Default Negation in Normal Logic Programs Considered as Minimal Abduction of Positive Hypotheses

Logic programs (LPs) are a practical tool for declarative knowledge representation and consist of normal rules and integrity constraints (ICs). Reasoning with LPs is parameterized by the particular semantics chosen. However, the declaratively of the knowledge represented by an LP is restricted if the semantics chosen for the normal rules allows them to play the role ICs already can have. Namely because odd loops over negation, such as in rule {p ← not p}, entail the absence of two-valued semantics models and complex odd loops over negation are often deliberately used as ICs. Here the authors propose a more flexible reading of default negation, such that NLPs always have a two-valued model before ICs are evaluated. To wit, the authors do so by allowing for minimally assuming (or abducing) positive hypotheses and hence still maximizing the assumption of negative hypotheses that preserve consistency. The authors show how that translates into a semantics for normal logic programs (NLPs) – the minimal hypotheses (MH) semantics – which safeguards declarativity in this sense and moreover enjoys useful semantic properties such as cumulativity and relevancy, besides existence. Moreover, the authors introduce a program transformation which allows to compute the MH models of a program as a selection of the stable models of the transform.