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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 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
Aguilera, J.P., Baaz, M.: Unsound inferences make proofs shorter. J. Symb. Log. 84(1), 102–122 (2019)
Gentzen., G.: Untersuchungen über das logische Schließen. Mathematische Zeitschrift 39, 176–210, 405–431 (1934–1935)
Mac Lane, S.: Abgekürzte Beweise im Logikkalkül. Hubert, Columbus (1934)
Robinson, J.A.: A machine-oriented logic based on the resolution principle. J. ACM (JACM) 12(1), 23–41 (1965)
Takeuti, G.: Proof Theory. Courier Dover Publications, Mineola (2013)
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer-Verlag GmbH Germany, part of Springer Nature
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-662-59533-6_29
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-59532-9
Online ISBN: 978-3-662-59533-6
eBook Packages: Computer ScienceComputer Science (R0)