Analytic Non-Labelled Proof-Systems for Hybrid Logic: Overview and a couple of striking facts

Abstract

This paper is about non-labelled proof-systems for hybrid logic, that is, proof-systems where arbitrary formulas can occur, not just satisfaction statements. We give an overview of such proof-systems, focusing on analytic systems: Natural deduction systems, Gentzen sequent systems and tableau systems. We point out major results and we discuss a couple of striking facts, in particular that non-labelled hybrid-logical natural deduction systems are analytic, but this is not proved in the usual way via step-by-step normalization of derivations.