Natural Deduction, Hybrid Systems and Modal Logics

A good title should be informative enough to illuminate a potential reader on the content of a book. We hope that the present title gives at least some hints of what this book is about. The notion of natural deduction or modal logic are rather well known, but the notion of hybrid system certainly needs some explanation. In short, this study may be seen as a kind of search for good deductive systems. We think of systems good in practice which may be applied with easenotonlybywelltrainedlogiciansbutalso, forexample, byphilosophers who need handy deductive tools accompanying their analyses. In parti- lar, we are interested in providing systems that may be widely applied in teaching logic. Nowadays one may observe that several courses in critical thinking tend to eliminate courses in practical logic. On the other hand, logic is often taught as a strictly mathematical discipline in very dema- ing courses. It is important to ?ll the gap between these extrema, and the crucial ingredient of any course which is supposed to teach how to use logic, is certainly a suitable deductive system. Since we address this work to a wide audience interested in applications of logic, we were trying to make it self-contained and accessible to a reader with no hard training in logic. The assumed reader should have some ba- ground in logic (an elementary course covering classical propositional and ?rst-order logic with basics of set theory is enough) but not necessarily in modal logic.

The first to show that the scope of application of Natural Deduction systems is far beyond the one usually considered The first comprehensive presentation of hybrid deductive systems mixing Natural Deduction with Resolution The first to label Natural Deduction systems for a wide spectrum of Temporal Logics Provides a detailed presentation of problems connected with the formalization of Logics of linear time Gives a detailed exposition of deductive systems for Hybrid Logics

Autorentext

Andrzej Indrzejczak is professor of logic and Head of the Department of General Methodology at the University of Lodz, Poland. His scientific interests include the proof theory for non-classical logics, the philosophy of logic and the methodology of science. He is the author of three books and numerous papers concerned mainly with the investigation of proof techniques for non-classical logics, published e.g. in Bulletin of the Section of Logic, Logic Journal of the IGPL, Logic and Logical Philosophy, Logica Trianguli, and Studia Logica.

Klappentext

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.

Inhalt
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.