On the Semantics of Primary Cause in Hybrid Dynamic Domains

2026-02-16Artificial Intelligence

Artificial Intelligence
AI summary

The authors address how to understand causes when changes happen in both step-by-step and smooth ways, which is common in the real world. They propose two ways to define primary causes in a system that combines these two kinds of changes, based on a logical framework called hybrid temporal situation calculus. One definition is basic, and the other uses the idea of contributions that can be checked by imagining what would happen if something didn't occur. They show that these two definitions essentially mean the same thing and that their approach makes intuitive sense for reasoning about causes.

actual causationhybrid systemscontinuous changediscrete changetemporal situation calculuscounterfactual reasoningbut-for testaction theorycausation definitions
Authors
Shakil M. Khan, Asim Mehmood, Sandra Zilles
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.