Approved models for normal logic programs

Authors:
Luís Moniz Pereira;Alexandre Miguel Pinto
Affiliations:
Centro de Inteligência Artificial, Universidade Nova de Lisboa, Caparica, Portugal;Centro de Inteligência Artificial, Universidade Nova de Lisboa, Caparica, Portugal
Venue:
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Year:
2007

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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.