An Abductive Counterfactual Reasoning Approach in Logic Programming

We construct a counterfactual statement when we reason conjecturally about an event which did or did not occur in the past: If an event had occurred, what would have happened? Would it be relevant? Real world examples, as studied by Byrne, Rescher and many others, show that these conditionals involve a complex reasoning process. An intuitive and elegant approach to evaluate counterfactuals, without deep revision mechanisms, is proposed by Pearl. His Do-Calculus identifies causal relations in a Bayesian network resorting to counterfactuals. Though leaving out probabilities, we adopt Pearl’s stance, and its prior epistemological justification to counterfactuals in causal Bayesian networks, but for programs. Logic programming seems a suitable environment for several reasons. First, its inferential arrow is adept at expressing causal direction and conditional reasoning. Secondly, together with its other functionalities such as abduction, integrity constraints, revision, updating and debugging (a form of counterfactual reasoning), it proffers a wide range of expressibility itself. We show here how programs under the weak completion semantics in an abductive framework, comprising the integrity constraints, can smoothly and uniformly capture well-known and off-the-shelf counterfactual problems and conundrums, taken from the psychological and philosophical literature. Our approach is adroitly reconstructable in other three-valued LP semantics, or restricted to two-valued ones.