  Our aim is to build a set of rules, such that reasoning over temporal
dependencies within gene regulatory networks is possible. The underlying
transitions may be obtained by discretizing observed time series, or they are
generated based on existing knowledge, e.g. by Boolean networks or their
nondeterministic generalization. We use the mathematical discipline of formal
concept analysis (FCA), which has been applied successfully in domains as
knowledge representation, data mining or software engineering. By the attribute
exploration algorithm, an expert or a supporting computer program is enabled to
decide about the validity of a minimal set of implications and thus to
construct a sound and complete knowledge base. From this all valid implications
are derivable that relate to the selected properties of a set of genes. We
present results of our method for the initiation of sporulation in Bacillus
subtilis. However the formal structures are exhibited in a most general manner.
Therefore the approach may be adapted to signal transduction or metabolic
networks, as well as to discrete temporal transitions in many biological and
nonbiological areas.
