Advances in the theory of  L  algebras

Abstract

Recently an expansion of LΠ 1 2 logic with fixed points has been considered [23]. In the present work we study the algebraic semantics of this logic, namely µ LΠ algebras, from algebraic, model theoretic and computational standpoints.We provide a characterisation of free µ LΠ algebras as a family of particular functions from [0, 1] n to [0,1]. We show that the first-order theory of linearly ordered µ LΠ algebras enjoys quantifier elimination, being, more precisely, the model completion of the theory of linearly ordered LΠ 1 2 algebras. Furthermore, we give a functional representation of any LΠ 1 2 algebra in the style of Di Nola Theorem for MV-algebras and finally we prove that the equational theory of µ LΠ algebras is in PSPACE.