Duality and universal models for the meet-implication fragment of IPC

Authors
Publication date 2015
Host editors
  • M. Aher
  • D. Hole
  • E. Jeřábek
  • C. Kupke
Book title Logic, Language, and Computation
Book subtitle 10th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2013, Gudauri, Georgia, September 23-27, 2013: revised selected papers
ISBN
  • 978-3-662-46905-7
ISBN (electronic)
  • 978-3-662-46906-4
Series Lecture Notes in Computer Science
Event 10th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2013
Pages (from-to) 97-116
Publisher Berlin: Springer
Organisations
  • Faculty of Science (FNWI)
  • Interfacultary Research - Institute for Logic, Language and Computation (ILLC)
Abstract
In this paper we investigate the fragment of intuitionistic logic which only uses conjunction (meet) and implication, using finite duality for distributive lattices and universal models. We give a description of the finitely generated universal models of this fragment and give a complete characterization of the up-sets of Kripke models of intuitionistic logic which can be defined by meet-implication-formulas. We use these results to derive a new version of subframe formulas for intuitionistic logic and to show that the uniform interpolants of meet-implication-formulas are not necessarily uniform interpolants in the full intuitionistic logic.
Document type Conference contribution
Language English
Published at https://doi.org/10.1007/978-3-662-46906-4_7
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