From: owner-standard-upper-ontology@listserv.ieee.org on behalf of John
F. Sowa [sowa@bestweb.net]
Sent: Tuesday, September 07, 2004 12:09 PM
To: standard-upper-ontology@listserv.ieee.org
Cc: barbara.heller@imise.uni-leipzig.de;
herre@informatik.uni-leipzig.de; cg@cs.uah.edu; cl@philebus.tamu.edu
Subject: General Ontological Language (GOL)

I recently came across another project to develop a
version of logic and an upper ontology, which builds
on and integrates much of the ongoing research:

http://www.onto-med.de/en/publications/scientific-reports/om-report-no7.pdf

This is a well documented study, which I believe
should be considered along with other candidate
documents for the SUO Working Group.

As I have said many times, I don't believe that
any single ontology (upper, middle, or lower)
deserves to be blessed as a universal standard.
However, I do believe that *all* promising
candidates should be accommodated.  And this
is indeed a very promising example.

Following is the table of contents from the GOL
document.  The two principal authors, Barbara Heller
and Heinrich Herre, are on the cc list above.

John Sowa
____________________________________________________

            General Ontological Language (GOL)
                      Version 1.0
             Barbara Heller, Heinrich Herre
                 in collaboration with
       Patryk Burek, Frank Loebe, Hannes Michalek
                      August 2004

Contents

1 Introduction ......................................... 7
1.1 Formal Ontology and Information Systems ............ 7
1.2 General Architecture of GOL ........................ 8
1.3 Applications ....................................... 9
1.4 Related Work ...................................... 10
1.5 Structure of the Report ........................... 11

2 Meta-Ontological Principles, Basic Assumptions, and
   Logical Methods ..................................... 13
2.1 Categories ........................................ 13
2.2 The Axiomatic Deductive Method .................... 13
2.3 Semantic Transformation and Interpretability ...... 14

3 Categories, Classes, Individuals, and Levels ........ 16
3.1 Types of Classes and Categories ................... 16
3.2 Individuals and Universals ........................ 16
3.3 Levels ............................................ 17

4 Space and Time ...................................... 19
4.1 Time .............................................. 19
4.2 Space ............................................. 21

5 Basic Categories of Individuals ..................... 22
5.1 Presentials, Persistants, and Processes ........... 22
5.2 Physical Structures ............................... 23
5.2.1 Physical Structures and Properties .............. 24
5.2.2 Physical Structures and Substrates .............. 24
5.2.3 Physical Structures and Space ................... 25
5.2.4 Boundaries of Physical Structures ............... 26
5.2.5 Physical Structures and Time .................... 27
5.2.6 Persistence and the Meaning of Proper Names ..... 27
5.3 Properties ........................................ 28
5.3.1 Property and Property Bearer .................... 29
5.3.2 Property Value .................................. 30
5.3.3 Quality and Quality Value ....................... 30
5.3.4 Classification of Properties .................... 31
5.4 Occurrents ........................................ 32
5.4.1 Processes ....................................... 32
5.4.2 Changes ......................................... 34
5.4.3 Discrete vs. Continuous Processes and States .... 34
5.4.4 Histories ....................................... 35
5.4.5 Simple and Complex Processes .................... 35
5.4.6 Relating Processes to Space ..................... 35
5.4.7 Process Classifications ......................... 36
5.5 Mental and Social Entities ........................ 37

6 Relations and Facts ................................. 39
6.1 Relations, Relators and Relational Roles .......... 39
6.1.1 Basic Notions ................................... 39
6.1.2 Classifications of Relations .................... 40
6.2 Facts, Propositions and Infons .................... 41
6.2.1 Basic Notions ................................... 41
6.2.2 Representing Facts .............................. 41
6.2.3 Classifications of Facts ........................ 43
6.2.4 Factual Universals .............................. 43
6.3 Formal Relations of the GFO ....................... 44
6.3.1 Class and Set-theoretical Relations ............. 44
6.3.2 Instantiation ................................... 45
6.3.3 Property Relations .............................. 45
6.3.4 Parthood and Its Neighbors ...................... 45
6.3.5 Relating to Time and Space ...................... 47
6.3.6 Association ..................................... 48
6.3.7 Ontical Connectedness ........................... 48
6.3.8 Existential Dependence .......................... 48
6.3.9 Future Extensions: Causality and Denotation ..... 49

