On the Semantics of Primary Cause in Hybrid Dynamic Domains
This work addresses a foundational gap in causal reasoning for hybrid systems, which is incremental as it builds on recent progress in the field.
The paper tackles the problem of defining primary causes in hybrid dynamic domains where change can be both discrete and continuous, proposing two equivalent definitions in a hybrid temporal situation calculus framework and proving their equivalence and intuitive properties.
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.