Paraconsistent First-Order Logic with restricted modus ponens rule and infinite hierarchy levels of contradiction LPω#LP^\#_ω. Axiomatical system HSTω#HST^\#_ω, as paraconsistent generalization of Hrbacek set theory HST

preprint2022arXivOpen access

Abstract

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

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