On Modal Logic

On Quantified Modal Logic

Propositional modal logic is a standard tool in many disciplines, but first-order modal logic is not. There are several reasons for this, including multiplicity of versions and inadequate syntax. In this paper we sketch a syntax and semantics for a natural, well-behaved version of first-order modal logic, and show it copes easily with several familiar difficulties. And we provide tableau proof ...

Notes on Mathematical Modal Logic

These notes were written by Wang Yafeng following a course of three intensive lectures on classical themes in mathematical modal logic given by Johan van Benthem in the Berkeley-Stanford Logic Circle, San Francisco, May 2015. Some of this material was collected in the monograph van Benthem [13], [16], other parts come from later publications. We will provide some references to further relevant ...

On an Intuitionistic Modal Logic

In this paper we consider an intuitionistic variant of the modal logic S4 (which we call IS4). The novelty of this paper is that we place particular importance on the natural deduction formulation of IS4—our formulation has several important metatheoretic properties. In addition, we study models of IS4, not in the framework of Kripke semantics, but in the more general framework of category theo...

Modal Logic

On Proof Realization on Modal Logic

Artemov’s Logic of Proof, LP, is an explicit proof counterpart of S4. Their formal connection is built through the realization theorem, that every S4 theorem can be converted to an LP theorem by substituting proof terms for provability modals. Instead of the realization of theorems, what is concerned in this paper is the realization of proofs. We will show that only a subclass of S4 proofs, cal...