Abstract
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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Notes
Strictly speaking in Reeves’ case it is n conclusions since he worked with tableux being upside-down versions of SC.
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Acknowledgements
I am greatly indebted to Nils Kürbis, René Gazzari, and to all reviewers for insightful remarks which helped to improve the final version of this text. The results reported in this paper are supported by the National Science Centre, Poland (Grant Number: DEC-2017/25/B/HS1/01268).
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Indrzejczak, A. A novel approach to equality. Synthese 199, 4749–4774 (2021). https://doi.org/10.1007/s11229-020-03000-8
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DOI: https://doi.org/10.1007/s11229-020-03000-8