G. Große, Josef Schneeberger, S. Hölldobler
Linear Deductive Planning
Journal of Logic and Computation, vol. 6, no. 2, pp. 233-262
Recently, three approaches to deductive planning were developed, which solve the technical frame problem without the need to state frame axioms explicitly. These approaches are based on the linear connection method, an equational Horn logic, and linear logic. At first glance these approaches seem to be very different. In the linear connection method a syntactical condition -- each literal is connected at most once -- is imposed on proofs. In the equational logic approach situations and plans are represented as terms and SLDE-resolution is applied as an inference rule. The linear logic approach is a Gentzen style proof system without weakening and contraction rules. On second glance, however, and as a consequence of the results rigourously proved in this paper, it will turn out that the three approaches are equivalent. They are based on the very same idea that facts about a situation are taken as resources which can be consumed and produced.
Josef Schneeberger, S. Hölldobler
A New Deductive Approach to Planning
New Generation Computing, vol. 8, no. 3, pp. 225-244
We introduce a new deductive approach to planning which is based on Horn clauses. Plans as well as situations are represented as terms and, thus, are first-class objects. We do neither need frame axioms nor state-literals. The only rule of inference is the SLDE-resolution rule, i.e. SLD-resolution, where the traditional unification algorithm has been replaced by anE-unification procedure. We exemplify the properties of our method such as forward and backward reasoning, plan checking, and the integration of general theories. Finally, we present the calculus and show that it is sound and complete.