Topological semantics for a non-self-extensional LFI

TL;DR

This paper introduces a new non-self-extensional Logic of Formal Inconsistency called $d$, along with a Hilbert-style presentation and a topological semantics, establishing soundness and completeness.

Contribution

It presents a novel non-self-extensional LFI with a topological semantics and formal proof of soundness and completeness.

Findings

Established soundness of the topological semantics for $d$

Proved completeness of the logic with respect to the semantics

Provided a Hilbert-style axiomatization for $d$

Abstract

In this article, we have introduced a Logic of Formal Inconsistency (LFI) that we call $\vd$. This logic is non-self-extensional, i.e., the replacement property, or the rule for substitution of equivalents, does not hold. A Hilbert-style presentation for the logic has been provided. Then, a topological semantics for $\vd$ has been described, subsequent to which we have established the Soundness and Completeness results for it with respect to this semantics.