On the Forcing Semantics for Monoidal t-norm Based Logic
Denisa Diaconescu, George Georgescu · Zenodo (CERN European Organization for Nuclear Research) · 2020
Abstract: MTL-algebras are algebraic structures for the Esteva-Godo monoidal tnorm based logic (MTL), a many-valued propositional calculus that formalizes the structure of the real interval [0, 1], induced by a left-continuous t-norm. Given a complete MTL-algebra X, we define the weak forcing value |ϕ|X and the forcing value [ϕ]X, for any formula ϕ of MTL in X. We establish some arithmetical properties of |.|X and [.]X, and prove the equality [ϕ]X =�ϕ�X,where�ϕ�X is the truth value of ϕ in X. Key Words: MTL logic, MTL-algebras, forcing semantics Category: F.4.1