  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 as partial orders and some as equivalences. We also
consider finite satisfiability of various extensions of our primary logic, in
particular capturing the concepts of nominals and role hierarchies known from
description logic. As the unary negation fragment can express unions of
conjunctive queries our results have interesting implications for the problem
of finite query answering, both in the classical scenario and in the
description logics setting.
