Example PhD

Qualitative spatial reasoning about conceptual spaces

Supervisor: Dr S. Schockaert

Keywords: Artificial intelligence, knowledge representation, common-sense reasoning, folksonomies

The field of qualitative spatial reasoning is concerned with inferring information about spatial configurations, based on qualitative statements such as "Wales is contained in the UK", "Paris is located East of London", or "the dining room is adjacent to the kitchen". For example, from the knowledge that "Cardiff is in Wales" and "Wales is in the UK", we can infer that "Cardiff is in the UK". Such qualitative descriptions play an important role in fields such as geographical information systems (where we may lack accurate geometric descriptions) and image understanding (where we need to abstract away from specific geometric descriptions), and much research efforts have been directed towards finding sound and complete inference procedures for increasingly richer sets of relations. Among others, mereo-topological relations (part of, adjacent to, partially overlapping, etc.), direction relations (left of, North of, etc.), relative motion (towards, away from, etc.), distance (close, far, etc.) and relative size have been considered in the literature, as well as certain combinations of the aforementioned types.

Gärdenfors' theory of conceptual spaces, on the other hand, posits that the meaning of natural language labels can be faithfully represented as convex regions in a (typically high-dimensional) geometric space, in which the dimensions correspond to cognitively elementary features. Colours, for example, can be represented in a three-dimensional conceptual space in which the dimensions correspond to hue, saturation and intensity. An important observation is that the spatial relationship between two regions in a conceptual space reflects the conceptual relationship of the corresponding properties. For example, the regions representing "orange" and "red" will be adjacent, and the region representing "light-red" will be contained in the region representing "red". Regions which are closer to each other will also be cognitively more similar. The actual conceptual space representation of most natural language properties is not known, however, and it may not even be clear what would be the relevant underlying dimensions. In such cases, we may still derive useful information about the meaning of properties if we have information about the conceptual relationship of different properties. In fact, many forms of common-sense reasoning effectively boil down to qualitative spatial reasoning about the conceptual space representations of natural language properties.

The application of QSR techniques to conceptual spaces introduces a number of challenges. For example, few results are known in the field of QSR about how the constraint that all regions should be convex affects reasoning procedures. Moreover, there are various types of relations that play an important role in the context of conceptual spaces, but which have not been fully addressed by the QSR community, e.g. betweenness, centrality and parallelism. The aim of this topic could therefore be to bridge the gap between the current state-of-the art in QSR and efficient reasoning about qualitative descriptions of conceptual spaces. Another topic would be to look at techniques to obtain qualitative descriptions of conceptual spaces from the web, using natural language processing techniques, or applying statistical techniques on folksonomies such as Flickr or last.fm. These conceptual relations could then be used to improve information retrieval systems (e.g. in the case of Flickr) or recommendation systems (e.g. in the case of last.fm).

Key Skills/Background: Open to computing or mathematics graduates and postgraduates.

Contact: Dr S. Schockaert to discuss this research topic.