On the forcing semantics for monoidal t-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 X, we define the weak forcing value |phi|x and the forcing value [phi] x, for any formula phi of MTL in X. We establish some arithmetical properties of |.| x and [.] x, and prove the equality [phi] X= ||phi|| x, where ||phi|| x is the truth value of phi in X.
forcing semantics mtl-algebras mtl logic