PP-2005-07: Guards, Bounds, and Generalized Semantics

PP-2005-07: van Benthem, Johan (2005) Guards, Bounds, and Generalized Semantics. [Report]

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The Guarded Fragment can be viewed in two ways: as a large decidable fragment of first-order logic over standard models, or as a reflection of a generalized semantics for the complete first-order language. We prove that the two perspectives are mutually reducible. We also show how this duality sheds new light on fixed-point logics. Next, we relate the use of guards to 'persistent' formulas from the earlier literature, which have only bounded quantifiers, making second-order logic effectively axiomatizable. Finally, we discuss some aspects of guarding which have not been investigated yet. This paper will appear in an issue of the "Journal of Logic, Language and Information",edited by Natasha Alechina, on 10 years of the Guarded Fragment.

Item Type: Report
Report Nr: PP-2005-07
Series Name: Prepublication (PP) Series
Year: 2005
Uncontrolled Keywords: first-order logic; decidability; guarded fragment; ; bounded fragment; generalized assignment; models; fixed-point logic; second-order logic
Subjects: Logic
Depositing User: Johan van Benthem
Date Deposited: 12 Oct 2016 14:36
Last Modified: 12 Oct 2016 14:36
URI: https://eprints.illc.uva.nl/id/eprint/152

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