JUCS - Journal of Universal Computer Science 13(11): 1550-1572, doi: 10.3217/jucs-013-11-1550
On the Forcing Semantics for Monoidal t-norm Based Logic
expand article infoDenisa Diaconescu‡, George Georgescu‡
‡ University of Bucharest, Bucharest, Romania

Corresponding author: Denisa Diaconescu ( ddenisuca@yahoo.com )

© Denisa Diaconescu, George Georgescu.
This article is freely available under the J.UCS Open Content License.
Citation: Diaconescu D, Georgescu G (2007) On the Forcing Semantics for Monoidal t-norm Based Logic. JUCS - Journal of Universal Computer Science 13(11): 1550-1572. https://doi.org/10.3217/jucs-013-11-1550
Open Access
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