A novel fault detection and isolation (FDI) method using set-valued observers (SVOs), for uncertain linear parameter-varying (LPV) systems, is introduced. The proposed method relies on SVO-based model invalidation to discard models incompatible with measured data. When compared to the most common strategies in the literature, the suggested approach: (i) under suitable conditions, guarantees false alarms are avoided; (ii) unlike residual-based architectures, does not require the computation of thresholds to declare faults; (iii) has applicability to a wide class of plants. The performance of the proposed approach is assessed in simulation, using the full nonlinear model of a fixed-wing aircraft longitudinal dynamics.