Behavioral Mereology: A Modal Logic for Passing Constraints

TL;DR

This paper introduces a modal logic framework for understanding how behavioral constraints are passed between parts of a system, generalizing traditional mereology with a topos-theoretic, behavior-based approach.

Contribution

It develops a novel behavioral mereology framework using a modal logic that generalizes classical mereology through a topos-theoretic, behavior-centric perspective.

Findings

Provides a formal inter-modal logic for behavioral constraints

Generalizes traditional mereology with a topos-theoretic approach

Offers a set-theoretic interpretation of the logic

Abstract

Mereology is the study of parts and the relationships that hold between them. We introduce a behavioral approach to mereology, in which systems and their parts are known only by the types of behavior they can exhibit. Our discussion is formally topos-theoretic, and agnostic to the topos, providing maximal generality; however, by using only its internal logic we can hide the details and readers may assume a completely elementary set-theoretic discussion. We consider the relationship between various parts of a whole in terms of how behavioral constraints are passed between them, and give an inter-modal logic that generalizes the usual alethic modalities in the setting of symmetric accessibility.