Some Properties of Logic N-GLukG
We present an extension of GLukG, a logic that was introduced in  as a three-valued logic under the name of G′3. GLukG is a paraconsistent logic defined in terms of 15 axioms, which serves as the formalism to define the p-stable semantics of logic programming. We introduce a new axiomatic system, N-GLukG, a paraconsistent logic that possesses strong negation. We use the 5-valued logic N′5, which is a conservative extension of GLukG, to help us to prove that N-GLukG is an extension of GLukG. N-GLukG can be used as the formalism to define the p-stable semantics as well as the stable semantics.
Keywordsparaconsistent knowledge representation semantics logic programming semantics
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