Maximal consistent extensions of information systems

The idea of representation of concurrent system by information system is due to Z. Pawlak [61, 73, 74] In such a representation attributes are interpreted as local processes of a concurrent system, values of attributes - as states of local processes, and objects (tuples of values of attributes on objects) - as global states of the considered concurrent system. The knowledge encoded in an information system can be represented by means of true rules which can be extracted from the information system. Besides "explicit" global states, corresponding to objects, the concurrent system generated by the considered information system can also have "hidden" global states, i.e., tuples of attribute values not belonging to a given information system but consistent with all the rules. Such "hidden" states can also be considered as realizable global states. This was a motivation for introducing in [73] maximal consistent extensions of information systems with both "explicit" and "hidden" global states. The maximal consistent extensions of information systems relative to the set of true and realizable deterministic rules were investigated in [70, 73, 85, 86]. © 2009 Springer-Verlag Berlin Heidelberg.