This paper presents a novel approach to cognitive planning based on an NP-complete logic of explicit and implicit belief whose satisfiability checking problem is reduced to SAT. We illustrate the potential for application of our model by formalizing and then implementing a human-machine interaction scenario in which an artificial agent interacts with a human agent through dialogue and tries to motivate her to practice a sport. To make persuasion effective, the artificial agent needs a model of the human's beliefs and desires which is built during interaction through a sequence of belief revision operations. We consider two cognitive planning algorithms and compare their performances, a brute force algorithm based on SAT and a QBF-based algorithm.