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Knowledge discovery is a rapidly expanding technique in business applications. One of the most important problems in it is the process to discover continuously knowledge in evolving business domain. According to the notion of active mining, a continuous knowledge discovery process is developed for inducing the local first-order rules and global evolutional rules, to trace dynamic evolution patterns. The definitions of main notions used in the process are proposed in a formal way, based on time granularity and first-order linear temporal logic. The framework represents a rule in quasi-Horn clause, defines the measures of the first-order formula valuating on a linear state structure with time multi-granule. The structure allows associating each time granule with an assignation of all symbols of a first-order language, and measures the extent of truth of a formula.