A Three-Valued Fregean Quantification Logic

Journal of Philosophical Logic 48 (2):409-423 (2019)
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Abstract

Kripke’s Fregean quantification logic FQ fails to formalize the usual first-order logic with identity due to the interpretation of the conditional operator. Motivated by Kripke’s syntax and semantics, the three-valued Fregean quantification logic FQ3 is proposed. This three valued logic differs from Kleene and Łukasiewicz’s three-valued logics. The logic FQ3 is decidable. A sound and complete Hilbert-style axiomatic system for the logic FQ3 is presented.

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Minghui Ma
Sun Yat-Sen University

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References found in this work

Introduction to metamathematics.Stephen Cole Kleene - 1952 - Groningen: P. Noordhoff N.V..
Uber Sinn und Bedeutung.Gottlob Frege - 1892 - Zeitschrift für Philosophie Und Philosophische Kritik 100 (1):25-50.
Introduction to Metamathematics.H. Rasiowa - 1954 - Journal of Symbolic Logic 19 (3):215-216.
Begriffsschrift.Gottlob Frege - 1967 - In Jean Van Heijenoort (ed.), From Frege to Gödel. Cambridge: Harvard University Press. pp. 1-83.

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