A method of Probabilistic logic reasoning on Bayesian networks

In making inferences from conditional probability information, there are critical problems. One of them is a discrepancy between logic and probability. Another is highly complex implementation calculation of higher-order logics. We propose and implement a Bayesian probabilistic logic reasoning approach, which combines Conditional Event Algebra and Markov Chain Monte Carlo simulating algorithm. By extending normal measurable space with conditional event, we first bring logic consistent with probability in denoting conditional probability information, and then we transform a higher-order conditional event to normal events and correspond logical combination events via Conditional Event Algebra. We use Gibbs simulation to sample the normal events to be a stationary state. By computing the quantitative values of the events, we can evaluate the quantitative value of higher-order conditional event at last. An example of application of our method shows how we make inferences from conditional probability information.