One-Step Algebras and Frames for Modal and Intuitionistic Logics
Frederik Möllerström Lauridsen
Abstract:
This thesis is about one-step algebras and frames and their relation to the proof theory of non-classical logics. We show how to adapt the framework of modal one-step algebras and frames from [11] to intuitionistic logic. We prove that, as in the modal case, extension properties of one-step Heyting algebras can characterize a certain weak analytic subformula property (the bounded proof property) of hypersequent calculi. We apply our methods to a number of hypersequent calculi for well-known intermediate logics. In particular, we present a hypersequent calculus for the logic BD3 with the bounded proof property. Finally, we establish a connection between modal one-step algebras and filtrations.
Keywords: logic, mathematics