Publisher Summary This chapter presents a theoretical analysis of modal logic that can be
applied to many application areas. It presents the central core of contemporary insight into …

Model theory for extended modal languages Balder David ten Cate In this thesis, several
extensions of the basic modal language are studied. Model theoretic and computational …

The present chapter is aimed at giving a conceptual exposition of the mathematical
principles underlying Sahlqvist correspondence theory. These principles are argued to be …

We extend the theory of unified correspondence to a broad class of logics with algebraic
semantics given by varieties of normal lattice expansions (LEs), also known as 'lattices with …

We define the algorithm ALBA for the language of the same distributive modal logic (DML)
for which a Sahlqvist theorem was proved by Gehrke, Nagahashi, and Venema. Successful …

Modal formulae express monadic second-order properties on Kripke frames, but in many
important cases these have first-order equivalents. Computing such equivalents is important …

We extend unified correspondence theory to Kripke frames with impossible worlds and their
associated regular modal logics. These are logics the modal connectives of which are not …

Taking Löb's Axiom in modal provability logic as a running thread, we discuss some general
methods for extending modal frame correspondences, mainly by adding fixed-point …

We prove the canonicity of inductive inequalities in a constructive meta-theory, for classes of
logics algebraically captured by varieties of normal and regular lattice expansions. This …

We develop a Sahlqvist theory by introducing the class of hybrid inductive formulas. Each
hybrid inductive formula is shown to have an effectively calculable first-order local frame …