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2010 A Syntactic Embedding of Predicate Logic into Second-Order Propositional Logic
Morten H. Sørensen, Paweł Urzyczyn
Notre Dame J. Formal Logic 51(4): 457-473 (2010). DOI: 10.1215/00294527-2010-029

Abstract

We give a syntactic translation from first-order intuitionistic predicate logic into second-order intuitionistic propositional logic IPC2. The translation covers the full set of logical connectives ∧, ∨, →, ⊥, ∀, and ∃, extending our previous work, which studied the significantly simpler case of the universal-implicational fragment of predicate logic. As corollaries of our approach, we obtain simple proofs of nondefinability of ∃ from the propositional connectives and nondefinability of ∀ from ∃ in the second-order intuitionistic propositional logic. We also show that the ∀-free fragment of IPC2 is undecidable.

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Morten H. Sørensen. Paweł Urzyczyn. "A Syntactic Embedding of Predicate Logic into Second-Order Propositional Logic." Notre Dame J. Formal Logic 51 (4) 457 - 473, 2010. https://doi.org/10.1215/00294527-2010-029

Information

Published: 2010
First available in Project Euclid: 29 September 2010

zbMATH: 1216.03029
MathSciNet: MR2741837
Digital Object Identifier: 10.1215/00294527-2010-029

Subjects:
Primary: 03B20, 03F03

Rights: Copyright © 2010 University of Notre Dame

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Vol.51 • No. 4 • 2010
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