7 Situoids, Situations, and Configurations ............ 50
7.1 Situations and Configurations ..................... 50
7.2 Situoids and Configuroids ......................... 51

8 Syntax of GOL ....................................... 53
8.1 Typed Representation Language RGOL ................ 53
8.1.1 Types ........................................... 53
8.1.2 Alphabet of the Language L(?) ................... 54
8.1.3 Formulas of L(?) ................................ 54
8.1.4 Axioms .......................................... 55
8.2 Type-free languages ............................... 56
8.2.1 Basic System BTF(GOL) ........................... 57
8.2.2 Extended System ................................. 58
8.2.3 First-order GOL (FO-GOL) ........................ 59
8.3 Conformance Principles and Summary of Languages ... 59
8.3.1 Dimensions of RGOL Subsystems ................... 59
8.3.2 Summary of Languages ............................ 59

9 Principles of Theory Building and Meta-Logical
   Properties .......................................... 60
9.1 Modularization and Independence ................... 60
9.2 Consistency and Paraconsistency ................... 61
9.3 Uncompleteness Degrees ............................ 62
9.4 Decidability and Axiomatizability ................. 62
9.5 Definability ...................................... 63

10 Ontological Mappings and Reference Ontologies ...... 65
10.1 Basic Principles ................................. 65
10.2 Ontological Mappings of Terminology Systems ...... 66
10.3 Related Work ..................................... 67

11 Axiomatics of GFO in FO-GOL ........................ 69
11.1 Axioms Pertaining to Part-of ..................... 69
11.1.1 Preliminaries .................................. 69
11.1.2 Abstract Part-of: System AM .................... 69
11.1.3 Material Part-of ............................... 70
11.1.4 Summary, Remarks, and Problems ................. 71
11.2 Axioms Pertaining to Time ........................ 71
11.2.1 Preliminaries .................................. 71
11.2.2 System T3: Temporal Boundaries ................. 73
11.2.3 System T3: Mereology of Time-regions ........... 73
11.2.4 System T3: Chronoids and Time-regions .......... 73
11.2.5 System T2 ...................................... 74
11.2.6 System T1: Temporal Boundaries ................. 74
11.2.7 System T1: Mereology of Chronoids .............. 74
11.2.8 Summary, Remarks, and Problems ................. 75
11.3 Axioms Pertaining to Space ....................... 76
11.3.1 Preliminaries .................................. 76
11.3.2 Mereology of Space ............................. 78
11.3.3 Spatial Boundaries and Topology ................ 79
11.3.4 Summary, Remarks, and Problems ................. 81
11.4 Axioms Pertaining to Presentials ................. 82
11.4.1 Preliminaries .................................. 82
11.4.2 Presentials and Presential Qualities ........... 84
11.4.3 Physical Structures and Space .................. 85
11.4.4 Physical Boundaries and Topology ............... 86
11.4.5 Classification of Physical Structures .......... 87
11.4.6 Summary, Remarks, and Problems ................. 88
11.5 Axioms Pertaining to Persistants ................. 89
11.5.1 Preliminaries .................................. 89
11.5.2 General Axioms ................................. 90
11.5.3 Ontical Connectedness .......................... 91
11.5.4 Classification of Persistants .................. 92
11.5.5 Persistants and Processes ...................... 92
11.6 Axioms Pertaining to Occurrents .................. 92
11.6.1 Preliminaries .................................. 92
11.6.2 General Axioms ................................. 93
11.6.3 Mereology of Processes ......................... 93
11.6.4 Processes and Boundaries ....................... 94
11.6.5 Processes and Properties ....................... 94
11.6.6 Processes and Space ............................ 95
11.6.7 Classification of Occurrents ................... 95
11.6.8 Summary, Remarks, and Problems ................. 96
11.7 Axioms Pertaining to Situoids and Situations ..... 97
11.7.1 Preliminaries .................................. 97
11.7.2 Situations: Global Axioms for Fixed Time-
        boundary and Signature ......................... 99
11.7.3 Situations: Local Axioms for Fixed Time-
        boundary and Signature ......................... 99
11.7.4 Situations: Global Axioms for Varying Time-
        boundary and Free Signature ................... 100
11.7.5 Situations: Local Axioms for Varying Time-
        boundary and Free Signature ................... 100
11.7.6 Situoids: General Axioms for Fixed Signature .. 101
11.7.7 Situoids: Local Axioms for Fixed Signature .... 102
11.7.8 Summary, Remarks, and Problems ................ 102

