Abstract
This note follows up an earlier paper in which a possibility of defining logical constants within abstract logical frameworks was discussed, by using duals as a general method of applying the idea of invariance under replacement as a criterion for logicality. In the present note, this approach is applied to the discussion on logicality of generalized quantifiers. It is demonstrated that generalized quantifiers are logical constants by this criterion.
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References
Bonnay, D., Westerståhl, D.: Consequence mining. J. Philosophical Logic 41, 671–709 (2012)
Feferman, S.: Which Quantifiers Are Logical? A Combined Semantical and Inferential Criterion. In: Torza, A. (ed.) Quantifiers, Quantifiers, and Quantifiers: Themes in Logic, Metaphysics, and Language, pp. 19–30. Springer, New Jersey (2015)
Keenan, E.: Excursions in natural logic, in: C. Casadio et al. (eds.), Language and Grammar: Studies in Mathematical Linguistics and Natural Language, CSLI Publications 31–52 (2005)
Perkov, T.: Abstract logical constants. Logica Universalis 12, 341–350 (2018)
Szymanik, J.: Quantifiers and Cognition: Logical and Computational Perspectives. Springer, NewYork (2016)
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This work has been supported by Croatian Science Foundation (HRZZ) under projects UIP-2017-05-9219 and IP-2018-01-7459.
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Perkov, T. A Note on Logicality of Generalized Quantifiers. Log. Univers. 15, 149–152 (2021). https://doi.org/10.1007/s11787-021-00271-8
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DOI: https://doi.org/10.1007/s11787-021-00271-8