Humans cannot always be treated as oracles for collaborative sensing. Robots thus need to maintain beliefs over unknown world states when receiving semantic data from humans, as well as account for possible discrepancies between human-provided data and these beliefs. To this end, this paper introduces the problem of semantic data association (SDA) in relation to conventional data association problems for sensor fusion. It then, develops a novel probabilistic semantic data association (PSDA) algorithm to rigorously address SDA in general settings. Simulations of a multi-object search task show that PSDA enables robust collaborative state estimation under a wide range of conditions.