This thesis aims at the logical analysis of discrete processes, in particular of such generated by gene regulatory networks. States, transitions and operators from temporal logics are expressed in the language of Formal Concept Analysis. By the attribute exploration algorithm, an expert or a computer program is enabled to validate a minimal and complete set of implications, e.g. by comparison of predictions derived from literature with observed data. Here, these rules represent temporal dependencies within gene regulatory networks including coexpression of genes, reachability of states, invariants or possible causal relationships. This new approach is embedded into the theory of universal coalgebras, particularly automata, Kripke structures and Labelled Transition Systems. A comparison with the temporal expressivity of Description Logics is made. The main theoretical results concern the integration of background knowledge into the successive exploration of the defined data structures (formal contexts). Applying the method a Boolean network from literature modelling sporulation in Bacillus subtilis is examined. Coregulation and mutual exclusion of genes were checked systematically. Conditions for sporulation were clarified by queries to the generated knowledge base. Finally, we developed an asynchronous Boolean network for extracellular matrix formation and destruction in the context of rheumatoid arthritis. By biologically plausible assumptions, the network was adapted to gene expression data obtained from synovial fibroblast cells stimulated by transforming growth factor beta I or by tumor necrosis factor alpha. The final simulations were analysed by attribute exploration integrating the observed time series in a fine-tuned and automated manner. The resulting temporal rules yielded new contributions to controversially discussed aspects of fibroblast biology and corroborated previously known facts, but also generated new hypotheses regarding literature knowledge.