We present a multi-modal action logic with first-order modalities, which contain terms which can be unified with the terms inside the subsequent formulas and which can be quantified. This makes it possible to handle simultaneously time and states. We discuss applications of this language to action theory where it is possible to express many temporal aspects of actions, as for example, beginning, end, time points, delayed preconditions and results, duration and many others. We present tableaux rules for a decidable fragment of this logic.
Javier Pinto has extended situation calculus in order to integrate time @cite_3 . He conserves the framework of situation calculus and introduces a notion of time. Intuitively, every situation @math has a starting time and an ending time, where @math meaning that situation @math ends when the succeeding situation @math is reached. The end of the situation @math is the same time point as the beginning of the next situation resulting from the occurrence of action @math in @math . The obvious asymmetry of the @math and @math functions is due to the fact that the situation space has the form of a tree whose root is the beginning state @math . Thus, every state has a unique preceding state but eventually more that one succeeding state.
@cite_3
1992170615
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 [22] and Pinto and Reiter’s work on actual lines of situations [27, 29]. 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 [13], each situation has a unique history. Then, occurrences are interpreted as constraints on valid histories. We argue that this new approach subsumes the linear approaches of Miller and Shanahan’s, and Pinto and Reiter’s. 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.