  The objectives of this research work which is intimately related to pattern
discovery and management are threefold: (i) handle the problem of pattern
manipulation by defining operations on patterns, (ii) study the problem of
enriching and updating a pattern set (e.g., concepts, rules) when changes occur
in the user's needs and the input data (e.g., object/attribute insertion or
elimination, taxonomy utilization), and (iii) approximate a "presumed" concept
using a related pattern space so that patterns can augment data with knowledge.
To conduct our work, we use formal concept analysis (FCA) as a framework for
pattern discovery and management and we take a joint database-FCA perspective
by defining operators similar in spirit to relational algebra operators,
investigating approximation in concept lattices and exploiting existing work
related to operations on contexts and lattices to formalize such operators.
