On the Undecidability of Coherent Logic

Through a reduction of the halting problem for register machines we prove that it is undecidable whether or not a coherent formula is a logical consequence of a coherent theory. We include a simple completeness proof for coherent logic. Although not published in the present form, these results seem...

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Bibliographic Details
Published inProcesses, Terms and Cycles: Steps on the Road to Infinity pp. 6 - 13
Main Author Bezem, Marc
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg 2005
SeriesLecture Notes in Computer Science
Subjects
Function Symbol
Horn Clause
Mathematical Linguistics
Program Counter
Proof System
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ISBN354030911X
9783540309116
ISSN0302-9743
1611-3349
DOI10.1007/11601548_2

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Summary:Through a reduction of the halting problem for register machines we prove that it is undecidable whether or not a coherent formula is a logical consequence of a coherent theory. We include a simple completeness proof for coherent logic. Although not published in the present form, these results seem to be folklore. Therefore we do not claim originality. Given the undecidability of the halting problem for register machines the presentation is self-contained.
ISBN:354030911X
9783540309116
ISSN:0302-9743
1611-3349
DOI:10.1007/11601548_2