Situated Transition Systems

TL;DR

This paper introduces situated transition systems as a monoidal category framework for modeling open systems with material histories, emphasizing compositionality and resource theories, including special cases like double-entry bookkeeping.

Contribution

It constructs a monoidal category of open transition systems parameterized by resource theories, with a focus on compact closed categories and their applications.

Findings

Material histories are generated by system components and combined compositionally.

The framework applies to systems modeled as double-entry bookkeeping accounts.

Special case of compact closed categories provides structured interpretations.

Abstract

We construct a monoidal category of open transition systems that generate material history as transitions unfold, which we call situated transition systems. The material history generated by a composite system is composed of the material history generated by each component. The construction is parameterized by a symmetric strict monoidal category, understood as a resource theory, from which material histories are drawn. We pay special attention to the case in which this category is compact closed. In particular, if we begin with a compact closed category of integers then the resulting situated transition systems can be understood as systems of double-entry bookkeeping accounts.