Expanding the universe of universal logic

Citation data:

Theoria (Spain), ISSN: 2171-679X, Vol: 29, Issue: 3, Page: 325-343

Publication Year:
2014
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Repository URL:
http://philsci-archive.pitt.edu/id/eprint/11284
DOI:
10.1387/theoria.11493
Author(s):
James Trafford
Publisher(s):
Euskal Herriko Unibertsitatea / Universidad del País Vasco
Tags:
Arts and Humanities
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article description
In (Béziau 2001), Béziau provides a means by which Gentzen's sequent calculus can be combined with the general semantic theory of bivaluations. In doing so, according to Béziau, it is possible to construe the abstract "core" of logics in general, where logical syntax and semantics are "two sides of the same coin". The central suggestion there is that, by way of a modification of the notion of maximal consistency, it is possible to prove the soundness and completeness for any normal logic (without invoking the role of classical negation in the completeness proof). However, the reduction to bivaluation may be a side effect of the architecture of ordinary sequents, which is both overly restrictive, and entails certain expressive restrictions over the language. This paper provides an expansion of Béziau's completeness results for logics, by showing that there is a natural extension of that line of thinking to n-sided sequent constructions. Through analogical techniques to Béziau's construction, it is possible, in this setting, to construct abstract soundness and completeness results for n-valued logics.

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