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2016 Non-Fregean Propositional Logic with Quantifiers
Joanna Golińska-Pilarek, Taneli Huuskonen
Notre Dame J. Formal Logic 57(2): 249-279 (2016). DOI: 10.1215/00294527-3470547

Abstract

We study the non-Fregean propositional logic with propositional quantifiers, denoted by SCIQ. We prove that SCIQ does not have the finite model property and that it is undecidable. We also present examples of how to interpret in SCIQ various mathematical theories, such as the theory of groups, rings, and fields, and we characterize the spectra of SCIQ-sentences. Finally, we present a translation of SCIQ into a classical two-sorted first-order logic, and we use the translation to prove some model-theoretic properties of SCIQ.

Citation

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Joanna Golińska-Pilarek. Taneli Huuskonen. "Non-Fregean Propositional Logic with Quantifiers." Notre Dame J. Formal Logic 57 (2) 249 - 279, 2016. https://doi.org/10.1215/00294527-3470547

Information

Received: 21 January 2013; Accepted: 7 November 2013; Published: 2016
First available in Project Euclid: 9 February 2016

zbMATH: 06585187
MathSciNet: MR3482746
Digital Object Identifier: 10.1215/00294527-3470547

Subjects:
Primary: 03B60
Secondary: 03C80, 68Q19

Rights: Copyright © 2016 University of Notre Dame

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Vol.57 • No. 2 • 2016
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