KNOWLEDGE REPRESENTATION
USING
CONCEPTUAL GRAPHS AND PEIRCE LOGIC
Dr John E. Heaton
PhD,
Loughborough University of Technology,
Leicestershire,
UK, LE11
3TU.
Introduction
This treatise is a set of chapters describing the theory of “Conceptual Graphs” by John Sowa and the graphical “Existential Logic” (Peirce logic) of Charles Peirce. Sowa's theory of conceptual graphs has been modified by almost everyone who has worked with it. In some cases the modifications are justified but in many cases the notation, semantics and operations on the graphs have been altered for no apparent reason. In this treatise we attempt to specify a version of conceptual graphs which maintains Sowa's original ideas as far as possible and extends them in a consistent manner where they are incomplete.
Original work on conceptual graphs with Peirce logic was carried out as part of an MSc project and then continued as a PhD project and thesis. Since completing this work the research has continued into finding ways of automating and optimising proofs, resulting in a resolution-like procedure developed especially for use under the “Open World” assumptions.
The Open World Logic System (OWLS) is a prototype fully automated knowledge base and theorem prover which uses conceptual graphs combined with Peirce logic using open world assumptions to provide a sound and complete system of first order logic with equality. It also goes beyond this by providing the means to express and compute with modal logic. In treating the answering of knowledge base queries as proofs of theorems the system is much more general and powerful than traditional database systems. Unlike many systems which are described on paper the OWLS system actually exists in a Prolog implementation.
The motivation of this work is to present the results of many years' work in the refinement of Sowa's theory and the experience gained in producing working systems that run on computers. The hope is that it will prevent others from going over the same ground since much work is done in the Conceptual Graphs community that is not recorded in the conference proceedings.
Since the purpose of this treatise is to offer an informal description of the knowledge representation language and its logic it does not offer rigorous proofs as a scientific treatment would. Some proofs of the calculus that has been developed for the theorem prover are given but proofs of the underlying logical system can be found elsewhere and the reader is encouraged to consult the bibliography.
Structure Of The Work
This
work is divided into 7 main sections and a bibliography. Each section
consists of a set of chapters and are largely self contained. However
the best way to read the material is to start at the beginning and
work through it in order. Many chapters are not yet complete and
those which are missing will either present a blank page or produce
an error. Please revisit the site from time to time.
Section 1 - Theory Of Conceptual Graphs:
Concepts
Relations
Actors
Graphs
Hierarchies
And Order
Definition,
Schemata And Prototypes
Contexts,
Modalities And Theories
Section 2 - Peirce's Existential Logic:
System
Alpha
System Beta
System
Gamma
Section 3 - Conceptual Graphs And Peirce Logic:
Extensions
To Notation
System
Alpha
System Beta
System
Gamma
Section 4 - Operations On Graphs:
Generalisation
And Specialisation
Projection
Joining
Of Graphs
Miscellaneous
Operations
Section 5 - Proofs And Proof Strategies:
Model Theory
Rule
Chaining
Resolution
Derived Rules Of Inference
Data Or Goal
Driven Strategies
Section 6 - The OWLS System:
Aims
Of The System
Open World Resolution
The Universal
Heuristic
Nonlogical Reasoning
The
OWLS User Guide (zip file best read with Wordpad once unzipped)
Section 7 – Variants Of Conceptual Graphs Notation:
Knowledge Interchange Format - KIF
Conceptual Graphs Interchange Format - CGIF
References And Bibliography:
References And Bibliography
Links:
Links to Conceptual Graphs web sites
Acknowledgements
Since this is work in progress there will be references to and quotations or paraphrases from the work of others who have not yet been given proper acknowledgement. This is especially the case with the work of the inventor of Conceptual Graphs, John Sowa, on whose excellent work in this field this treatise is based.