Paraconsistent First-Order Logic with restricted modus ponens rule and infinite hierarchy levels of contradiction $LP^\#_{\omega}$. Axiomatical system $HST^\#_{\omega}$, as paraconsistent generalization of Hrbacek set theory HST

TL;DR

This paper introduces a new paraconsistent first-order logic with an infinite hierarchy of contradictions and develops a corresponding set theory, generalizing Hrbacek set theory within a paraconsistent framework.

Contribution

It proposes LP^{#}_{} logic with restricted modus ponens and hierarchy levels, and constructs HST^{#}_{} as its set-theoretic counterpart, extending prior paraconsistent set theories.

Findings

Development of LP^{#}_{} with hierarchy levels of contradiction

Formulation of KSth^{#}_{} set theory based on LP^{#}_{}

Axiomatization of HST^{#}_{} as a paraconsistent extension of Hrbacek set theory

Abstract

In this paper paraconsistent first-order logic LP^{#}_{\omega} with restricted modus ponens rule and infinite hierarchy levels of contradiction is proposed. Corresponding paraconsistent set theory KSth^{#}_{\omega} is discussed.Axiomatical system HST^{#}_{\omega} as paraconsistent generalization of Hrbacek set theory HST is considered.