Deductive plan generation
Lecture Notes in Computer Science
Understanding and modeling the ability of humans to reason about actions, change, and causality is one of the key issues in Artificial Intelligence and Cognitive Science. Since logic appears to play a fundamental rôle for intelligent behavior, many deductive methods for reasoning about change were developed and thoroughly investigated. It became apparent that a straightforward use of classical logic lacks the essential property that facts describing a world state may change in the course of
... . To overcome this problem, the truth value of a particular fact has to be associated with a particular state. This solution brings along the famous technical frame problem. It amounts to the difficulty of expressing that the truth values of facts not affected by some action are not changed by the execution of this action  . The problem of classical logic is that propositions are not treated as resources  . A proposition cannot be produced and consumed in the course of time. To handle this problem J. McCarthy, P. Hayes  , and C. Green  introduced frame axioms; one for each action and each atomic fact. The obvious problem with this solution is that the number of frame axioms rapidly increases when many actions and many facts occur. R. Kowalski reduced the number of frame axioms to become linear with respect to the number of different actions  . Some years later, it was again J. McCarthy who proposed the use of nonmonotonic inference rules to tackle the frame problem  . He uses a default rule called law of inertia which states that a proposition does not change its value when executing an action unless the contrary is known. Some years ago we developed a modified version of the connection method to solve the frame problem without the need of any frame axioms  . In the linear connection method proofs are restricted such that each literal is connected at most once [2, 4, 3] . Thus, connecting a literal during the inference process simulates consumption of the corresponding fact. Conversely, if the conditions of an implication are fulfilled then the conclusion can be used and, thus, the literals occurring in the conclusion are produced. This treatment of literals resembles the concept of resources.