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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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Abstract

The present paper is a sequel to Robles et al. (J Logic Lang Inf 29(3):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 (vsp) and vsp-related properties.

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Acknowledgements

This work is supported by the Spanish Ministry of Economy, Industry and Competitiveness [FFI2017-82878-P]. We sincerely thank three reviewers of the JoLLI for their comments and suggestions on a previous version of this paper.

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Authors and Affiliations

  1. Dpto. de Psicología, Sociología y Filosofía, Universidad de León, Campus de Vegazana, s/n, 24071, León, Spain

    Gemma Robles

  2. Universidad de Salamanca, Campus Unamuno, Edificio FES, 37007, Salamanca, Spain

    José M. Méndez

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  1. Gemma Robles
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  2. José M. Méndez
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Correspondence to Gemma Robles.

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Robles, G., Méndez, J.M. 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. J of Log Lang and Inf 30, 533–556 (2021). https://doi.org/10.1007/s10849-021-09336-9

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