Caracterizaci\'on sem\'antico-deductiva de la l\'ogica doble LD y los gr\'aficos existenciales Gamma-LD

TL;DR

This paper introduces the deductive system LD, a logic that combines classical and intuitionist features, characterized by possible worlds semantics and Gamma-LD graphs, capable of addressing paradoxes like the liar's paradox.

Contribution

It rigorously defines LD's semantics, proves its key logical properties, and situates it among related logical systems using Peircean existential graphs.

Findings

LD includes classical and intuitionist theorems

LD can fix the liar's paradox where other logics fail

LD's semantics are characterized by possible worlds and Gamma-LD graphs

Abstract

This work presents the deductive system Double Propositional Logic, LD, along with the semantics of possible worlds that characterize it. LD includes an alternate affirmation operator and an alternate negation operator and is not valid for the principle of the excluded third when one of the disjunctions is one of the alternate operators. The LD system includes as theorems, the theorems of the Classic Propositional Logic LC. In LD, the intuitionist connec-tives are recovered from the classics and the alternates, which implies that, the LD system includes as theorems, the theorems of the Propositional Intuitionist Logic LI. It is rigorously and detailed to prove that theorems of con-sistency, validity and completeness. It illustrates LD's ability to fix a version of the liar's paradox, where LC and LI fail. Finally, the location of the LD system is precisely determined in relation to the systems that made it possi-ble to intuit the structure of LD, such as, Basic Logic for the Aristotelian Truth LBVA, the Logic of Tautologies LT and the Basic Logic for Truth and Falsehood LBVF. LD is characterized by Gamma-LD Existential Graphs, in the style of Peirce, so the semantics of possible worlds presented in this work also characterizes Gamma-LD.