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Azamat Sh. Abdoullaev

ABSTRACT.

There is constructed a formal representation of the world as a unified theory of entities and relationships serving as the universal language for computers and persons. The integral combination of the global schema and fundamental mathematics resulted in a standard model of universe (of discourse) involving substances and objects; states and properties; changes, actions, processes, and events; relationships, connections, and associations. The general framework provided a system of knowledge standards (as elements and primitives) underlying the key concepts of scientific knowledge, the basic constructs of minds, the major categories of languages, as well as the entity data types and reasoning rules of knowledge systems and so constituting a representational and inferential framework for a new class of intelligent applications. It is shown that the standard formal ontology makes the single foundation upon which knowledge domains of physical, mental, or cultural worlds as well as natural language constructions are raised. As a consequence, the natural language is proved to be the most general knowledge and reasoning language not only for persons but also for computing machines, which to become truly intelligent systems should be able to process and communicate semantic information about the world and its domains in NL forms. This, as shown, opens up the possibility of natural language applications of encyclopedic intelligence such as a Virtual or Digital Aristotle and global knowledge resources as the Onto-Semantic Web. To meet the challenging undertakings, the formal world model was developed as underpinning computational upper ontologies, the ER extended data models, data integration systems, and Web ontology languages. Representing reality to formal reason of humans and computing machines suggests an effective way to powerful intelligent systems:

(Reality or the World) ® Knowledge of the World {(Universal Ontology + Mathematics + Semantics + Science) + Logic of Things} ® Natural Language ® Informatics and Computer Science ® NL Engineering and AI Technology ® NL Knowledge and Reasoning Machines (systems, applications, agents, robots, software programs, tools) ® Encyclopedic Intelligences (Virtual or Digital Aristotle) ® Onto-Semantic World Wide Web ® Global Intelligent Cyberspace.

INTRODUCTION: a Standard for Science, Upper Ontologies, and Web Ontology Languages 7

I. The Unified World Description: the EIS Standard Ontology

Introduction 19

I.1. Reality Representation 20

I. 1. 1. Top-Level Ontologies and Languages 20

I. 1. 2. Ontological Fundamentals 23

I. 1. 3. The Elements and Principles of Reality 28

I. 1. 4. Carving Reality at its Joints, or How to Classify Things, Beings, or Entities 32

I. 2. The Mathematics of Reality or Causal Mathematics 36

I. 2. 1. The World-Formula and the Lattice of Entities 37

I. 2. 2. The Categories of the World 43

II. Ontological Fundamentals and Rules

Introduction 46

II.1. The Primary Entities

II. 1.1. The Class of Substances (Objects, Material and Nonmaterial) 47

II. 1. 2. The Class of States (Properties, Qualities, and Quantities) 52

II. 1. 3. The Class of Changes (Actions, Activities, and Events) 57

III. Relations and Relationships

Introduction 65

III. 1. The Class of Relations 66

III. 1. 1. The Basics of Relationships 66

III. 1. 2. The Mathematics of Relationships 76

III. 1. 3. The Formal Ontology of Relationships 82

IV. The Life-or-Death Relationship

Introduction 89

IV. 1. Causality, Reverse Causality, and Causation 89

IV. 1. 1. The Unified Causal Theory 90

IV. 1. 2. The Mathematics of Causality 99

IV. 2. The Universal Logic of Things: An Ontological Predicate Calculus 112

IV. 2.1. The Kinds of Human and Machine Thinking 113

IV. 2. 2. The Rules of Reasoning about the World and the Internet’s Web Rules Language 116

V. Natural Language: General Knowledge and Reasoning Language

Introduction 123

V. 1. Universal Formal Ontology and General Semantics 124

V. 1. 1. The Sort of Semantics Language Needs

V. 1. 2. Ontological Linguistics as a Unified Theory of Language 127

V. 1. 3. Universal Namespace and Web Namespaces: the EIS Language Constructions 133

V. 1. 4. Prepositions and Adverbs: Nature, Meaning, and Classification 142

V. 2. VerbSpace and Sentence Patterns 144

V. 2. 1. Verbs, Predicates, and Entity Types 144

V. 2. 2. Sentences, RDF Triples, and Causal Statements 148

VI. Natural Language Intelligences: the Virtual or Digital Aristotle

Introduction 160

VI. 1. A General Query System 162

VI. 1. 1. Entity Categories for Question Answering Systems 162

VI. 1. 2. The Standard Ontology and the WordNet Taxonomy 166

VI. 2. The World Representation and Reasoning Systems 173

VI. 2. 1. The Nature of Knowledge and World Knowledge Systems 174

VI. 2. 2. The Meaning Processing in the Virtual Aristotle 179

VI. 2. 3. Ontology Machinery and Universal Knowledge Transducer 187

VI. 2. 4. The Encyclopedic Knowledge Base of the Virtual Aristotle 190

Conclusion: the EIS Standard Universal Ontology 194

REFERENCES 197

Illustrations: Diagrams and Figures 204

The List of Figure Captions:

Figure 1. The Sources of Standard Universal Ontology 204

Figure 2. The Universal Classification of Things 205

Figure 3. The Hierarchy of Natural Entities 206

Figure 4. The Lattice of Reality 207

Figure 5. The Causal Order of the World Categories 208

Figure 6. The Taxonomy of States 209

Figure 7. Mental Processes: the Materials of the Mind 210

Figure 8. The Lattice of Relations 211

Figure 9. Causal Relationships as a Preordered Category 212

Figure 10. A Causal Model of Complex Processes 213

Figure 11. The Relationships of Language, Mind and Reality 214

Figure 12. The Word Network for Entities and Relations 215

Figure 13. The Meaning of Symbols 216

Figure 14. The Classification of Machinery 217

Figure 15. The Knowledge Level of the Virtual Aristotle Machine 218

Figure 16. The Relationships of Knowledge Domains 219

The List of Tables:

