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IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
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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 N9. 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 N9 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 N9 has the Interpolation Property.