In recent years, the emergence and development of crowd-sourced geospatial data has provided challenges and opportunities to national mapping agencies as well as commercial mapping organisations. Crowd-sourced data involves non-specialists in data collection, sharing and maintenance. Compared to authoritative geospatial data, which is collected by surveyors or other geodata professionals, crowd-sourced data is less accurate and less structured, but often provides richer user-based information and reflects real world changes more quickly at a much lower cost. In order to maximize the synergistic use of authoritative and crowd-sourced geospatial data, this research investigates the problem of how to establish and validate correspondences (matches) between spatial features from disparate geospatial datasets. To reason about and validate matches between spatial features, a series of new qualitative spatial logics was developed. Their soundness, completeness, decidability and complexity theorems were proved for models based on a metric space. A software tool `MatchMaps' was developed, which generates matches using location and lexical information, and verifies consistency of matches using reasoning in description logic and qualitative spatial logic. MatchMaps was evaluated by the author and experts from Ordnance Survey, the national mapping agency of Great Britain. In experiments, it achieved high precision and recall, as well as reduced human effort. The methodology developed and implemented in MatchMaps has a wider application than matching authoritative and crowd-sourced data and could be applied wherever it is necessary to match two geospatial datasets of vector data.