, Volume 1, Issue 2, pp 99-131

Transaction Logic with Partially Defined Actions

Abstract

In this paper we develop a novel logic formalism, ${\mathcal{T} \, \mathcal{R}^{PAD}}$ (Transaction Logic with Partially Defined Actions), designed for reasoning about the effects of complex actions. ${\mathcal{T} \, \mathcal{R}^{PAD}}$ is based on a subset of Transaction Logic, but extends it with a new kind of formulas, called premise-formulas, which express information about states and the execution of actions. This makes the formalism more suitable for specifying partial knowledge about actions. We develop a sound and complete proof theory for ${\mathcal{T} \, \mathcal{R}^{PAD}}$ and illustrate the formalism on a number of instructive examples. In addition, we show that an expressive subset of ${\mathcal{T} \, \mathcal{R}^{PAD}}$ is reducible to standard logic programming and define a precise sense in which this reduction is sound and complete.