Abstract

see [2]. Temporal reasoning has always been a major test case for knowledge representation formalisms. In this paper, we develop an inductive variant of the situation calculus using the Logic for Non-Monotone Inductive Definitions (NMID). This is an extension of classical logic that allows for uniform representation of various forms of definitions, including monotone inductive definitions and non-monotone forms of inductive definitions such as iterated induction and induction over well-founded posets [1]. Here, we demonstrate an application of NMID-logic. The aim is two-fold. First, we illustrate the role of NMID-logic and non-monotone inductive definitions for knowledge representation by presenting a variant of the situation calculus which we call inductive situation calculus. We show that ramification rules can be naturally modeled through a non-monotone iterated inductive definition. Second, we illustrate the use of our recently developed modularity techniques for NMID-logic in order to translate a theory of the inductive situation calculus into a classical logic theory of Reiter’s situation calculus [3].

Citations