Algebraization, parametrized local deduction theorem and interpolation for substructural logics over FL

Studia Logica 83 (1-3):279 - 308 (2006)
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.
Keywords Substructural logic  pointed residuated lattice  algebraic semantics  parametrized local deduction theorem  interpolation
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