Atomic Entailment and Atomic Inconsistency and Classical Entailment

TL;DR

This paper introduces atomic entailment and inconsistency concepts within predicate calculus, proposing a new classical entailment framework, addressing relevant logic challenges with novel definitions and systems.

Contribution

It presents a new atomic entailment system, defines atomic inconsistency, and introduces a revised classical entailment, advancing the understanding of relevant logics.

Findings

Constructed an atomic entailment system for predicate calculus

Defined atomic inconsistency with infinite non-trivial inconsistent systems

Developed a new classical entailment definition

Abstract

In this paper we put forward a new solution of the well-known problem of relevant logics, i.e. we construct an atomic entailment. Hence, we construct a system of predicate calculus based on the atomic entailment. Next, we establish the definition of atomic inconsistency. The atomic inconsistency establishes an infinite class of inconsistent, but non-trivial systems. In this paper we construct the new definition of the classical entailment, into the bargain.