LPi Logic with Fixed Points
We study a system, $\mu$L$\Pi$, obtained by an expansion of L$\Pi$ logic with fixed points connectives. The first main result of the paper is that $\mu$L$\Pi$ is standard complete, i.e. complete with regard to the unit interval of real numbers endowed with a suitable structure.
We also prove that the class of algebras which forms algebraic semantics for this logic is generated, as a variety, by its linearly ordered members and that they are precisely the interval algebras of real closed fields. This correspondence is extended to a categorical equivalence between the whole category of those algebras and another category naturally arising from real closed fields.
Finally, we show that this logic enjoys implicative interpolation.
Tags: Fixed Point, LΠLogic, Łukasiewicz logic, Many-Valued Logic, Product logic, real closed field, standard completeness
