Contradiction-tolerant process algebra with propositional signals

TL;DR

This paper introduces a version of process algebra built on paraconsistent logic, enabling the modeling of systems that can handle self-contradictory states without inconsistency issues.

Contribution

It extends previous ACP-style process algebra to incorporate paraconsistent propositional logic, allowing for the analysis of systems with contradictory states.

Findings

Supports modeling of self-contradictory states

Enables analysis of systems with inconsistent information

Provides a formal framework based on paraconsistent logic

Abstract

In a previous paper, an ACP-style process algebra was proposed in which propositions are used as the visible part of the state of processes and as state conditions under which processes may proceed. This process algebra, called ACPps, is built on classical propositional logic. In this paper, we present a version of ACPps built on a paraconsistent propositional logic which is essentially the same as CLuNs. There are many systems that would have to deal with self-contradictory states if no special measures were taken. For a number of these systems, it is conceivable that accepting self-contradictory states and dealing with them in a way based on a paraconsistent logic is an alternative to taking special measures. The presented version of ACPps can be suited for the description and analysis of systems that deal with self-contradictory states in a way based on the above-mentioned paraconsistent logic.