Abstract

In this paper, we propose a new method to deal with continuously varying quantity in the situation calculus based on the concept of the nonstandard analysis. The essential point of the method is to devise a new model called nonstandard situation calculus, which is an interpretation of the situation calculus in the set of hyperreals. This nonstandard model allows discrete but uncountable (hyperfinite) state transition, so that we can describe and reason about the continuous dynamics which are usually treated with differential equations. In this enlarged perspective of the nonstandard situation calculus, we discuss about an infinitesimal action, infinite plan and an abnormality theory for the temporal prediction based on the differentiability.