Transforming Situation Calculus Action Theories for Optimised Reasoning

Among the most frequent reasoning tasks in the situation calculus are projection queries that query the truth of conditions in a future state of affairs. However, in long running action sequences solving the projection problem is complex. The main contribution of this work is a new technique which allows the length of the action sequences to be reduced by reordering independent actions and removing dominated actions; maintaining semantic equivalence with respect to the original action theory. This transformation allows for the removal of actions that are problematic with respect to progression, allowing for periodical update of the action theory to reflect the current state of affairs. We provide the logical framework for the general case and give specific methods for two important classes of action theories. The work provides the basis for handling more expressive cases, such as the reordering of sensing actions in order to delay progression, and forms an important step towards facilitating ongoing planning and reasoning by long-running agents. It provides a mechanism for minimising the need for keeping the action history while appealing to both regression and progression.