Abstract
In this paper we introduce the olog, or ontology log, a category-theoretic model for knowledge representation (KR). Grounded in formal mathematics, ologs can be rigorously formulated and cross-compared in ways that other KR models (such as semantic networks) cannot. An olog is similar to a relational database schema; in fact an olog can serve as a data repository if desired. Unlike database schemas, which are generally difficult to create or modify, ologs are designed to be user-friendly enough that authoring or reconfiguring an olog is a matter of course rather than a difficult chore. It is hoped that learning to author ologs is much simpler than learning a database definition language, despite their similarity. We describe ologs carefully and illustrate with many examples. As an application we show that any primitive recursive function can be described by an olog. We also show that ologs can be aligned or connected together into a larger network using functors. The various methods of information flow and institutions can then be used to integrate local and global world-views. We finish by providing several different avenues for future research.
Highlights
Scientists have a pressing need to organize their experiments, their data, their results, and their conclusions into a framework such that this work is reusable, transferable, and comparable with the work of other scientists
The structure of ologs is based on a branch of mathematics called category theory
Such a fact is either presented as a checkmark between the two paths or by an equation. Every such equivalence should be declared; i.e., no fact should be considered too obvious to declare. The reader at this point hopefully sees an olog as a kind of ‘‘concept map,’’ and it is one, albeit a concept map with a formal structure and specific rules of good practice
Summary
Scientists have a pressing need to organize their experiments, their data, their results, and their conclusions into a framework such that this work is reusable, transferable, and comparable with the work of other scientists. Since our types are not fixed sets (see Section 3), we preferred a term that was less formal, namely ‘‘aspects’’.) Suppose we wish to say that a thing classified as X has an aspect f whose result set is Y This means there is a functional relationship called f between X and Y , which can be denoted f : X ?Y. Note that the top line in Diagram (18) might be considered as existing at the ‘‘data level’’ rather than at the ‘‘olog level.’’ In other words, one could see John Doe as an ‘‘instance’’ of a person , rather than as a type in and of itself, and see 150 as an instance of a real number This idea of an olog having a ‘‘data level’’ is the subject of the Section 3. Every such equivalence should be declared; i.e., no fact should be considered too obvious to declare
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