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

arXiv: https://arxiv.org/abs/1609.05616 · HTML: https://mlsanity.com/paper/1609.05616/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Sep 2016.

## Built on by (most cited first, 1 of 1)

- [Do AI Agents Know When a Task Is Simple? Toward Complexity-Aware Reasoning and Execution](https://mlsanity.com/paper/2607.13034/) (2026)

## Abstract (arXiv)

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.