Modelling theories of actions by Equational Logic Programs

A sound and complete approach for encoding the action description language A developed by M. Gelfond and V. Lifschitz in an equational logic program is given. Our results allow the comparison of the resource-oriented equational logic based approach and various other methods designed for reasoning about actions, most of them based on variants of the situation calculus, which were also related to the action description language recently. A non-trivial extension of A is proposed which allows to handle uncertainty in form of non-deterministic action descriptions, i.e. where actions may have alternative randomized eeects. It is described how the equational logic programming approach forms a sound and complete encoding of this extended action description language A ND as well.