We consider a modified version of the situation calculus built using a two-variable fragment of the first-order logic extended with counting quantifiers. We mention several additional groups of axioms that need to be introduced to capture taxonomic reasoning. We show that the regression operator in this framework can be defined similarly to regression in the Reiter's version of the situation calculus. Using this new regression operator, we show that the projection problem (that is the main reasoning task in the situation calculus) is decidable in the modified version. We mention possible applications of this result to formalization of Semantic Web services.
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