Logical models of objects and of processes

This paper discusses the properties of certain languages for expressing and reasoning about physical or biological, manufacturing, or computational systems. These languages resemble those of symbolic logic and support formal procedures for interpretation and inference. The focus is on two aspects of such languages: on the relation between a physical object or system and the processes that run on it; and on the sense in which knowledge-bases can have languages that differ in expressive power. Objects or processes can be modeled by the action of a category C based on a finite directed graph G whose arrows are inputs or programs, respectively. An action D is a simplification of C if there is a left-invertible functor F:D→C. Thus, a system supports a lattice of processes, in which linguistic structures can be semantically interpreted