# Abductive Reasoning in a Paraconsistent Framework

arXiv: https://arxiv.org/abs/2408.07287 · HTML: https://mlsanity.com/paper/2408.07287/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 2 of its 33 references that are in the map.
- First posted on arXiv 1 Aug 2024.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 2 of 2)

- [Prime Implicates and Prime Implicants: From Propositional to Modal Logic](https://mlsanity.com/paper/1401.3475/) (2014)
- [Propositional dynamic logic with Belnapian truth values](https://mlsanity.com/paper/1608.06084/) (2016)

## Built on by (most cited first, 2 of 2)

- [ABox Abduction for Inconsistent Knowledge Bases under Repair Semantics](https://mlsanity.com/paper/2605.01341/) (2026)
- [LAF-Based Evaluation and UTTL-Based Learning Strategies with MIATTs](https://mlsanity.com/paper/2604.20944/) (2026)

## Abstract (arXiv)

We explore the problem of explaining observations starting from a classically inconsistent theory by adopting a paraconsistent framework. We consider two expansions of the well-known Belnap--Dunn paraconsistent four-valued logic mathsfBD: mathsfBD_circ introduces formulas of the form circφ (the information on φ is reliable), while mathsfBD_triangle augments the language with triangleφ's (there is information that φ is true). We define and motivate the notions of abduction problems and explanations in mathsfBD_circ and mathsfBD_triangle and show that they are not reducible to one another. We analyse the complexity of standard abductive reasoning tasks (solution recognition, solution existence, and relevance / necessity of hypotheses) in both logics. Finally, we show how to reduce abduction in mathsfBD_circ and mathsfBD_triangle to abduction in classical propositional logic, thereby enabling the reuse of existing abductive reasoning procedures.