Sahlqvist Correspondence for Intuitionistic Modal Mu-Calculus
Yves Fomatati
Abstract:
The motivation of this thesis is the idea of extending the results in
[13] to the case of logics with fixpoints and with a non-classical
base. We focus in particular on the intuitionistic modal
mu-calculus. We enhance the ALBA algorithm [26] for the elimination of
monadic second order variables so that mu-formulas can be treated in
which all the variables occur inside the scope of fixpoint binders. We
prove that this enhancement is sound thanks to the order-theoretic
properties of the interpretation of fixpoint binders in the algebraic
semantics for intuitionistic mu-calculus. We define the class of
recursive inequalities and informally justify that the enhanced ALBA
is successful on this class.
Keywords: Logic, Mathematics