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Restricted Positive Quantification Is Not Elementary

Authors Aleksy Schubert, Pawel Urzyczyn, Daria Walukiewicz-Chrzaszcz

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Aleksy Schubert
Pawel Urzyczyn
Daria Walukiewicz-Chrzaszcz

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Aleksy Schubert, Pawel Urzyczyn, and Daria Walukiewicz-Chrzaszcz. Restricted Positive Quantification Is Not Elementary. In 20th International Conference on Types for Proofs and Programs (TYPES 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 39, pp. 251-273, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/LIPIcs.TYPES.2014.251

Abstract

We show that a restricted variant of constructive predicate logic with positive (covariant) quantification is of super-elementary complexity. The restriction is to limit the number of eigenvariables used in quantifier introductions rules to a reasonably usable level. This construction suggests that the known non-elementary decision algorithms for positive logic may actually be best possible.
Keywords
  • constructive logic
  • complexity
  • automata theory

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