Logical AI involves representing knowledge of an agent's world, its goals and the current situation by sentences in logic. The agent decides what to do by inferring that a certain action or course of action was appropriate to achieve the goals. The inference may be monotonic, but the nature of the world and what can be known about it often requires that the reasoning be nonmonotonic.
Logical AI has both epistemological problems and heuristic problems. The former concern the knowledge needed by an intelligent agent and how it is represented. The latter concerns how the knowledge is to be used to decide questions, to solve problems and to achieve goals. These are discussed in [MH69]. Neither the epistemological problems nor the heuristic problems of logical AI have been solved. The epistemological problems are more fundamental, because the form of their solution determines what the heuristic problems will eventually be like.
This article has links to other articles of mine. I'd like to supplement the normal references by direct links to such articles as are available.