Transaction Logic with Partially Defined Actions

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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.