The present monograph is a slightly revised version of my Habilitations-
schrift Proof-theoretic Aspects of Intensional and Non-Classical Logics,
successfully defended at Leipzig University, November 1997. It collects
work on proof systems for modal and constructive logics I have done over
the last few years. The main concern is display logic, a certain
refinement of Gentzen's sequent calculus developed by Nuel D. Belnap.
This book is far from offering a comprehensive presentation of
generalized sequent systems for modal logics broadly conceived. The
proof-theory of non-classical logics is a rapidly developing field, and
even the generalizations of the ordinary notion of sequent listed in
Chapter 1 can hardly be presented in great detail within a single
volume. In addition to further investigating the various approaches
toward generalized Gentzen systems, it is important to compare them and
to discuss their relative advantages and disadvantages. An initial
attempt at bringing together work on different kinds of proof systems
for modal logics has been made in [188]. Another step in the same
direction is [196]. Since Chapter 1 contains introductory
considerations and, moreover, every remaining chapter begins with some
surveying or summarizing remarks, in this preface I shall only emphasize
a relation to philosophy that is important to me, register the sources
of papers that have entered this book in some form or another, and
acknowledge advice and support.
