Formalising Overdetermination in a Labelled Transition System

In the Knowledge Representation and Reasoning field, causality has mainly been used to determine the effects of actions. However, in legal or ethical reasoning, causality is used to determine the causal origin of a consequence. Such a posteriori reasoning is the focus of the Actual Causality field which has been extensively studied by lawyers, philosophers, mathematicians, and computer scientists. While most of the situations are easy to solve, there are several overdetermination cases that are far from trivial and that are still a source of disagreements in the field. Recent works have undertaken to adapt causality results into languages for Reasoning about Action and Change (RAC). In this paper, we aim to provide means to effectively address overdetermination issues to researchers seeking to incorporate actual causality into their RAC methods. To do so, we propose a definition of overdetermination in a Labelled Transition System and we formalise and enrich the existing typology of classical cases of overdetermination within this formalisation. The formal typology obtained enables the description of axiomatic properties of RAC methods that deal with overdetermination. To illustrate this, we describe the properties of a recent RAC formalisation of causality in light of this typology. We think that this way of doing can be generalised to all causality RAC formalisations. CCS CONCEPTS • Computing methodologies → Causal reasoning and diagnostics; Planning for deterministic actions.