Cognitive Binary Logic - The Natural Unified Formal Theory of Propositional Binary Logic

TL;DR

This paper introduces Cognitive Binary Logic, a unified formal system for propositional logic that integrates syntax, semantics, proofs, and deduction within a single computational framework, also addressing the Liar Paradox.

Contribution

It presents a novel formal theory that unifies propositional logic, proof systems, and paradox deconstruction within a single semantically closed language.

Findings

Formalizes propositional logic as a semantically closed language

Enables proof and deduction within the same computational framework

Addresses the Liar Paradox within the theory

Abstract

This paper presents a formal theory which describes propositional binary logic as a semantically closed formal language, and allows for syntactically and semantically well-formed formulae, formal proofs (demonstrability in Hilbertian acception), deduction (Gentzen's view of demonstrability), CNF-ization, and deconstruction to be expressed and tested in the same (computational) formal language, using the same data structure. It is also shown here that Cognitive Binary Logic is a self-described theory in which the Liar Paradox is deconstructed.