Occurrences and narratives as constraints in the branching structure of the situation calculus

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Abstract
The Situation Calculus is a logic of time and change in which there is a distinguished initial situation, and all other situations arise from the different sequences of actions that might be performed starting in the initial one. Within this framework, it is difficult to incorporate the notion of an occurrence, since all situations after the initial one are hypothetical. These occurrences are important, for instance, when one wants to represent narratives. There have been proposals to incorporate the notion of an action occurrence in the language of the Situation Calculus, namely Miller and Shanahan‘s work on narratives and Pinto and Reiter’s work on actual lines of situations. Both approaches have in common the idea of incorporating a linear sequence of situations into the tree described by theories written in the Situation Calculus language. Unfortunately, several advantages of the Situation Calculus are lost when reasoning with a narrative line or with an actual line of occurrences. In this paper we propose a different approach to dealing with action occurrences and narratives, which can be seen as a generalization of narrative lines to narrative trees. In this approach we exploit the fact that, in the discrete Situation Calculus, each situation has a unique history, and interpret occurrences as constraints on valid histories. We argue that this new approach subsumes the linear approaches of Miller and Shanahan, and Pinto and Reiter. In this framework, we are able to represent various kinds of occurrences; namely, conditional, preventable and non-preventable occurrences. Other types of occurrences, not discussed in this article, can also be accommodated.

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