Obligation versus factual conditionals under the weak completion semantics

Abstract

Conditionals play a prominent role in human reasoning and, hence, all cognitive theories try to evaluate conditionals like humans do. In this paper, we are particularly interested in the Weak Completion Semantics, a new cognitive theory based on logic programming, the weak completion of a program, the three-valued Łukasiewicz logic, and abduction. We show that the evaluation of conditionals within the Weak Completion Semantics as defined so far leads to counterintuitive results. We propose to distinguish between obligation and factual conditionals with necessary or sufficient conditions, and adapt the set of abducibles accordingly. This does not only remove the previously encountered counterintuitive results, but also leads to a new model for the Wason Selection Task