Typed Formal Concept Analysis

Formal Concept Analysis (FCA) appears to be ideal for interpreting data in domains that are a-priori unstructured. In our research we focus on complex contexts with very large and rapidly changing numbers of real-world objects – for instance, data generated on-line and tracking real-time contexts in transport, enterprise warehousing, manufacturing control or social networking activities on the web. The ontology of such contexts, i.e., the types of attribute data and those of objects, and their interrelation (such as subtyping or which objects have which attributes or reference which other objects via surrogate attributes) is partly known to domain experts. Because of incomplete knowledge however, missing classes and relationships need to be inferred. In addition, domain experts need assistance in checking the partial ontology declarations against FCA interpretations added to the context. To make FCA more accessible in such applications, we explore the use of types similar to those available in object-oriented design and programming, for which methods, tools, training and skills are widely available. We present typed FCA and report about supporting tools. We also introduce typed priming and show that it is consistent with conceptual scaling without requiring the generation of binary lattices.