Journal of Logic, Language and Information

, Volume 14, Issue 3, pp 263–279 | Cite as

Guards, Bounds, and Generalized Semantics

  • Johan van Benthem


Some initial motivations for the Guarded Fragment still seem of interest in carrying its program further. First, we stress the equivalence between two perspectives: (a) satisfiability on standard models for guarded first-order formulas, and (b) satisfiability on general assignment models for arbitrary first-order formulas. In particular, we give a new straightforward reduction from the former notion to the latter. We also show how a perspective shift to general assignment models provides a new look at the fixed-point extension LFP(FO) of first-order logic, making it decidable. Next, we relate guarded syntax to earlier quantifier restriction strategies for achieving effective axiomatizability in second-order logic – pointing at analogies with ‘persistent’ formulas, which are essentially in the Bounded Fragment of many-sorted first-order logic. Finally, we look at some further unexplored directions, including the systematic use of ‘quasi-models’ as a semantics by itself.


Artificial Intelligence Quantifier Restriction Assignment Model General Assignment Restriction Strategy 
These keywords were added by machine and not by the authors.


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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Johan van Benthem
    • 1
    • 2
  1. 1.Amsterdam Institute for Logic Language and Computation (ILLC)University of AmsterdamAmsterdam
  2. 2.Stanford UniversityStanford

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