Abstract

OSORIO, Mauricio  and  CARBALLIDO, José Luis. A 4-Valued Logic that Extends the Paraconsistent Logic G’3. Comp. y Sist. [online]. 2023, vol.27, n.1, pp.297-302.  Epub June 16, 2023. ISSN 2007-9737.  https://doi.org/10.13053/cys-27-1-4563.

We introduce a new 4-valued logic that we call $M4M4$. We show that $M4M4$ is conservative extension of the 3-valued logic ${G^{\prime }}_3$, 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 ${G^{\prime }}_3$. In addition, $M4M4$ also includes a strong negation operator that is the new feature of this logic with respect to ${G^{\prime }}_3$. 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 $M4M4$.

Keywords : Knowledge representation; stable semantics; logic programming.

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