexes, which were recently used to model knowledge in distributed systems. We show that the logic is sound and complete with respect to the intended semantics. We also show a further connection of chromatic hypergraphs with neighborhood frames.