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Expanding the Universe

Trafford, James (2014) Expanding the Universe. THEORIA. An International Journal for Theory, History and Foundations of Science, 29 (3). pp. 325-343. ISSN ISSN 2171-679X

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In (Béziau 2001), Béziau provides a means by which Gentzen’s sequent calculus can be combined with the general semantic theory of bivaluations. In do- ing 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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Item Type: Published Article or Volume
Additional Information: ISSN: 0495-4548 (print)
Keywords: Universal logic; N-valued logics; Bivaluation; Sequent calculus
Depositing User: Unnamed user with email
Date Deposited: 13 Feb 2015 03:46
Last Modified: 13 Feb 2015 03:46
Item ID: 11284
Journal or Publication Title: THEORIA. An International Journal for Theory, History and Foundations of Science
Publisher: Euskal Herriko Unibertsitatea / Universidad del País Vasco
Official URL:
DOI or Unique Handle: 10.1387/theoria.11493
Date: September 2014
Page Range: pp. 325-343
Volume: 29
Number: 3
ISSN: ISSN 2171-679X

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