Behavioral Mereology (Proofs and Properties)
Brendan Fong, David Jaz Myers, David I. Spivak

TL;DR
This paper introduces a general, topos-theoretic behavioral approach to mereology, focusing on how parts of systems relate through behavioral constraints, and develops an inter-modal logic to formalize these relationships.
Contribution
It presents a novel, abstract framework for mereology based on system behaviors and formalizes it using an inter-modal logic, extending traditional mereological concepts.
Findings
Develops a topos-theoretic, behavior-based mereology framework
Formalizes part relationships using an inter-modal logic
Provides a general, elementary set-theoretic perspective
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.
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Taxonomy
TopicsLogic, Reasoning, and Knowledge · Advanced Algebra and Logic · Logic, programming, and type systems
