A method of backward probabilistic logic reasoning of decision problems

There are critical problems in reasoning of decision problems with casual relations. One is how to process backward reasoning. Another is the discrepancy between logic and probability in denoting casual relations. We propose and implement a backward probabilistic logic reasoning approach, which combines conditional event algebra and Markov Monte Carlo simulating algorithm. By partly changing casual relations in a decision problem, we first make the problem of backward reasoning possible, and then bring the logic consistent with the probability in denoting casual relation by extending normal measurable space with conditional event. We transform the conditional event to normal events and corresponding logical combination events via conditional event algebra, and use Gibbs simulation to sample the normal events to be a stationary state. By computing the quantitative values of the stationary events, we can evaluate the quantitative value of conjunction and disjunction operations of conditional event at last and finish backward reasoning. An application of our method shows how we process a backward reasoning in a sequential decision.