Nonmonotonic Temporal Reasoning: A Logic-Based Approach to Declarative Modeling

Abstract

This paper sets out a framework for modeling causal or predictive dynamic systems and is concerned with bridging the gap between the theory and practice of nonmonotonic temporal reasoning. The central result is a nonmonotonic reasoning methodology that subsumes Shoham's chronological ignorance formalism for causal theories. The new formalism uses an extension of Reiter's default logic and, unlike chronological ignorance, the approach is proof-theoretic. This leads to a simple proof procedure based on classical deduction. We suggest several improvements over Shoham's s . approach, including removing the need for a modal or other epistemic logic. The result is a simple framework for predictive modeling that can be implemented using a standard theorem prover. To illustrate this framework declarative models are developed for two small assembly processes. The ability to model dynamic processes mathematically is an important aspect of automatic control. Although traditional control theory has been proven successful for modeling and controlling continuous dynamic systems, it is not applicable to many domains that are naturally characterized by discrete events} so-called discrete-ev ent dynam ic syss . tems DEDSs . Typical examples include manufacturing and assembly