In this article we give a detailed presentation of state event logic which is a modal logic for reasoning about concurrent events and causality between events [8] State event logic differs from previous approaches in the following directions: First, events enjoy the same attention as states. In the same way as states can be viewed as models of the formulae describing the facts that hold in them we...

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 tx: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.

Recently three approaches for solving planning problems deductively were proposed each of which does not require to state frame axioms explicitly. These approaches are based on the linear connection method, an equational logic programming language, and on linear logic. In this paper, we brie∞y review these approaches and show that they are equivalent. Moreover, we illustrate that these approaches are not only restricted to deductive planning, but can be applied whenever actions are to be modelled in logic. We show that the approaches essentially amount on building predicates over the data structure multiset. Such multisets are interpreted as resources, which are consumed and produced by actions. We give a minimal and complete uniflcation algorithm for the equational theory which deflnes the multisets. Finally, we discuss possible extensions of the equational logic programming approach.