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The Marktoberdorf Summer Schools on Informatics were started in
1970, with the intention to convene every second or third year a
group of top researchers in computing, devoted to preach their most
recent results to an elite of advanced students - young and most
promising people - and prepared to stand their questions, criticism
and suggestions. The themes of these Advanced Study In stitutes
under the sponsorship of the NATO Scientific Affairs Division
varied slightly over the years, oscillating more or less around
Programming Methodo logy, as the following list shows: 1970 Data
Structures and Computer Systems 1971 Program Structures and
Fundamental Concepts of Programming 1973 Structured Programming and
Programmed Structures 1975 Language Hierarchies and Interfaces 1978
Program Construction 1981 Theoretical Foundations of Programming
Methodology 1984 Control Flow and Data Flow: Concepts of
Distributed Programming 1986 Logic of Programming and Calculi of
Discrete Design 1988 Constructive Methods in Computing Science 1989
Logic, Algebra, and Computation Logic, Algebra, and Computation is
the theme of the summer school to which this volume is devoted. It
is the tenth in succession, but it is also the first in a new
series (the "blue" series) that is intended to alternate in future
with the traditional (the "red" series) arrangement; in fact the
tenth summer school in the "red" series with the title "Programming
and Mathematical Method" , held in 1990, was the subject of
celebrating both its serial number and the twenty years of
Marktoberdorf Summer Schools altogether.
This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of first-order logic formalization. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic, logic programming theory, category theory, modal logic, linear logic, first-order arithmetic and second-order logic. In each case the authors illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. For the new edition, they have rewritten many sections to improve clarity, added new sections on cut elimination, and included solutions to selected exercises. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence.
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