Linear Deductive Planning

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 rigorously 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.