Guards, Bounds, and generalized semantics

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.
Keywords Philosophy   Logic   Artificial Intelligence   Semantics
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DOI 10.1007/s10849-005-5786-y
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References found in this work BETA
Erich Grädel (1999). On the Restraining Power of Guards. Journal of Symbolic Logic 64 (4):1719-1742.
J. F. A. K. van Benthem (1983). Modal Logic and Classical Logic. Distributed in the U.S.A. By Humanities Press.

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Anne Preller (2007). Toward Discourse Representation Via Pregroup Grammars. Journal of Logic, Language and Information 16 (2):173-194.

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