Algebraization, Parametrized Local Deduction Theorem and Interpolation for Substructural Logics over FL |
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Authors: | Nikolaos Galatos Hiroakira Ono |
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Institution: | (1) Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan |
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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.
Dedicated to the memory of Willem Johannes Blok |
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Keywords: | Substructural logic pointed residuated lattice algebraic semantics parametrized local deduction theorem interpolation |
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