# GRANULARITY **Abstract:** Let us assume the world, in whatever complexity the machine is capable of dealing with, is represented in a global theory, which we may take to be a first-order logical theory To- Our approach to granularity will be to extract from To smaller, more computationally tractable, local theories. Let Po be the set of predicates of To, and So its domain of interpretation. Suppose a subset R of Po has been determined to be the predicates relevant to the situation at hand. We can then define an indistinguishability relation ~ on So by means of the following second-order axiom: This paper presents a framework for a theory of granularity, which is seen as a means of constructing simple theories out of more complex ones. A transitive indistinguishability relation can be defined by means of a set of relevant predicates, allowing simplification of a theory of complex phenomena into computationally tractable local theories, or granularities. Nontransitive indistinguishability relations can be characterized in terms of relevant partial predicates, and idealization allows simplification into tractable local theories. Various local theories must be linked with each other by means of articulation axioms, to allow shifts of perspective. Such a treatment of granularity must be built into the very foundation of the reasoning processes of intelligent agents in a complex world. That is, x and y are indistinguishable if no relevant predicate distinguishes between them. In general, of course, it is a **Authors:** [[Jerry R. Hobbs]]