On the undecidability of coherent logic

Authors:
Marc Bezem
Affiliations:
Department of Computer Science, University of Bergen, Bergen, Norway
Venue:
Processes, Terms and Cycles
Year:
2005

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Abstract

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.