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.
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