12 Axiomatics of GFO in RGOL ......................... 103
12.1 Type System ..................................... 103
12.2 Primitives ...................................... 103
12.3 Axioms on Categories ............................ 104
12.4 Axioms on Classes ............................... 105

13 Meta-logical Analyses ............................. 106
13.1 Abstract Part-of Relation ....................... 106
13.2 Ontology of Time ................................ 108
13.2.1 Preliminaries ................................. 108
13.2.2 Primitives and Model Structure ................ 108
13.2.3 Definitions ................................... 108
13.2.4 Axioms ........................................ 109
13.3 Comparison to Allen-Hayes’ Theory of Time ....... 111
13.3.1 Interpretation of T(AH) in T1 ................. 111
13.3.2 Interpretation of T1 in T(AH) ................. 112

14 Semantics of GOL .................................. 113
14.1 Model-theoretic Semantics ....................... 113
14.2 Situation and Situoid Semantics in General ...... 114
14.3 Situations ...................................... 114
14.4 Situoids ........................................ 118
14.4.1 Types of Infons in Situoids ................... 119
14.4.2 Types of Extensions of Situoids ............... 120

15 Comparison to Other Top-Level Ontologies .......... 124
15.1 Comparison to DOLCE ............................. 124
15.1.1 Ontological Levels ............................ 124
15.1.2 Classes, Universals and Individuals ........... 125
15.1.3 Time and Space ................................ 125
15.1.4 Presentials, Persistants and Endurants ........ 125
15.1.5 Properties, Qualities, Quality Values and
        Qualia ........................................ 126
15.1.6 Processes and Perdurants ...................... 127
15.2 Comparison to Sowa’s Ontology ................... 130
15.2.1 Introduction: Construction Method ............. 130
15.2.2 Physical and Abstract Categories .............. 130
15.2.3 Firstness, Secondness and Thirdness ........... 131
15.2.4 Continuants and Occurrents .................... 132
15.2.5 Combination of the Distinctions ............... 132
15.2.6 Conclusion .................................... 132

16 Examples .......................................... 136
16.1 Example for Comparison: The Statue and the Clay . 136
16.1.1 Source Material ............................... 136
16.1.2 Ontological Analysis .......................... 136
16.1.3 Comparison with the DOLCE Formalization ....... 137
16.2 The Race Example ................................ 138
16.2.1 Source Material ............................... 138
16.2.2 Ontological Analysis .......................... 138
16.3 Staging Example ................................. 141
16.3.1 Source Material ............................... 141
16.3.2 Ontological Embedding into GFO ................ 141
16.3.3 Domain-specific Extension ..................... 143

Acknowledgements ..................................... 144

Appendix A: GFO Category and Relation Hierarchies .... 145

Appendix B: Diagrammatic Schemes ..................... 149

Bibliography ......................................... 154

Index ................................................ 160

Index of Symbols ..................................... 163