A Logic for Paraconsistent Transition Systems

TL;DR

This paper introduces paraconsistent transition systems and their modal logic to model and reason about inconsistent information in complex systems like biological, quantum, and knowledge-based systems.

Contribution

It generalizes Belnap-Dunn four-valued logic by defining PTS with positive/negative relations and a metric over truth values, enabling precise handling of inconsistency.

Findings

Defines paraconsistent transition systems (PTS) with dual accessibility relations.

Develops a modal logic framework for PTS.

Provides a formal basis for reasoning in inconsistent information scenarios.

Abstract

Modelling complex information systems often entails the need for dealing with scenarios of inconsistency in which several requirements either reinforce or contradict each other. In this kind of scenarios, arising e.g. in knowledge representation, simulation of biological systems, or quantum computation, inconsistency has to be addressed in a precise and controlled way. This paper generalises Belnap-Dunn four-valued logic, introducing paraconsistent transition systems (PTS), endowed with positive and negative accessibility relations, and a metric space over the lattice of truth values, and their modal logic.