Table 1. The World structure and mathematical representations 41

Table 2. The Meaning of Relative Operations 87

Supplement 220

INTRODUCTION: a Standard for Science, Upper Ontologies, and Web Ontology Languages

Of all sorts of intellectual pursuits, nothing appears of greater import than to give a formal account of the world understandable both by humans and computing machines. Art, religion, science, and technology by their specific ways seek to model, explain, or represent reality, but only one branch of knowledge is thoroughly and systematically committed to the grand cause of technical inquiry into Thing or Entity, its cardinal classes, properties, and relations. Such challenging search for world knowledge, the hardest, most exacting as well as mostly awarding and winning, is designated as ontology suggesting the most general theories about the world and thus being fully concentrated and devoted to the profound accounting of beings, things, or entities. All kinds of science, basic or applied, natural, social, formal, or humanitarian, as domain specific ontologies to some substantial degree partake in the general theory of entities and relationships. Again, all types of knowledge, theoretical experimental or practical, presuppose essential, ontological knowledge of things. Implicitly or explicitly, ontological principles can be found among mostly general theories, mostly universal axioms and laws, and in mostly interesting scientific problems. As ideas, ontological concepts, notions, and terms lead the list of great ideas making the very substance of the grand elemental conceptions. For they are the abstractions by which thought knows the world and minds think things, the terms in which we formulate major principles and facts of reality, the notions in which we make definitions, put fundamental questions, and solve decisive problems. Ontological ideas constitute the very framework of mental contents and cognitive processes as the heart of mental life. With that, they reside in language as mind in body, as pungency in pepper; our human language is pervaded with ontological categories, for the syntactic, grammatical categories and semantic classes are tied to world things, eventually describing and explaining constituents and properties of being, thereby predicting the behavior of the real world. Wherefore, all great human actions and intellectual achievements, all our rational practice and moral conduct intrinsically guided by ontological rules and principles, the basic truths of reality. Still this is not all the outstanding accomplishments of the science of reality. Much more impressive things are coming with the beginning of the third millennium.

Nowadays, when computers as grounded to electronic measuring devices, transducers, and telemetric systems are transforming into integrated worldwide information processing networks, ontology is getting a long-waiting and fully deserved recognition of a critical factor in the 21st century intelligent technology, particularly, in building the most advanced knowledge technologies and meaningful computing machines, purposed to manage the world’s collective knowledge online and that presented in digital form.

As far as computing is concerned with computable structures and processes and ontology reveals general structures and patterns of relationships in the world, the latter permeates the key branches of computer science: knowledge engineering in AI, conceptual modeling in information systems and databases, type systems and domain modeling in programming languages design: object-oriented, procedural, or relational. It can be said that the action, the most important and breakthrough technological works, is no longer in artificial intelligence but rather in ontology design and engineering. Today ontologies are actively used in all basic fields of computer science and technology: artificial intelligence, computing networks, informatics, knowledge engineering, programming languages, computational linguistics, etc. It is increasingly realized that computing knowledge products ought to be founded on comprehensive world models represented in precise (formal) language of things with clear syntax and strict semantics.

The close examples of such understanding are the fundamental research projects initiated within the AI and Web communities, aimed to construct domain-independent ontologies and ontology languages for developing extensive knowledge and reasoning applications. So, under the auspices of the Institute of Electrical and Electronic Engineers (IEEE), it has been started the ambitious project of 'a standard upper ontology of high-level concepts, definitions and relationships processable by computers' constructed as a general purpose, formal system of things rooted in the notion of entity or thing [IEEE SUO, 2004; SUMO, 2004; CYC, 2003; SUO IFF, 2004]. As the starting candidates the IEEE SUO includes the IFF (Information Flow Framework) foundation meta-ontology based on a mathematical category theory [SUO IFF, 2004]; the SUMO (suggested upper merged ontology) targeted to sort out more than 20k common notions of objects, physical and abstract, and processes. These both were joined with the CYC ontology which commonsense knowledge base boasting more than 100k terms, 10k predicates, and 1M assertions taking their source from the notion of thing as the universal collection of all other individuals, physical, partially intangible and formal [CYC, 2003]. Recently, the number of candidates was increased with the Shell's data model of things as a sample of 4D ontology, named Lifecycle Integration Schema, and the multi-source ontology (MSO) aimed to unite some of these taxonomies. On the whole, the SUO project is running under the belief that the standard model can be built as a library of modules by mapping, merging, and integration of different source ontologies [IEEE SUO]. Another outstanding technological undertaking is performed under the World Wide Web Consortium (W3C) Semantic Web Activity [W3C, 2004], where the all-important role in the cause of transforming the World Wide Web into the Semantic Web is assigned to ontology [Berners-Lee and Fischetti, 1999; Berners-Lee, Hendler, Lassila, 2001]. The former is planned to develop radically novel features with respect to the latter, traditional Web usually defined as an information space of resources and web agents interrelated by hypertext links, and which architecture is based on three principles: identification of resources by global identifiers; representation of resources states, or data formats; and interaction protocols [Berners-Lee, 2004]. Whereas, the coming Onto-Semantic Web is viewed as the worldwide distributed body of electronic contents and knowledge resources (programs, databases, Web pages, models, and sensors) communicating by intelligent agents via the ontology language underpinned by the Internet markup languages, schemas, a