Abstract
In answer set programming, an extended logic program may have no answer set, or only one trivial answer set. In this paper, we propose a new stable model semantics based on the restricted four-valued logic to overcome both inconsistences and incoherences in answer set programming. Our stable models coincide with classical answer sets when reasoning on consistent and coherent logic programs, and can be solved by transformation in existing ASP solvers. We also show the connection between our stable models and the extensions of default logic.
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