Web pages of Luca Spada

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