Axiomatic extensions of Monoidal Logic

Joan Gispert

University of Barcelona

In this communication we will present an algebraic study of some axiomatic extensions of the Monoidal Logic, also named FLew (Full Lambda Calculus plus exchange and weakening). In particular we will deal withaxiomatic extensions that satisfy the pre-linearity condition and wil study their associated algebras: MTL-algebras. Not much is known on how to construct MTL-algebras. Althouguht MTL-algebras are very close to BL-algebras, they lack to have a representation theorem like the representation as ordinal sum. Jenei presented some contructions for the case of involutive MTL- algebras. We associate to each construction an equational class, we study its associated logic, we answer the question of having or not standard completeness. Moreover we generalise those classes to the non involutive case.