Non-Fregean Propositional Logic with Quantifiers

Notre Dame Journal of Formal Logic 57 (2):249-279 (2016)
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Abstract

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

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Author's Profile

Joanna Golinska-Pilarek
University of Warsaw

Citations of this work

Hyperintensionality and Normativity.Federico L. G. Faroldi - 2019 - Cham, Switzerland: Springer Verlag.
A Modal Loosely Guarded Fragment of Second-Order Propositional Modal Logic.Gennady Shtakser - 2023 - Journal of Logic, Language and Information 32 (3):511-538.

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References found in this work

Abolition of the Fregean Axiom.Roman Suszko - 1975 - Lecture Notes in Mathematics 453:169-239.
Investigations into the sentential calculus with identity.Roman Suszko & Stephen L. Bloom - 1972 - Notre Dame Journal of Formal Logic 13 (3):289-308.
Identity connective and modality.Roman Suszko - 1971 - Studia Logica 27 (1):7-39.
Quasi-completeness in non-Fregean logic.Roman Suszko - 1971 - Studia Logica 29 (1):7-16.

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