Formal Basis for Commonsense Abstraction of Dynamic Systems

Abstraction is an essential technique in reasoning about complex systems involving a large number of variables and interconnections. Aggregation of dynamic systems is an abstraction technique whose application is easily observable in everyday life. The basic intuition behind aggregation of variables may be summarized as follows: if variables in a large dynamic system can be partitioned into subsets such that variables in each subset are more strongly connected to each other than to variables in other subsets, one can describe the short-run behavior of each subsystem independently of other subsystems. Furthermore, one can describe the long-run behavior of the entire system in terms of these subsets instead of individual variables, treating each subset as a black box. This paper provides a formal justification for commonsense abstraction based on aggregation of a dynamic system and presents a procedure for doing so.ion is an essential technique in reasoning about complex systems involving a large number of variables and interconnections. Aggregation of dynamic systems is an abstraction technique whose application is easily observable in everyday life. The basic intuition behind aggregation of variables may be summarized as follows: if variables in a large dynamic system can be partitioned into subsets such that variables in each subset are more strongly connected to each other than to variables in other subsets, one can describe the short-run behavior of each subsystem independently of other subsystems. Furthermore, one can describe the long-run behavior of the entire system in terms of these subsets instead of individual variables, treating each subset as a black box. This paper provides a formal justification for commonsense abstraction based on aggregation of a dynamic system and presents a procedure for doing so.