String Diagrams for Layered Explanations

TL;DR

This paper introduces a categorical graphical framework using layered props to model and reason about layered scientific explanations across diverse fields, enabling visual translation between explanation levels and partial explanations.

Contribution

It develops a unified graphical calculus for layered explanations, allowing partial translations and formal reasoning, applicable to biology, circuits, and concurrency.

Findings

Unified diagrammatic framework for explanations

Supports partial and multi-level explanations

Enables formal reasoning about counterfactuals

Abstract

We propose a categorical framework to reason about scientific explanations: descriptions of a phenomenon meant to translate it into simpler terms, or into a context that has been already understood. Our motivating examples come from systems biology, electrical circuit theory, and concurrency. We demonstrate how three explanatory models in these seemingly diverse areas can be all understood uniformly via a graphical calculus of layered props. Layered props allow for a compact visual presentation of the same phenomenon at different levels of precision, as well as the translation between these levels. Notably, our approach allows for partial explanations, that is, for translating just one part of a diagram while keeping the rest of the diagram untouched. Furthermore, our approach paves the way for formal reasoning about counterfactual models in systems biology.