Reasoning Method Based on Intervals with Symmetric Truncated Normal Density

Abstract

Error parameters are inevitable in systems. In formal verification, previous reasoning methods seldom considered the probability information of errors. In this article, errors are described as symmetric truncated normal intervals consisting of the intervals and symmetric truncated normal probability density. Furthermore, we also rigorously prove lemmas and a theorem to partially simplify the calculation process of truncated normal intervals and independently verify the formulas of variance and expectation of symmetric truncated interval given by some scholars. The mathematical derivation process or verification codes are provided for most of the key formulas in this article. Hence, we propose a new reasoning method that combines the probability information of errors with the previous statistical reasoning methods. Finally, an engineering example of the reasoning verification of train acceleration is provided. After simulating the large-scale cases, it is shown that the simulation results are consistent with the theoretical reasoning results. This method needs more calculation, while it is more effective in detecting non-error’s fault factors than other error reasoning methods.

Keywords

• formal verification
• reasoning method
• truncated normal intervals
• polynomial
• theorem proving