This work is licensed under the Creative Commons Attribution License. Formal Contexts, Formal Concept Analysis, and Galois Connections

Formal concept analysis (FCA) is built on a special type of Galois connections called polarities. We present new results in formal concept analysis and in Galois connections by presenting new Galois connection results and then applying these to formal concept analysis. We also approach FCA from the perspective of collections of formal contexts. Usually, when doing FCA, a formal context is fixed. We are interested in comparing formal contexts and asking what criteria should be used when determining when one formal context is better than another formal context. Interestingly, we address this issue by studying sets of polarities. 1 Formal Concept Analysis and Order-Reversing Galois Connections We study formal concept analysis (FCA) from a “larger ” perspective than is commonly done. We em-phasize formal contexts. For example, we are interested in questions such as if we are working with a given formal context K, that is, we are working with a set of objects G, a set of properties M, and a relation R⊂G×M, what do we do if we want to replace K with a better formal context. Of course, this raises the question: what makes one formal context better than another formal context. We address this question in multiple ways. We look at sets of formal contexts such that each formal context has the same set of objects