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Algebraization, Parametrized Local Deduction Theorem and Interpolation for Substructural Logics over FL

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Abstract

Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and establish a weak form of the deduction theorem that is known as parametrized local deduction theorem. Finally, we study certain interpolation properties and explain how they imply the amalgamation property for certain varieties of residuated lattices.

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Authors and Affiliations

  1. Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa, 923-1292, Japan

    Nikolaos Galatos & Hiroakira Ono

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  1. Nikolaos Galatos
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  2. Hiroakira Ono
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Correspondence to Nikolaos Galatos.

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Dedicated to the memory of Willem Johannes Blok

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Galatos, N., Ono, H. Algebraization, Parametrized Local Deduction Theorem and Interpolation for Substructural Logics over FL. Stud Logica 83, 279–308 (2006). https://doi.org/10.1007/s11225-006-8305-5

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