Guided Tour of Ontology

John F. Sowa

This web page organizes some of the papers on this web site in a systematic reading list. Paper #1 presents a general overview of ontology and ongoing work in developing and applying ontologies to modern computer systems. The remaining papers address more specialized topics. The final paper is a tutorial on the mathematics and logic commonly used in publications about ontology and knowledge representation. All bibliographical references can be found in the combined bibliography for this web site.

1. Building, Sharing, and Merging Ontologies

For centuries, philosophers have sought universal categories for classifying everything that exists, lexicographers have sought universal terminologies for defining everything that can be said, and librarians have sought universal headings for storing and retrieving everything that has been written. During the 1970s, the ANSI SPARC committee proposed the three-schema architecture for defining and integrating the database systems that manage the world economy. Today, the semantic web has enlarged the task to the level of classifying, labeling, defining, finding, integrating, and using everything on the World Wide Web, which is rapidly becoming the universal repository for all the accumulated knowledge, information, data, and garbage of humankind. This paper surveys the issues involved, the approaches that have been successfully applied to small systems, and the ongoing efforts to extend them to distributed, interconnected, rapidly growing, heterogeneous systems.


  1. What is Ontology?
  2. Some Modern Systems
  3. Trees, Lattices, and Other Hierarchies
  4. Notations for Logic
  5. Ontology Sharing and Merging
  6. Glossary

2. Ontology, Metadata, and Semiotics

The Internet is a giant semiotic system. It is a massive collection of Peirce's three kinds of signs: icons, which show the form of something; indices, which point to something; and symbols, which represent something according to some convention. But current proposals for ontologies and metadata have overlooked some of the most important features of signs. A sign has three aspects: it is (1) an entity that represents (2) another entity to (3) an agent. By looking only at the signs themselves, some metadata proposals have lost sight of the entities they represent and the agents human, animal, or robot which interpret them. With its three branches of syntax, semantics, and pragmatics, semiotics provides guidelines for organizing and using signs to represent something to someone for some purpose. Besides representation, semiotics also supports methods for translating patterns of signs intended for one purpose to other patterns intended for different but related purposes. This article shows how the fundamental semiotic primitives are represented in semantically equivalent notations for logic, including controlled natural languages and various computer languages.


  1. Problems and Issues
  2. Signs of Signs
  3. Logical Primitives
  4. Combining Logic with Ontology
  5. Extracting Logic from Language

3. Concepts in the Lexicon

The lexicon is the bridge between a language and the knowledge expressed in that language. Every language has a different vocabulary, but every language provides the grammatical mechanisms for combining its stock of words to express an open-ended range of concepts. Different languages, however, differ in the grammar, the words, and the concepts they express. For each word in the vocabulary of a language, the lexical entry must contain all the information needed to construct a semantic representation for sentences that contain the word. This paper surveys semantic issues in natural languages and the requirements they impose on the information represented in the lexicon.


  1. Introduction
  2. Semantics from the Point of View of the Lexicon
  3. Review of Lexical Representations
  4. Metaphysical Baggage and Observable Results
  5. Language Games
  6. Interactions of the Lexical and Conceptual Systems
  7. Information Extraction by Filling Templates

4. The Challenge of Knowledge Soup

People have a natural desire to organize, classify, label, and define the things, events, and patterns of their daily lives. But their best-laid plans are overwhelmed by the inevitable change, growth, innovation, progress, evolution, diversity, and entropy. These rapid changes, which create difficulties for people, are far more disruptive for the fragile databases and knowledge bases in computer systems. The term knowledge soup better characterizes the fluid, dynamically changing nature of the information that people learn, reason about, act upon, and communicate. This article addresses the complexity of the knowledge soup, the problems it poses for computer systems, and the methods for managing it. The most important requirement for any intelligent system is flexibility in accommodating and making sense of the knowledge soup.


  1. Issues in Knowledge Representation
  2. Attempts to Organize and Formalize Knowledge
  3. Knowledge Soup
  4. Cognitive Processing
  5. Directions for Future Research

5. KR Ontology

The KR ontology is a formal ontology based on Whithead's process philosophy and Peirce's semiotic that has been designed to serve as a foundation for knowledge representation in databases, knowledge bases, and natural language processing. The version presented on this web site is based on axioms and definitions given in the book Knowledge Representation by John F. Sowa. The complete system, however, is a work in progress whose further development depends on ongoing research in logic, linguistics, philosophy, and empirical studies in every branch of science and technology.


  1. Top level
  2. Processes
  3. Relations
  4. Causality
  5. Agents
  6. Thematic roles

6. Tutorial on Mathematics and Logic

This paper is a 43-page summary and overview of the basic topics in mathematics and logic that are used in discussions of logic, ontology, and knowledge representation. It is not intended as an exhaustive textbook on these topics, but as a brief introduction for students who are beginning their studies or as a quick review for readers who may have forgotten what they once learned. It is a revised and extended version of Appendix A from the book Conceptual Structures by John F. Sowa. Section #14 is a commentary on Peirce's own tutorial on existential graphs.

  1. Sets, Bags, and Sequences
  2. Functions
  3. Lambda Calculus
  4. Graphs
  5. Relations
  6. Representing Relations by Graphs
  7. Lattices
  8. Propositional Logic
  9. Predicate Logic
  10. Axioms and Proofs
  11. Formal Grammars
  12. Game Graphs
  13. Model Theory
  14. Peirce's Existential Graphs

Copyright ©2001, 2005, by John F. Sowa. Permission is hereby granted for anyone to make verbatim copies of these documents for teaching, self-study, or other noncommercial purposes provided that the copies cite the author, the URL of this document, and this permission statement. Send comments to John F. Sowa.

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