Preorder-Based Triangle: A Modified Version of Bilattice-Based Triangle for Belief Revision in Nonmonotonic Reasoning

TL;DR

This paper introduces a preorder-based triangle structure as an improved algebraic framework for belief revision in nonmonotonic reasoning, addressing limitations of the bilattice-based triangle in handling repetitive revisions and intuitive ordering.

Contribution

It proposes a novel preorder-based triangle structure with logical connectives, enhancing reasoning with uncertain information in nonmonotonic contexts.

Findings

Preorder-based triangle better handles belief revisions.

It provides more intuitive interval ordering.

Demonstrates improved reasoning in uncertain scenarios.

Abstract

Bilattice-based triangle provides an elegant algebraic structure for reasoning with vague and uncertain information. But the truth and knowledge ordering of intervals in bilattice-based triangle can not handle repetitive belief revisions which is an essential characteristic of nonmonotonic reasoning. Moreover the ordering induced over the intervals by the bilattice-based triangle is not sometimes intuitive. In this work, we construct an alternative algebraic structure, namely preorder-based triangle and we formulate proper logical connectives for this. It is also demonstrated that Preorder-based triangle serves to be a better alternative to the bilattice-based triangle for reasoning in application areas, that involve nonmonotonic fuzzy reasoning with uncertain information.