Automata, Languages and Programming
Volume 62 of the series Lecture Notes in Computer Science pp 268288
Arithmetical completeness in logics of programs
 David HarelAffiliated withLaboratory for Computer Science, Massachusetts Institute of Technology
Abstract
We consider the problem of designing arithmetically complete axiom systems for proving general properties of programs; i.e. axiom systems which are complete over arithmetical universes, when all firstorder formulae which are valid in such universes are taken as axioms. We prove a general Theorem of Completeness which takes care of a major part of the responsibility when designing such systems. It is then shown that what is left to do in order to establish an arithmetical completeness result, such as those appearing in [12] and [14] for the logics DL and DL^{+}, can be described as a chain of reasoning which involves some simple utilizations of arithmetical induction. An immediate application of these observations is given in the form of an arithmetical completeness result for a new logic similar to that of Salwicki [22]. Finally, we contrast this discipline with Cook's [5] notion of relative completeness.
 Title
 Arithmetical completeness in logics of programs
 Book Title
 Automata, Languages and Programming
 Book Subtitle
 Fifth Colloquium, Udine, Italy, July 17–21, 1978
 Pages
 pp 268288
 Copyright
 1978
 DOI
 10.1007/3540088601_20
 Print ISBN
 9783540088608
 Online ISBN
 9783540358077
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 62
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Authors

 David Harel ^{(1)}
 Author Affiliations

 1. Laboratory for Computer Science, Massachusetts Institute of Technology, 02139, Cambridge, MA
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