Concept Lattices and Logical Inference

Galois closure is a way of discovering maximal sets of objects with a common set of properties. Rudolf Wille exploited this characterization in his development of concept lattices.

We have extended this technique to extract all logically consistent, universally quantified, assertions that can be made given a collection of existentially quantified facts. This has also been called discrete, deterministic data mining, or DDDM, because it extracts necessary, not just statistically probable, associations from the input data.

Finally, our attention has been focused on the transformation of closure systems. The ability to smoothly transform one closure system into another lies at the heart of successful DDDM as described in [P01]. But, it is expected that since we have proven that closed, complete transformations, or morphisms, induce a well-defined, cartesian closed, category of discrete closure systems [P04a, PS12] we will uncover many more applications of interest to computer science. For example, separation in social networks behaves differently under continuous transformations than one would expect [P12].