Expanding the universe of universal logic

Trafford, James (2014) Expanding the universe of universal logic. Theoria, 29 (3). pp. 325-343. ISSN 0495-4548

Creators:
Trafford, James
Description/Abstract:

In [5], 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.

Item Type:
Article
Date:
2014
Identification Number:
10.1387/theoria.11493
Schools:
School of Communications
Related URLs:
Depositing User:
Dr James Trafford
Date Deposited:
08 Sep 2014 12:23
Last Modified:
05 Mar 2022 04:31
Trafford, James:
ORCID iD: https://orcid.org/0000-0002-6762-2918
URI:
https://research.uca.ac.uk/id/eprint/1801

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