Preorder-Based Triangle: A Modified Version of Bilattice-Based Triangle for Belief Revision in Nonmonotonic Reasoning
This work addresses a foundational issue in nonmonotonic reasoning for AI and logic, though it appears incremental as it modifies an existing algebraic structure.
The paper tackled the limitations of bilattice-based triangle in handling repetitive belief revisions and non-intuitive orderings in nonmonotonic reasoning by constructing a preorder-based triangle with proper logical connectives, demonstrating it as a better alternative for nonmonotonic fuzzy reasoning with uncertain information.
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.