Studia Logica

, Volume 83, Issue 1, pp 279-308

First online:

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

  • Nikolaos GalatosAffiliated withJapan Advanced Institute of Science and Technology Email author 
  • , Hiroakira OnoAffiliated withJapan Advanced Institute of Science and Technology

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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.


Substructural logic pointed residuated lattice algebraic semantics parametrized local deduction theorem interpolation