A robotic vision system is being developed which uses three-dimensional laser range data to sense its environment. The recognition subsystem incorporates topological as well as geometric information to identify viewed objects. Theorem-proving techniques are used to produce symbolic pattern matches. The major contributions of the recognition subsystem are 1) the use of viewpoint independent descriptors as the basis for representing known object models and 2) the use of theorem proving techniques to hypothesize object identities and recognize the viewed object as an instance of the appropriate viewpoint independent model descriptor. The representation scheme permits describing objects at a variety of topological and geometric levels. Furthermore, the use of viewpoint independent descriptors facilitates object recognition from a single arbitrary view despite missing information or the inclusion of viewpoint dependent artifacts. The theorem-proving approach establishes a symbolic correspondence between viewpoint independent features in the (recognized) model and features in the observed data. The recognition process uses a three-phase approach. First, hypotheses are generated which correspond to model descriptors that are likely to match the data. Evidence is applied to viable hypotheses to produce a partial match. The partial match is then used to constrain the full recognition process which leads to object identification. This strategy has been found to constrain strongly the search space of possible matches and leads to large reductions in recognition times. Results of the recognition process on synthetic and actual laser range data are presented for several objects. The system is shown to operate with robustness and alacrity.