David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Philosophical Logic 24 (4):379 - 403 (1995)
A (normal) system of propositional modal logic is said to be complete iff it is characterized by a class of (Kripke) frames. When we move to modal predicate logic the question of completeness can again be raised. It is not hard to prove that if a predicate modal logic is complete then it is characterized by the class of all frames for the propositional logic on which it is based. Nor is it hard to prove that if a propositional modal logic is incomplete then so is the predicate logic based on it. But the interesting question is whether a complete propositional modal logic can have an incomplete extension. In 1967 Kripke announced the incompleteness of a predicate extension of S4. The purpose of the present article is to present several such systems. In the first group it is the systems with the Barcan Formula which are incomplete, while those without are complete. In the second group it is those without the Barcan formula which are incomplete, while those with the Barcan Formula are complete. But all these are based on propositional systems which are characterized by frames satisfying in each case a single first-order sentence
|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
G. E. Hughes (1968/1972). An Introduction to Modal Logic. London,Methuen.
Saul A. Kripke (1963). Semantical Considerations on Modal Logic. Acta Philosophica Fennica 16 (1963):83-94.
George Boolos (1979). The Unprovability of Consistency: An Essay in Modal Logic. Cambridge University Press.
Silvio Ghilardi (1991). Incompleteness Results in Kripke Semantics. Journal of Symbolic Logic 56 (2):517-538.
Citations of this work BETA
James W. Garson (2005). Unifying Quantified Modal Logic. Journal of Philosophical Logic 34 (5/6):621 - 649.
Mirosław Szatkowski (2011). Partly Free Semantics for Some Anderson-Like Ontological Proofs. Journal of Logic, Language and Information 20 (4):475-512.
Similar books and articles
W. J. Blok (1979). An Axiomatization of the Modal Theory of the Veiled Recession Frame. Studia Logica 38 (1):37 - 47.
Heinrich Wansing (1999). Predicate Logics on Display. Studia Logica 62 (1):49-75.
H. Kushida & M. Okada (2003). A Proof-Theoretic Study of the Correspondence of Classical Logic and Modal Logic. Journal of Symbolic Logic 68 (4):1403-1414.
Horacio Arló-Costa & Eric Pacuit (2006). First-Order Classical Modal Logic. Studia Logica 84 (2):171 - 210.
Nobu-Yuki Suzuki (1995). Constructing a Continuum of Predicate Extensions of Each Intermediate Propositional Logic. Studia Logica 54 (2):173 - 198.
Tatsuya Shimura (2000). Kripke Incompleteness of Predicate Extensions of the Modal Logics Axiomatized by a Canonical Formula for a Frame with a Nontrivial Cluster. Studia Logica 65 (2):237-247.
Dmitrij Skvortsov (1998). On Some Kripke Complete and Kripke Incomplete Intermediate Predicate Logics. Studia Logica 61 (2):281-292.
Giovanna Corsi (2002). A Unified Completeness Theorem for Quantified Modal Logics. Journal of Symbolic Logic 67 (4):1483-1510.
Melvin Fitting (2012). Barcan Both Ways. Journal of Applied Non-Classical Logics 9 (2-3):329-344.
Added to index2009-01-28
Total downloads33 ( #97,829 of 1,726,249 )
Recent downloads (6 months)4 ( #183,615 of 1,726,249 )
How can I increase my downloads?