A generalization of falsity in finitely-many valued logics

TL;DR

This paper introduces a novel negation concept in multi-valued logics, offering a new perspective on truth and falsity definitions in many-valued logical systems.

Contribution

It proposes a new type of negation and a general framework for defining truth and falsity in arbitrary finitely-valued logics.

Findings

New negation concept for multi-valued logics

Generalized definitions of truth and falsity

Enhanced understanding of logical negation in many-valued systems

Abstract

The paper proposes a new type of negation in multi-valued logics, providing a different way to answer the following question: what does it mean that some object language formula does not have a given truth-value. Along the way, the paper provides a general definition of truth and falsity in an arbitrary many-valued logic.