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On the Restraining Power of Guards
 Journal of Symbolic Logic
, 1998
"... Guarded fragments of firstorder logic were recently introduced by Andr'eka, van Benthem and N'emeti; they consist of relational firstorder formulae whose quantifiers are appropriately relativized by atoms. These fragments are interesting because they extend in a natural way many proposit ..."
Abstract

Cited by 121 (2 self)
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Guarded fragments of firstorder logic were recently introduced by Andr'eka, van Benthem and N'emeti; they consist of relational firstorder formulae whose quantifiers are appropriately relativized by atoms. These fragments are interesting because they extend in a natural way many propositional modal logics, because they have useful modeltheoretic properties and especially because they are decidable classes that avoid the usual syntactic restrictions (on the arity of relation symbols, the quantifier pattern or the number of variables) of almost all other known decidable fragments of firstorder logic. Here, we investigate the computational complexity of these fragments. We prove that the satisfiability problems for the guarded fragment (GF) and the loosely guarded fragment (LGF) of firstorder logic are complete for deterministic double exponential time. For the subfragments that have only a bounded number of variables or only relation symbols of bounded arity, satisfiability is EXPTI...
On Logics with Two Variables
 Theoretical Computer Science
, 1999
"... This paper is a survey and systematic presentation of decidability and complexity issues for modal and nonmodal twovariable logics. A classical result due to Mortimer says that the twovariable fragment of firstorder logic, denoted FO 2 , has the finite model property and is therefore decidable ..."
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Cited by 43 (8 self)
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This paper is a survey and systematic presentation of decidability and complexity issues for modal and nonmodal twovariable logics. A classical result due to Mortimer says that the twovariable fragment of firstorder logic, denoted FO 2 , has the finite model property and is therefore decidable for satisfiability. One of the reasons for the significance of this result is that many propositional modal logics can be embedded into FO 2 . Logics that are of interest for knowledge representation, for the specification and verification of concurrent systems and for other areas of computer science are often defined (or can be viewed) as extensions of modal logics by features like counting constructs, path quantifiers, transitive closure operators, least and greatest fixed points etc. Examples of such logics are computation tree logic CTL, the modal ¯calculus L¯ , or popular description logics used in artificial intelligence. Although the additional features are usually not firstorder...
Guarded Fragments of FirstOrder Logic: A Perspective for New Description Logics?
 IN PROC. OF 1998 INT. WORKSHOP ON DESCRIPTION LOGICS DL `98, TRENTO, CEUR ELECTRONIC WORKSHOP PROCEEDINGS
, 1998
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