Notre Dame Journal of Formal Logic

A Syntactic Embedding of Predicate Logic into Second-Order Propositional Logic

Morten H. Sørensen and Paweł Urzyczyn

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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.

Article information

Source
Notre Dame J. Formal Logic Volume 51, Number 4 (2010), 457-473.

Dates
First available in Project Euclid: 29 September 2010

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1285765799

Digital Object Identifier
doi:10.1215/00294527-2010-029

Mathematical Reviews number (MathSciNet)
MR2741837

Subjects
Primary: 03B20: Subsystems of classical logic (including intuitionistic logic) 03F03: Proof theory, general

Keywords
propositional quantification IPC2

Citation

Sørensen, Morten H.; Urzyczyn, Paweł. A Syntactic Embedding of Predicate Logic into Second-Order Propositional Logic. Notre Dame Journal of Formal Logic 51 (2010), no. 4, 457--473. doi:10.1215/00294527-2010-029. http://projecteuclid.org/euclid.ndjfl/1285765799.


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