A Class of Implicative Expansions of Kleene’s Strong Logic, a Subclass of Which Is Shown Functionally Complete Via the Precompleteness of Łukasiewicz’s 3-Valued Logic Ł3

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Journal of Logic, Language and Information 30 (3):533-556 (2021)
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Abstract

The present paper is a sequel to Robles et al. :349–374, 2020. https://doi.org/10.1007/s10849-019-09306-2). A class of implicative expansions of Kleene’s 3-valued logic functionally including Łukasiewicz’s logic Ł3 is defined. Several properties of this class and/or some of its subclasses are investigated. Properties contemplated include functional completeness for the 3-element set of truth-values, presence of natural conditionals, variable-sharing property and vsp-related properties.

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10.1007/s10849-021-09336-9

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Author Profiles

Gemma Robles
Universidad de León
José M. Méndez
Universidad de Salamanca

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References found in this work

Introduction to metamathematics.Stephen Cole Kleene - 1952 - Groningen: P. Noordhoff N.V..
An algebraic approach to non-classical logics.Helena Rasiowa - 1974 - Warszawa,: PWN - Polish Scientific Publishers.
The logic of paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
Theory of Logical Calculi: Basic Theory of Consequence Operations.Ryszard Wójcicki - 1988 - Dordrecht, Boston and London: Kluwer Academic Publishers.
Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219-241.

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