On the Forcing Semantics for Monoidal t-norm Based Logic

Denisa Diaconescu (University of Bucharest, Romania)

George Georgescu (University of Bucharest, Romania)

Abstract: 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 Χ, we define the weak forcing value |φ|_χ and the forcing value [φ]_χ, for any formula φ of MTL in Χ. We establish some arithmetical properties of|.|_χ and [.]_χ, and prove the equality [φ]_χ=||φ||_χ, where ||φ||_χ is the truth value of φ in Χ.

Keywords: MTL logic, MTL-algebras, forcing semantics

Categories: F.4.1