Studia Logica 102 (6):1295-1322 (2014)

Authors
Andrzej Indrzejczak
University of Lodz
Abstract
The paper is a brief survey of some sequent calculi which do not follow strictly the shape of sequent calculus introduced by Gentzen. We propose the following rough classification of all SC: Systems which are based on some deviations from the ordinary notion of a sequent are called generalised; remaining ones are called ordinary. Among the latter we distinguish three types according to the proportion between the number of primitive sequents and rules. In particular, in one of these types, called Gentzen’s type, we have a subtype of standard SC due to Gentzen. Hence by nonstandard ones we mean all these ordinary SC where other kinds of rules are applied than those admitted in standard Gentzen’s sequent calculi. We describe briefly some of the most interesting or important nonstandard SC belonging to the three abovementioned types.
Keywords Sequent Calculi  Natural Deduction  Proof Methods
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DOI 10.1007/s11225-014-9567-y
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References found in this work BETA

Display Logic.Nuel D. Belnap - 1982 - Journal of Philosophical Logic 11 (4):375-417.
Logical Constants as Punctuation Marks.Kosta Došen - 1989 - Notre Dame Journal of Formal Logic 30 (3):362-381.
Natural Deduction with General Elimination Rules.Jan von Plato - 2001 - Archive for Mathematical Logic 40 (7):541-567.
The Method of Hypersequents in the Proof Theory of Propositional Non-Classical Logics.Arnon Avron - 1996 - In Wilfrid Hodges (ed.), Logic: Foundations to Applications. Oxford: pp. 1-32.

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Citations of this work BETA

Gödel’s Natural Deduction.Kosta Došen & Miloš Adžić - 2018 - Studia Logica 106 (2):397-415.
A Sequent Systems Without Improper Derivations.Katsumi Sasaki - 2022 - Bulletin of the Section of Logic 51 (1):91-108.

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