The Semijoin Algebra and the Guarded Fragment

Authors:
Dirk Leinders;Maarten Marx;Jerzy Tyszkiewicz;Jan Bussche
Affiliations:
Limburgs Universitair Centrum, Diepenbeek, Belgium;Informatics Institute, Universiteit van Amsterdam, The Netherlands;Institute of Informatics, University of Warsaw, Warszawa, Poland;Limburgs Universitair Centrum, Diepenbeek, Belgium
Venue:
Journal of Logic, Language and Information
Year:
2005

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Abstract

In the 1970s Codd introduced the relational algebra, with operators selection, projection, union, difference and product, and showed that it is equivalent to first-order logic. In this paper, we show that if we replace in Codd's relational algebra the product operator by the "semijoin" operator, then the resulting "semijoin algebra" is equivalent to the guarded fragment of first-order logic. We also define a fixed point extension of the semijoin algebra that corresponds to 驴GF.