Reasoning Method between Polynomial Error Assertions

Abstract

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.