Every finitely reducible logic has the finite model property with respect to the class of ♦-formulae
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 62 (2):177 - 200 (1999)
In this paper a unified framework for dealing with a broad family of propositional multimodal logics is developed. The key tools for presentation of the logics are the notions of closure relation operation and monotonous relation operation. The two classes of logics: FiRe-logics (finitely reducible logics) and LaFiRe-logics (FiRe-logics with local agreement of accessibility relations) are introduced within the proposed framework. Further classes of logics can be handled indirectly by means of suitable translations. It is shown that the logics from these classes have the finite model property with respect to the class of -formulae, i.e. each -formula has a -model iff it has a finite -model. Roughly speaking, a -formula is logically equivalent to a formula in negative normal form without occurrences of modal operators with necessity force. In the proof we introduce a substantial modification of Claudio Cerrato's filtration technique that has been originally designed for graded modal logics. The main core of the proof consists in building adequate restrictions of models while preserving the semantics of the operators used to build terms indexing the modal operators.
|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
Xavier Caicedo & Ricardo O. Rodriguez (2010). Standard Gödel Modal Logics. Studia Logica 94 (2):189 - 214.
Vladimir V. Rybakov (1994). Criteria for Admissibility of Inference Rules. Modal and Intermediate Logics with the Branching Property. Studia Logica 53 (2):203 - 225.
C. J. Van Alten (2005). The Finite Model Property for Knotted Extensions of Propositional Linear Logic. Journal of Symbolic Logic 70 (1):84 - 98.
Stéphane Demri & Dov Gabbay (2000). On Modal Logics Characterized by Models with Relative Accessibility Relations: Part I. Studia Logica 65 (3):323-353.
David Gabelaia, Agi Kurucz, Frank Wolter & Michael Zakharyaschev (2005). Products of 'Transitive' Modal Logics. Journal of Symbolic Logic 70 (3):993-1021.
R. Hirsch, I. Hodkinson & A. Kurucz (2002). On Modal Logics Between K × K × K and $S5 \Times S5 \Times S5$. Journal of Symbolic Logic 67 (1):221 - 234.
Stéphane Demri & Dov Gabbay (2000). On Modal Logics Characterized by Models with Relative Accessibility Relations: Part II. Studia Logica 66 (3):349-384.
Ágnes Kurucz (2000). Arrow Logic and Infinite Counting. Studia Logica 65 (2):199-222.
Frank Wolter (1995). The Finite Model Property in Tense Logic. Journal of Symbolic Logic 60 (3):757-774.
Lauri Hella, Phokion G. Kolaitis & Kerkko Luosto (1996). Almost Everywhere Equivalence of Logics in Finite Model Theory. Bulletin of Symbolic Logic 2 (4):422-443.
Added to index2009-01-28
Total downloads2 ( #405,789 of 1,679,298 )
Recent downloads (6 months)1 ( #183,420 of 1,679,298 )
How can I increase my downloads?