Paradeduction in Axiomatic Formal Systems

TL;DR

This paper introduces paradeduction as a method to handle contradictions in axiomatic systems, enabling the transformation of classical logics into paraconsistent ones to manage inconsistent information.

Contribution

It formalizes the concept of paradeduction and demonstrates how to convert any axiomatic system into a paraconsistent logic.

Findings

Paradeduction allows reasoning with inconsistent information.

Any axiomatic system can be transformed into a paraconsistent logic.

The approach provides a foundation for managing contradictions in formal systems.

Abstract

The concept of paradeduction is presented in order to justify that we can overlook contradictory information taking into account only what is consistent. Besides that, paradeduction is used to show that there is a way to transform any logic, introduced as an axiomatic formal system, into a paraconsistent one.