Abstract
This paper introduces a new method for defining the argumentative semantics of Normal Logic Programs. In doing so, our single and unified approach allows one to obtain the Stable Models [11] as a special case, or the more general Revision Complete Scenarios here defined. Normal Logic Programs are approached as assumption-based argumentation systems. We generalize this setting by allowing both negative and positive assumptions. Negative assumptions are made maximal, consistent with existence of a semantics, and positive assumptions are adopted only insofar as they guarantee such existence. Our argumentation semantics thus extends the classical one of [7], and guarantees existence of semantics for any Normal Logic Program, whilst providing all the scenarios corresponding to Stable Models semantics. Additionally, we provide equivalent and correct algorithms for incrementally computing our scenarios, with three variants. One starts by assuming all atoms as positive assumptions; another assumes them all negative; a third rests on a combination of the first two, and may start with any choice of assumptions. The latter may be employed to address the problem of finding those complete scenarios most compatible with an initial collection of complete scenarios. Consequently, argumentation can be put to collaborative use, not just an antagonistic one. Our results are achieved by generalizing the definitions of the classical approach, which allows only for negative hypotheses, and our definitions fall back on the classical ones when specialized to disallow positive hypotheses. Finally, integrity constraints are introduced to prune undesired scenarios, whilst permitting these to be produced nevertheless.

URL:
http://rewerse.net/publications/rewerse-publications.html#REWERSE-RP-2007-067

BibTeX:

@inproceedings{REWERSE-RP-2007-067,
	author = {Luís Moniz Pereira and Alexandre Miguel Pinto},
	title = {Reductio ad Absurdum Argumentation in Normal Logic Programs},
	booktitle = {Proceedings of Workshop on Argumentation and Non-Monotonic Reasoning, Tempe, Arizona, USA (14th May 2007)},
	year = {2007},
	url = {http://rewerse.net/publications/rewerse-publications.html#REWERSE-RP-2007-067}
}