Progressions in reasoning about structure–property relationships

Reasoning about Spatial Relationships

We explore a new architecture for representing spatial information in neural networks. The method binds object information to position via element-wise multiplication of complex-valued vectors. This approach extends Holographic Reduced Representations by providing additional tools for processing and manipulating spatial information. In many cases these computations can be performed very efficie...

Reasoning about Gradual Changes of Topological Relationships

Spatial relationships between geographic objects are time-dependent and can change due to various phenomena. Water levels of rivers or lakes may rise causing flodding of buildings and roads near the shore line; contamination of soils may spread causing hazards for people living in affected areas; hurricanes may pass over islands or reach the continent; and market areas may expand so that they e...

Reasoning about social choices and social relationships

We study inferences about social choices—choices that affect people besides the chooser. Social choices depend on the relationships between the people involved: for example, whether they are friends, strangers, or enemies. We propose that these different social relationships correspond to different ways in which the chooser weights another person’s utility relative to her own. We describe a pro...

Reasoning About Spatial Relationships in Picture Retrieval Systems

In this paper, we consider various spatial relationships that are of general interest in pictorial database systems. We present a set of rules that allow us to deduce new relationships from a given set of relationships. A deductive mechanism using these rules can be used in query processing systems that retrieve pictures by content. The given set of rules are shown to be sound, i.e. the deducti...

Representation and Process in Reasoning about Logical Relationships