On the Semantics of Primary Cause in Hybrid Dynamic Domains

TL;DR

This paper introduces two equivalent definitions of primary cause within a hybrid dynamic framework, addressing causation involving both discrete and continuous changes, and verifies their properties and counterfactual aspects.

Contribution

It proposes novel, equivalent formal definitions of primary cause in hybrid domains using the hybrid temporal situation calculus, advancing causation theory in mixed discrete-continuous systems.

Findings

Two definitions of primary cause are shown to be equivalent.

The definitions satisfy intuitive properties of causation.

Causation can be verified via a modified counterfactual 'but-for' test.

Abstract

Reasoning about actual causes of observed effects is fundamental to the study of rationality. This important problem has been studied since the time of Aristotle, with formal mathematical accounts emerging recently. We live in a world where change due to actions can be both discrete and continuous, that is, hybrid. Yet, despite extensive research on actual causation, only few recent studies looked into causation with continuous change. Building on recent progress, in this paper we propose two definitions of primary cause in a hybrid action-theoretic framework, namely the hybrid temporal situation calculus. One of these is foundational in nature while the other formalizes causation through contributions, which can then be verified from a counterfactual perspective using a modified ``but-for'' test. We prove that these two definitions are indeed equivalent. We then show that our definitions of causation have some intuitively justifiable properties.