Distributive Full Lambek Calculus Has the Finite Model Property

摘要

We prove the Finite Model Property (FMP) for Distributive Full Lambek Calculus (DFL) whose algebraic semantics is the class of distributive residuated lattices (DRL). The problem was left open in [8, 5]. We use the method of nuclei and quasi–embedding in the style of [10, 1]. Keywords Full Lambek calculus - Residuated lattice - Distributive lattice - Finite model property - Decidability - Nucleus Presented by Daniele Mundici.