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On the Predicate Logic of Linear Kripke Frames and some of its Extensions
Studia Logica 81 (2):261-282 (2005)
Abstract
We propose a new, rather simple and short proof of Kripke-completeness for the predicate variant of Dummett's logic. Also a family of Kripke-incomplete extensions of this logic that are complete w.r.t. Kripke frames with equality (or equivalently, w.r.t. Kripke sheaves [8]), is described.My notes
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Citations of this work
Epsilon theorems in intermediate logics.Matthias Baaz & Richard Zach - 2022 - Journal of Symbolic Logic 87 (2):682-720.
Kripke Sheaf Completeness of some Superintuitionistic Predicate Logics with a Weakened Constant Domains Principle.Dmitrij Skvortsov - 2012 - Studia Logica 100 (1-2):361-383.
References found in this work
Presheaf semantics and independence results for some non-classical first-order logics.Silvio Ghilardi - 1989 - Archive for Mathematical Logic 29 (2):125-136.
On logics intermediate between intuitionistic and classical predicate logic.Toshio Umezawa - 1959 - Journal of Symbolic Logic 24 (2):141-153.
Completeness theorem for Dummett's LC quantified and some of its extensions.Giovanna Corsi - 1992 - Studia Logica 51 (2):317 - 335.
Directed frames.Giovanna Corsi & Silvio Ghilardi - 1989 - Archive for Mathematical Logic 29 (1):53-67.
On finite linear intermediate predicate logics.Hiroakira Ono - 1988 - Studia Logica 47 (4):391 - 399.
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