An expansion of Basic Logic with fixed points

Abstract

We introduce an expansion of Basic Logic (BL) with new connectives which express fixed points of continuous formulas, i.e. formulas of BL whose connectives are among $$ \{ \& ,\vee ,\wedge \}$${&,ź,ź}. The algebraic semantics of this logic is studied together with some of its subclasses corresponding to extensions of the above-mentioned expansion. The axiomatic extensions are proved to be standard complete.