David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 54 (1):79 - 88 (1995)
In [Ono 1987] H. Ono put the question about axiomatizing the intermediate predicate logicLFin characterized by the class of all finite Kripke frames (Problem 4,P41). It was established in [Skvortsov 1988] thatLFin is not recursively axiomatizable. One can easily show that for any finite posetM, the predicate logic characterized byM is recursively axiomatizable, and its axiomatization can be constructed effectively fromM. Namely, the set of formulas belonging to this logic is recursively enumerable, since it is embeddable in the two-sorted classical predicate calculusCPC 2 (the definition of the truth in a Kripke model may be expressed by a formula ofCPC 2). Thus the logicLFin is II 2 0 -arithmetical.Here we give a more explicit II 2 0 -description ofLFin: it is presented as the intersection of a denumerable sequence of finitely axiomatizable Kripke-complete logics. Namely, we give an axiomatization of the logicLB n P m + characterized by the class of all posets of the finite height m and the finite branching n. A finite axiomatization of the predicate logicLP m + characterized by the class of all posets of the height m is known from [Yokota 1989] (this axiomatics is essentially first-order; the standard propositional axiom of the height m is not sufficient [Ono 1983]). We prove thatLB n P m + =(LP m + +B n),B n being the propositional axiom of the branching n (see [Gabbay, de Jongh 1974]).
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Dmitrij Skvortsov (2012). Kripke Sheaf Completeness of Some Superintuitionistic Predicate Logics with a Weakened Constant Domains Principle. Studia Logica 100 (1-2):361-383.
Similar books and articles
Pierluigi Minari, Mitio Takano & Hiroakira Ono (1990). Intermediate Predicate Logics Determined by Ordinals. Journal of Symbolic Logic 55 (3):1099-1124.
M. J. Cresswell (1995). Incompleteness and the Barcan Formula. Journal of Philosophical Logic 24 (4):379 - 403.
Dmitrij Skvortsov (1998). On Some Kripke Complete and Kripke Incomplete Intermediate Predicate Logics. Studia Logica 61 (2):281-292.
Sergei Artemov & Giorgie Dzhaparidze (1990). Finite Kripke Models and Predicate Logics of Provability. Journal of Symbolic Logic 55 (3):1090-1098.
Hiroakira Ono (1988). On Finite Linear Intermediate Predicate Logics. Studia Logica 47 (4):391 - 399.
Nobu-Yuki Suzuki (1993). Some Results on the Kripke Sheaf Semantics for Super-Intuitionistic Predicate Logics. Studia Logica 52 (1):73 - 94.
Nobu -Yuki Suzuki (1990). Kripke Bundles for Intermediate Predicate Logics and Kripke Frames for Intuitionistic Modal Logics. Studia Logica 49 (3):289 - 306.
Dmitrij Skvortsov (2004). On Intermediate Predicate Logics of Some Finite Kripke Frames, I. Levelwise Uniform Trees. Studia Logica 77 (3):295 - 323.
Dmitrij Skvortsov (1997). Not Every "Tabular" Predicate Logic is Finitely Axiomatizable. Studia Logica 59 (3):387-396.
Dmitrij Skvortsov (2005). The Superintuitionistic Predicate Logic of Finite Kripke Frames Is Not Recursively Axiomatizable. Journal of Symbolic Logic 70 (2):451 - 459.
Added to index2009-01-28
Total downloads6 ( #211,419 of 1,099,906 )
Recent downloads (6 months)1 ( #303,846 of 1,099,906 )
How can I increase my downloads?