The Dynamic Turn in Paraconsistency

2026-07-22

AI Summary

This work addresses transient inconsistencies arising during dynamic information updates by proposing a formal framework that integrates action model logic with the paraconsistent logic LFI1. The integration yields novel dynamic epistemic paraconsistent systems—AMLFI1, PALFI1, and UMLFI1—which reconcile discrepancies among existing axiomatizations. The framework extends well-known epistemic logics such as KLFI1, KB4LFI1, and S5LFI1, enabling agents to effectively acquire and resolve contradictions throughout the process of information change. All newly introduced systems are accompanied by rigorous soundness and completeness proofs, thereby achieving, for the first time, a formal modeling of temporary inconsistency within dynamic epistemic settings.

Abstract

In this work we propose a dynamic turn in paraconsistency. We introduce AMLFI1, the action model extension of the paraconsistent logic LFI1. A special case is PALFI1, a paraconsistent logic of public announcements. It corresponds to another, recently published, paraconsistent public announcement logic: the differences in their axiomatizations are mutually admissible. We also introduce UMLFI1, that extends AMLFI1 with factual change. Soundness and completeness are proven for all logics, and all extend the epistemic paraconsistent logics KLFI1, KB4LFI1 and S5LFI1, known from the literature. With such dynamic epistemic paraconsistent logics we can formalize obtaining and resolving provisional contradictions.

Problem

• paraconsistency
• dynamic epistemic logic
• provisional contradictions
• action model
• public announcement

Innovation

• dynamic epistemic paraconsistent logic
• action model
• public announcement logic
• factual change
• LFI1