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 μGF.
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This author has been partially supported by the European Community Research Training Network “Games and Automata for Synthesis and Validation” (GAMES), contract HPRN-CT-2002-00283.
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Leinders, D., Marx, M., Tyszkiewicz, J. et al. The Semijoin Algebra and the Guarded Fragment. J Logic Lang Inf 14, 331–343 (2005). https://doi.org/10.1007/s10849-005-5789-8
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DOI: https://doi.org/10.1007/s10849-005-5789-8