A Syntactic Embedding of Predicate Logic into Second-Order Propositional Logic
Morten H. Sørensen and Paweł Urzyczyn
Source: Notre Dame J. Formal Logic Volume 51, Number 4
(2010), 457-473.
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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Links and Identifiers
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
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Notre Dame Journal of Formal Logic
