Realization Problem for Formal Concept Analysis

Formal Concept Analysis (FCA) is an approach to knowledge engineering, representation, and analysis. A `standard' FCA-workflow starts with some `experimental' data, classifies "objects" and their "attributes" in the data, represents relations between objects and attributes by a number of cross-tables (matrices), couples compatible sets of objects and attributes into concepts, and builds a number of concept lattices. In contrast, FCA realization problem starts with `fragments' of some crosstables and concept lattices and try to generate data that match these fragments of cross-tables and concept lattices simultaneously. The paper defines formally the FCA realization problem and proves that it is decidable. It is done by reduction of the problem to the consistency problem for description logic ALBO. But it is still an open question whether FCA-realization problem have better complexity bound than ALBO has.

• Type: Conference
• Year: 2008
• Where: DLOG
• Authors: Nikolay Shilov
• Keywords: Automated Reasoning, Concept Lattices, DLOG 2008, FCA Realization Problem, Formal Concept Analysis