## Advances in the theory of muLPi algebras

Recently an expansion of \(\rm L {\rm\Pi\frac{1}{2}}\) logic with fixed points has been considered. In the present work we study the algebraic semantics of this logic, namely \(\mu L\Pi\) algebras, from algebraic, model theoretic and computational standpoints.

We provide a characterisation of free \(\mu L\Pi\) algebras as a family of particular functions from \([0,1]^{n}\) to \([0,1]\). We show that the first-order theory of linearly ordered \(\mu L\Pi\)-algebras enjoys quantifier elimination, being, more precisely, the model completion of the theory of linearly ordered \(\rm L {\rm\Pi\frac{1}{2}}\) algebras. Furthermore, we give a functional representation of any \(\rm L {\rm\Pi\frac{1}{2}}\) algebra in the style of Di Nola Theorem for MV-algebras and finally we prove that the equational theory of \(\mu L\Pi\) algebras is in PSPACE.

Advances in the theory of muLPi algebras