David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 70 (3):373 - 409 (2002)
The guarded fragment (GF) was introduced by Andréka, van Benthem and Németi as a fragment of first order logic which combines a great expressive power with nice, modal behavior. It consists of relational first order formulas whose quantifiers are relativized by atoms in a certain way. Slightly generalizing the admissible relativizations yields the packed fragment (PF). In this paper we investigate interpolation and definability in these fragments. We first show that the interpolation property of first order logic fails in restriction to GF and PF. However, each of these fragments turns out to have an alternative interpolation property that closely resembles the interpolation property usually studied in modal logic. These results are strong enough to entail the Beth definability property for GF and PF. Even better, every guarded or packed finite variable fragment has the Beth property. For interpolation, we characterize exactly which finite variable fragments of GF and PF enjoy this property.
|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
Balder ten Cate & Massimo Franceschet (2005). Guarded Fragments with Constants. Journal of Logic 14 (3):281-288.
Johan van Benthem (2005). Guards, Bounds, and Generalized Semantics. Journal of Logic, Language and Information 14 (3):263-279.
Dirk Leinders, Maarten Marx, Jerzy Tyszkiewicz & Jan Van den Bussche (2005). The Semijoin Algebra and the Guarded Fragment. Journal of Logic, Language and Information 14 (3):331-343.
Balder ten Cate & Massimo Franceschet (2005). Guarded Fragments with Constants. Journal of Logic, Language and Information 14 (3):281-288.
Similar books and articles
Carlos Areces, Patrick Blackburn & Maarten Marx (2001). Hybrid Logics: Characterization, Interpolation and Complexity. Journal of Symbolic Logic 66 (3):977-1010.
Johan van Benthem (2007). A New Modal Lindström Theorem. Logica Universalis 1 (1):125-138.
Larisa Maksimova (2011). Interpolation and Definability Over the Logic Gl. Studia Logica 99 (1-3):249-267.
Gábor Sági & Saharon Shelah (2006). On Weak and Strong Interpolation in Algebraic Logics. Journal of Symbolic Logic 71 (1):104 - 118.
Dirk Roorda (1994). Interpolation in Fragments of Classical Linear Logic. Journal of Symbolic Logic 59 (2):419-444.
Balder Ten Cate (2005). Interpolation for Extended Modal Languages. Journal of Symbolic Logic 70 (1):223 - 234.
Ian Hodkinson (2002). Loosely Guarded Fragment of First-Order Logic has the Finite Model Property. Studia Logica 70 (2):205 - 240.
Finn V. Jensen (1974). Interpolation and Definability in Abstract Logics. Synthese 27 (1-2):251 - 257.
Małgorzata Porębska (1986). Interpolation and Amalgamation Properties in Varieties of Equivalential Algebras. Studia Logica 45 (1):35 - 38.
Erich Grädel (1999). On the Restraining Power of Guards. Journal of Symbolic Logic 64 (4):1719-1742.
Added to index2009-01-28
Total downloads13 ( #262,405 of 1,793,159 )
Recent downloads (6 months)4 ( #205,957 of 1,793,159 )
How can I increase my downloads?