On the Semantics of Primary Cause in Hybrid Dynamic Domains

2026-02-16

AI Summary

This work addresses the challenge of causal reasoning in hybrid dynamical systems, where discrete and continuous changes coexist. Within a hybrid temporal situation calculus framework, it proposes two formal definitions of primary cause: one grounded in foundational semantics and the other based on causal contribution augmented with an improved “but-for” counterfactual test. The study establishes, for the first time in hybrid systems, the equivalence between these two notions and demonstrates that they satisfy several intuitive causal properties. By integrating semantic foundations with a verifiable mechanism, the approach introduces a counterfactual testing method tailored to continuous dynamics, thereby providing a rigorous yet practical theoretical foundation for causal reasoning in hybrid systems.

Technology Category

• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Action, Change, and Causality
• Machine Learning: Causal Learning

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

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.

Problem

• actual causation
• hybrid dynamic domains
• primary cause
• continuous change
• causal reasoning

Innovation

• hybrid dynamic domains
• actual causation
• primary cause
• situation calculus
• counterfactual reasoning