The Predication-based Semantic Indexing (PSI) approach encodes both symbolic and distributional information into a semantic space using a permutation-based variant of Random Indexing. In this paper, we develop and evaluate a computational model of abductive reasoning based on PSI. Using distributional information, we identify pairs of concepts that are likely to be predicated about a common third concept, or middle term. As this occurs without the explicit identification of the middle term concerned, we refer to this process as a “logical leap”. Subsequently, we use further operations in the PSI space to retrieve this middle term and identify the predicate types involved. On evaluation using a set of 1000 randomly selected cue concepts, the model is shown to retrieve with accuracy concepts that can be connected to a cue concept by a middle term, as well as the middle term concerned, using nearest-neighbor search in the PSI space. The utility of quantum logical operators as a means to identify alternative paths through this space is also explored.