Approved Models for Normal Logic Programs

Abstract

We introduce an original 2-valued semantics for Normal Logic Programs (NLPs) extending the well-known Argumentation work of Phan Minh Dung on Admissible Arguments and Preferred Extensions. In the 2-valued Approved Models Semantics set forth, an Approved Model (AM) correspond to the minimal positive strict consistent 2-valued completion of a Dung Preferred Extension. The AMs Semantics enjoys several non-trivial useful properties such as (1) Existence of a 2-valued Model for every NLP; (2) Relevancy, and (3) Cumulativity. Crucially, we show that the AMs Semantics is a conservative extension to the Stable Models (SMs) Semantics in the sense that every SM of a NLP is also an AM, thus providing every NLP with a model: a property not enjoyed by SMs. Integrity constraints, written in a simpler way, are introduced to identify undesired semantic scenarios, whilst permitting these to be produced nevertheless. We end the paper with some conclusions and mention of future work.