Advances in the theory of LP algebras

Recently an expansion of LP1/2 logic with fixed points has been considered. In the present work we study the algebraic semantics of this logic, namely μLP algebras, from algebraic, model theoretic and computational standpoints. We provide a characterisation of free μLP algebras as a family of particular functions from [0,1]n to [0,1]. We show that the first-order theory of linearly ordered μLP algebras enjoys quantifier elimination, being, more precisely, the model completion of the theory of linearly ordered LP1/2 algebras. Furthermore, we give a functional representation of any LP1/2 algebra in the style of Di Nola Theorem for MV-algebras and finally we prove that the equational theory of μLP algebras is in PSPACE.