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Classification is an important task in the field of machine learning. Most classifiers based on offline learning are invalid for open data streams. In contrast, incremental learning is feasible for continuous data. This paper presents the Incremental Bayesian Classifier “Incremental_BC”, which continuously updates the probabilistic information according to each new training sample via recursive calculation. Further, the Incremental_BC is improved to deal with the flowing data whose distribution and property evolve with time, i.e., the concept drift. The effectiveness of the proposed methods has been verified by the results of simulation tests on benchmark data sets.

Error coefficients are ubiquitous in systems. In particular, errors in reasoning verification must be considered regarding safety-critical systems. We present a reasoning method that can be applied to systems described by the polynomial error assertion (PEA). The implication relationship between PEAs can be converted to an inclusion relationship between zero sets of PEAs; the PEAs are then transformed into first-order polynomial logic. Combined with the quantifier elimination method, based on cylindrical algebraic decomposition, the judgment of the inclusion relationship between zero sets of PEAs is transformed into judgment error parameters and specific error coefficient constraints, which can be obtained by the quantifier elimination method. The proposed reasoning method is validated by proving the related theorems. An example of intercepting target objects is provided, and the correctness of our method is tested through large-scale random cases. Compared with reasoning methods without error semantics, our reasoning method has the advantage of being able to deal with error parameters.