We study fragments of first-order logic and of least fixed point logic that allow only unary negation: Outdoor Swivel Chair w/Cushion (set of 2) negation of formulas with at most one free variable.These logics generalize many interesting known formalisms, including modal logic and the $mu$-calculus, as well as conjunctive queries and monadic Datalog.We show that satisfiability and finite satisfiability are decidable for Course a pied - Enfant - Chaussures - Neutre both fragments, and we pinpoint the complexity of satisfiability, finite satisfiability, and model checking.We also show that the unary negation fragment of first-order logic is model-theoretically very well behaved.In particular, it enjoys Craig Interpolation and the Projective Beth Property.