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SCI–Sequent Calculi, Cut Elimination and Interpolation Property

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Janusz Czelakowski on Logical Consequence

Part of the book series: Outstanding Contributions to Logic ((OCTR,volume 27))

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Abstract

We discuss the methods for providing sequent calculi for Suszko’s basic non-Fregean Logic with sentential identity SCI. After examination of possible strategies and already proposed systems we focus on the new calculus and its modification. It does not satisfy full cut elimination but a slightly generalised form of the subformula property holds for it. It is also standard in the sense of satisfying several conditions on rules formulated by Gentzen and his followers. We examine also the problem of providing a constructive proof of the interpolation theorem in the setting of this sequent calculus.

Second reader: Heinrich Wansing

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Notes

  1. 1.

    One may easily notice that axioms 2 and 4 are analogues of usual congruency principles for identity with respect to unary and binary predicates. Only axiom 3 has no direct counterpart in identity laws for terms.

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Authors and Affiliations

  1. Department of Logic, University of Łódź, Łódź, Poland

    Andrzej Indrzejczak

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  1. Andrzej Indrzejczak
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Correspondence to Andrzej Indrzejczak .

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Editors and Affiliations

  1. Institute of Philosophy and Sociology, Polish Academy of Sciences, Warsaw, Poland

    Jacek Malinowski

  2. Department of Logic, Nicolaus Copernicus University, Toruń, Poland

    Rafał Palczewski

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Indrzejczak, A. (2024). SCI–Sequent Calculi, Cut Elimination and Interpolation Property. In: Malinowski, J., Palczewski, R. (eds) Janusz Czelakowski on Logical Consequence. Outstanding Contributions to Logic, vol 27. Springer, Cham. https://doi.org/10.1007/978-3-031-44490-6_11

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