Bijective Faithful Translations among Default Logics

TL;DR

This paper investigates bijective faithful translations between variants of default logics, ensuring a one-to-one correspondence of extensions, and explores conditions under which these translations can be efficiently computed.

Contribution

It introduces a framework for bijective translations among default logics, bridging previous research on restricted and non-bijective translations.

Findings

Established conditions for polynomial-time bijective translations

Extended understanding of translation properties between default logic variants

Filled a gap between previous studies on default logic translations

Abstract

In this article, we study translations between variants of defaults logics such that the extensions of the theories that are the input and the output of the translation are in a bijective correspondence. We assume that a translation can introduce new variables and that the result of translating a theory can either be produced in time polynomial in the size of the theory or its output is polynomial in that size; we however restrict to the case in which the original theory has extensions. This study fills a gap between two previous pieces of work, one studying bijective translations among restrictions of default logics, and the other one studying non-bijective translations between default logics variants.