Preliminaries -- Standard Natural Deduction -- Other Deductive Systems -- Extended Natural Deduction -- Survey of Modal Logics -- Standard Approach to Basic Modal Logics -- Beyond Basic Logics and Standard Systems -- Labelled Systems in Modal Logics -- Logics of Linear Frames -- Analytic Labelled ND and Proof Search -- Modal Hybrid Logics -- Proof Methods for MHL.

This volume provides an extensive treatment of Natural Deduction and related types of proof systems, with a focus on the practical aspects of proof methods. The book has two main aims: Its first aim is to provide a systematic and historical survey of the variety of Natural Deduction systems in Classical and Modal Logics. The second aim is to present some systems of hybrid character, mixing Natural Deduction with other kinds of proof methods (including Sequent systems, Tableaux, Resolution). Such systems tend to be more universal and effective, because of the possibility of mixing strategies of proof search from different areas. All necessary background material is provided, in particular, a detailed presentation of Modal Logics, including First-Order Modal and Hybrid Modal Logics. The deduction systems presented in the book may be of interest to working logicians, researchers on automated deduction and teachers of logic.