Finite Satisfiability of Unary Negation Fragment with Transitivity
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We show that the finite satisfiability problem for the unary negation fragment with arbitrary number of transitive relations is decidable and 2-ExpTime-complete. Our result actually holds for a more general setting in which one can require that some binary symbols are interpreted as arbitrary transitive relations, some are interpreted as partial orders and some as equivalences. As the unary negation fragment can express (negations of) unions of conjunctive queries this gives in particular the decidability of the classical problem from database theory, finite open-world query answering, for some interesting scenarios involving the above mentioned semantic constraints. We also consider finite satisfiability of some extensions of our primary logic, in particular capturing the concept of role hierarchies known from description logic.
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