The guarded fragment (GF) was introduced in [ABN98] as a fragment of first order logic which combines a great expressive power with nice modal behavior. It consists of relationeil first order formulas whose qucintüiers are relativized by atoms in a certain way. While GF hsis been established as a particularly well-behaved fragment of first order logic in many respects, interpolation fails in restriction to GF, [HM99]. In this paper we consider the Beth property of first order logic and show that, despite the failure of interpolation, it is retained in restriction to GF. Being a closure property w.r.t. definability, the Beth property is of independent interest, both theoretically and for typical potential appUcations of GF, e.g., in the context of description logics. The Beth property for GF is here established on the basis of a limited form of interpolation, which more closely resembles the interpolation property that is usuEdly studied in modetl logics. From this we obtzün that, more specifically, even every n-variable guarded fragment with up to n-aiy relations has the Beth property.
CITATION STYLE
Hoogland, E., Marx, M., & Otto, M. (1999). Beth definability for the guarded fragment. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1705 LNAI, pp. 273–285). Springer Verlag. https://doi.org/10.1007/3-540-48242-3_17
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