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Note on Globally Sound Analytic Calculi for Quantifier Macros

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Logic, Language, Information, and Computation (WoLLIC 2019)

Abstract

This paper focuses on a globally sound but possibly locally unsound analytic sequent calculus for the quantifier macro Q defined by \(Q_{x,y} A(x,y) = \forall x \exists y A(x,y)\). It is demonstrated that no locally sound analytic representation exists.

M. Baaz—This work is partially supported by FWF Project P 31063.

A. Lolic—Recipient of a DOC Fellowship of the Austrian Academy of Sciences at the Institute of Logic and Computation at TU Wien.

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Notes

  1. 1.

    Macros of connectives and quantifiers have a wide range of application in mathematics and are used to deal with explicit definitions, for example the handling of integrals as objects. In logic it is known that hierarchies of macros can be used to abbreviate proofs [3].

References

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  5. Takeuti, G.: Proof Theory. Courier Dover Publications, Mineola (2013)

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Correspondence to Matthias Baaz or Anela Lolic .

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Baaz, M., Lolic, A. (2019). Note on Globally Sound Analytic Calculi for Quantifier Macros. In: Iemhoff, R., Moortgat, M., de Queiroz, R. (eds) Logic, Language, Information, and Computation. WoLLIC 2019. Lecture Notes in Computer Science(), vol 11541. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-59533-6_29

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  • DOI: https://doi.org/10.1007/978-3-662-59533-6_29

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-59532-9

  • Online ISBN: 978-3-662-59533-6

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