Choice Sequences: A Chapter of Instuitionistic Mathematics (Oxford Logic Guides)

Science & Math

Troelstra, A.S.

Mathematics

Oxford University Press

Constructivism in Mathematics: An Introduction (Volume 121) (Studies in Logic and the Foundations of Mathematics, Volume 121)

Van Dalen, D.

North-Holland

<p>This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. There are numerous exercises throughout the text. 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. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to selected exercises have been included.</p>

Basic Proof Theory (Cambridge Tracts in Theoretical Computer Science, Series Number 43)

Computers & Technology

Schwichtenberg, H.

Computer Science

Cambridge University Press

<p>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.</p>

Programming Languages

The initial sections of this text deal with syntactical matters such as logical formalism, cut-elimination, and the embedding of intuitionistic logic in classical linear logic. Concluding chapters focus on proofnets for the multiplicative fragment and the algorithmic interpretation of cut-elimination in proofnets.

Lectures on Linear Logic (Volume 29) (Lecture Notes)

Center for the Study of Language and Inf

Basic Proof Theory (Cambridge Tracts in Theoretical Computer Science)

Constructivism in Mathematics Vol.2

Elsevier Science

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