2015 | OriginalPaper | Chapter
On the Mints Hierarchy in First-Order Intuitionistic Logic
Authors : Aleksy Schubert, Paweł Urzyczyn, Konrad Zdanowski
Published in: Foundations of Software Science and Computation Structures
Publisher: Springer Berlin Heidelberg
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We study the decidability and complexity of fragments of intuitionistic first-order logic over ( ∀ , → ) determined by the alternation of positive and negative occurrences of quantifiers (Mints hierarchy). We prove that fragments Π
2
and Σ
2
are undecidable and that Σ
1
is
Expspace
-complete.