# On the Semantics of Primary Cause in Hybrid Dynamic Domains

arXiv: https://arxiv.org/abs/2602.14994 · HTML: https://mlsanity.com/paper/2602.14994/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 36 references that are in the map.
- First posted on arXiv 16 Feb 2026.

## Builds on (most cited first, 6 of 6)

- [A Modification of the Halpern-Pearl Definition of Causality](https://mlsanity.com/paper/1505.00162/) (2015)
- [Reasoning About Causal Models With Infinitely Many Variables](https://mlsanity.com/paper/2112.11362/) (2021)
- [Hybrid Temporal Situation Calculus](https://mlsanity.com/paper/1807.04861/) (2018)
- [Counterfactual Causality from First Principles?](https://mlsanity.com/paper/1710.03393/) (2017)
- [A Non-Interventionist Approach to Causal Reasoning based on Lewisian Counterfactuals](https://mlsanity.com/paper/2505.12972/) (2025)
- [Reasoning about Actual Causes in Nondeterministic Domains -- Extended Version](https://mlsanity.com/paper/2412.16728/) (2024)

## Abstract (arXiv)

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.