A 4-Valued Logic that Extends the Paraconsistent Logic G’3

Abstract

We introduce a new 4-valued logic that we call M4M4. We show that M4M4 is conservative extensión of the 3-valued logic G′ 3, which serves as the formalism to define the p-stable semantics of logic programming. M4M4 possesses two negation operators. The weak negation operator that corresponds to the negation operator of G′ 3. In addition, M4M4 also includes a strong negation operator that is the new feature of this logic with respect to G′ 3. It is well known that allowing these two negations is very useful in knowledge representation. M4M4 can be used as the formalism to define the p-stable semantics as well as the stable semantics. We also present other suitable properties of M4M4.