On Deductive Planning and the Frame Problem

We review some logic formalisms which were designed in order to reason about situations, goals, and actions. In particular, we focuss on the so-called frame problem, ie. the technical problem of how to formalize the assumption that unless an action explicitly causes a certain fact to hold or not to hold, the facts are preserved by the action. It is shown that there is no need to explicitly state frame axioms, ie. axioms which deal with the frame problem, if the logic formalism treats facts as resources which are produced and consumed. The linear connection method, the linear logic as well as a particular equational logic are such formalisms. Moreover, we demonstrate that these three formalisms are equivalent for a large class of planning problems.