On the Forcing Semantics for Monoidal τ-norm Based Logic

MTL-algebras are algebraic structures for the Esteva-Godo monoidal t-norm 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 ?, we define the weak forcing value |φ|Х and the forcing value [φ]Х, for any formula f of MTL in Х. We establish some arithmetical properties of|φ|Х and [φ]Х, and prove the equality [φ]Х=||φ||Х, where ||φ||Х is the truth value of f in Х