Studia Logica 102 (5):1003-1020 (2014)

Gillman Payette
University of British Columbia
Peter Schotch
Dalhousie University
In the late 1960s and early 1970s, Dana Scott introduced a kind of generalization (or perhaps simplification would be a better description) of the notion of inference, familiar from Gentzen, in which one may consider multiple conclusions rather than single formulas. Scott used this idea to good effect in a number of projects including the axiomatization of many-valued logics (of various kinds) and a reconsideration of the motivation of C.I. Lewis. Since he left the subject it has been vigorously prosecuted by a number of authors under the heading of abstract entailment relations where it has found an important role in both algebra and theoretical computer science. In this essay we go back to the beginnings, as presented by Scott, in order to make some comments about Scott’s cut rule, and show how much of Scott’s main result may be applied to the case of single-conclusion logic.
Keywords Dana Scott  Lindenbaum  Abstract entailment relations  Structural rules
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DOI 10.1007/s11225-013-9519-y
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References found in this work BETA

Multiple-Conclusion Logic.D. J. Shoesmith & T. J. Smiley - 1978 - Cambridge, England / New York London Melbourne: Cambridge University Press.
On Engendering an Illusion of Understanding.Dana Scott - 1971 - Journal of Philosophy 68 (21):787-807.
Multiple Conclusion Logic.N. Tennant - 1980 - Philosophical Quarterly 30 (121):379-382.
On Preserving.Gillman Payette & Peter K. Schotch - 2007 - Logica Universalis 1 (2):295-310.

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Citations of this work BETA

Cut Elimination for Entailment Relations.Davide Rinaldi & Daniel Wessel - 2019 - Archive for Mathematical Logic 58 (5-6):605-625.

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