David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 76 (3):329 - 342 (2004)
In this paper, we are going to analyze the phenomenon of modal incompleteness from an algebraic point of view. The usual method of showing that a given logic L is incomplete is to show that for some L and some cannot be separated from by a suitably wide class of complete algebras — usually Kripke algebras. We are going to show that classical examples of incomplete logics, e.g., Fine logic, are not complete with respect to any class of complete BAOs. Even above Grz it is possible to find a continuum of such logics, which immediately implies the existence of a continuum of neighbourhood-incomplete Grz logics. Similar results can be proved for Löb logics. In addition, completely incomplete logics above Grz may be found uniformly as a result of failures of some admissible rule of a special kind.
|Keywords||Philosophy Logic Mathematical Logic and Foundations Computational Linguistics|
|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
No citations found.
Similar books and articles
Johan van Benthem, Guram Bezhanishvili & Mai Gehrke (2003). Euclidean Hierarchy in Modal Logic. Studia Logica 75 (3):327-344.
I. L. Humberstone (1990). Expressive Power and Semantic Completeness: Boolean Connectives in Modal Logic. Studia Logica 49 (2):197 - 214.
V. V. Rybakov (1995). Hereditarily Structurally Complete Modal Logics. Journal of Symbolic Logic 60 (1):266-288.
M. J. Cresswell (1995). Incompleteness and the Barcan Formula. Journal of Philosophical Logic 24 (4):379 - 403.
Tadeusz Litak & Frank Wolter (2005). All Finitely Axiomatizable Tense Logics of Linear Time Flows Are CoNP-Complete. Studia Logica 81 (2):153 - 165.
W. J. Blok (1980). The Lattice of Modal Logics: An Algebraic Investigation. Journal of Symbolic Logic 45 (2):221-236.
Roy A. Benton (2002). A Simple Incomplete Extension of T Which is the Union of Two Complete Modal Logics with F.M.P. Journal of Philosophical Logic 31 (6):527-541.
Dmitrij Skvortsov (1998). On Some Kripke Complete and Kripke Incomplete Intermediate Predicate Logics. Studia Logica 61 (2):281-292.
Vladimir V. Rybakov (2011). Best Unifiers in Transitive Modal Logics. Studia Logica 99 (1-3):321-336.
David Gabelaia, Agi Kurucz, Frank Wolter & Michael Zakharyaschev (2005). Products of 'Transitive' Modal Logics. Journal of Symbolic Logic 70 (3):993-1021.
Added to index2009-01-28
Total downloads9 ( #223,851 of 1,696,632 )
Recent downloads (6 months)3 ( #186,707 of 1,696,632 )
How can I increase my downloads?