Abduction and Beyond in Logic Programming with Application to Morality

In this paper we emphasize two different aspects of abduction in Logic Programming (LP): (1) the engineering of LP abduction systems, and (2) application of LP abduction, complemented with other non-monotonic features, to model morality issues. For the LP engineering part, we present an implemented tabled abduction technique in order to reuse priorly obtained (and tabled) abductive solutions, from one abductive context to another. Aiming at the interplay between LP abduction and other LP non-monotonic reasoning, this tabled abduction technique is combined with our own-developed LP updating mechanism – the latter also employs tabling mechanisms, notably incremental tabling of XSB Prolog. For the application part, we formulate LP-based counterfactual reasoning, based on Pearl’s structural theory, via the aforementioned unified approach of our LP abduction and updating. The formulation of counterfactuals allows us to demonstrate its application to model moral permissibility, according to the Doctrines of Double and Triple Effect, and to provide its justification. The applications are shown through classic moral examples from the literature, and tested in our prototype, Qualm, an implementation based on the presented unified approach.