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Completeness Theorems via the Double Dual Functor

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Abstract

The aim of this paper is to apply properties of the double dual endofunctor on the category of bounded distributive lattices and some extensions thereof to obtain completeness of certain non-classical propositional logics in a unified way. In particular, we obtain completeness theorems for Moisil calculus, n-valued Łukasiewicz calculus and Nelson calculus. Furthermore we show some conservativeness results by these methods.

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Authors and Affiliations

  1. Universidad de La Plata, Canada

    Adriana Galli & Marta Sagastume

  2. Université de Montréal, Canada

    Gonzalo E. Reyes

Authors
  1. Adriana Galli
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  2. Marta Sagastume
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  3. Gonzalo E. Reyes
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Galli, A., Sagastume, M. & Reyes, G.E. Completeness Theorems via the Double Dual Functor. Studia Logica 64, 61–81 (2000). https://doi.org/10.1023/A:1005238330484

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  • DOI: https://doi.org/10.1023/A:1005238330484

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