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Category Theory and Computer Science : 7th International Conference, CTCS'97, Santa Margherita Ligure Italy, September 4-6, 1997, Proceedings
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ISBN: 354063455X 3540695524 9783540634553 Year: 1997 Volume: 1290 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,

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Abstract

This book constitutes the refereed proceedings of the 7th International Conference on Category Theory and Computer Science, CTCS'97, held in Santa Margheria Ligure, Italy, in September 1997. Category theory attracts interest in the theoretical computer science community because of its ability to establish connections between different areas in computer science and mathematics and to provide a few generic principles for organizing mathematical theories. This book presents a selection of 15 revised full papers together with three invited contributions. The topics addressed include reasoning principles for types, rewriting, program semantics, and structuring of logical systems.

Keywords

Computer science --- Categories (Mathematics) --- Mathematics --- Congresses. --- Computer Science --- Engineering & Applied Sciences --- Congresses --- Informatics --- Computer science. --- Architecture, Computer. --- Programming languages (Electronic computers). --- Computer logic. --- Mathematical logic. --- K-theory. --- Computer Science. --- Computer System Implementation. --- Programming Languages, Compilers, Interpreters. --- Logics and Meanings of Programs. --- Mathematical Logic and Formal Languages. --- K-Theory. --- Mathematical Logic and Foundations. --- Computer network architectures. --- Logic design. --- Logic, Symbolic and mathematical. --- Design, Logic --- Design of logic systems --- Digital electronics --- Electronic circuit design --- Logic circuits --- Machine theory --- Switching theory --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Architectures, Computer network --- Network architectures, Computer --- Computer architecture --- Algebraic topology --- Homology theory --- Science --- Computer science logic --- Logic, Symbolic and mathematical --- Computer languages --- Computer program languages --- Computer programming languages --- Machine language --- Electronic data processing --- Languages, Artificial --- Architecture, Computer --- Computer science - Mathematics - Congresses --- Categories (Mathematics) - Congresses.


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Concepts of Proof in Mathematics, Philosophy, and Computer Science

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Abstract

A proof is a successful demonstration that a conclusion necessarily follows by logical reasoning from axioms which are considered evident for the given context and agreed upon by the community. It is this concept that sets mathematics apart from other disciplines and distinguishes it as the prototype of a deductive science. Proofs thus are utterly relevant for research, teaching and communication in mathematics and of particular interest for the philosophy of mathematics. In computer science, moreover, proofs have proved to be a rich source for already certified algorithms. This book provides the reader with a collection of articles covering relevant current research topics circled around the concept 'proof'. It tries to give due consideration to the depth and breadth of the subject by discussing its philosophical and methodological aspects, addressing foundational issues induced by Hilbert's Programme and the benefits of the arising formal notions of proof, without neglecting reasoning in natural language proofs and applications in computer science such as program extraction.

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