Synthese 199 (1-2):4749-4774 (2021)

Andrzej Indrzejczak
University of Lodz
A new type of formalization of classical first-order logic with equality is introduced on the basis of the sequent calculus. It serves to justify the claim that equality is a logical constant characterised by well-behaved rules satisfying properties usually regarded as essential. The main feature of this approach is the application of sequents built not only from formulae but also from terms. Two variants of sequent calculus are examined, a structural and a logical one. The former is defined in accordance with Dos̆en’s criteria for logical constants. The latter is a standard Gentzen’s sequent calculus and satisfies Hacking’s criteria for logicality, including cut elimination. It is also shown that provided rules are harmonious in the sense advocated by Gratzl and Orlandelli.
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DOI 10.1007/s11229-020-03000-8
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References found in this work BETA

Tractatus logico-philosophicus.Ludwig Wittgenstein - 1922 - Filosoficky Casopis 52:336-341.
Uber Sinn und Bedeutung.Gottlob Frege - 1892 - Zeitschrift für Philosophie Und Philosophische Kritik 100 (1):25-50.
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Basic Proof Theory.A. S. Troelstra - 2000 - Cambridge University Press.

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The Calculus of Natural Calculation.René Gazzari - 2021 - Studia Logica 109 (6):1375-1411.

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