Abstract
We present an alternative model theory for answer sets based on the possible worlds semantics proposed by Routley (1974) as a framework for the propositional logics of Fitch and Nelson. By introducing a falsity constant or second negation into Routley models, we show how paraconsistent as well as ordinary answer sets can be represented via a simple minimality condition on models. This means we can define a paraconsistent version of equilibrium logic, or paraconsistent answer sets (PAS) for propositional theories. The underlying logic of PAS is denoted by N 9. We characterise it axiomatically and algebraically, showing it to be the least conservative extension of the logic of here-and-there with strong negation. In addition, we show that N 9 captures the strong equivalence of programs in the paraconsistent case and can thus serve as a useful mathematical foundation for PAS. We end by showing that N 9 has the Interpolation Property.
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Odintsov, S., Pearce, D. (2005). Routley Semantics for Answer Sets. In: Baral, C., Greco, G., Leone, N., Terracina, G. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2005. Lecture Notes in Computer Science(), vol 3662. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11546207_27
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DOI: https://doi.org/10.1007/11546207_27
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