'MCRT: An Upper Ontology for General Purpose Reality Modeling'
By Marc Geddes
Sydney, Australia
22th March, 2008
Abstract
In this paper I explore the consequence of two assumptions:
(1) A model of reality can be entirely captured by an Upper Ontology
and Data Models are Logical Communications
(2) A method of general purpose reality modeling is equivalent to a
Universal Parser
Introduction
To design a general purpose method of reality modeling I assume that
such a method is equivalent to a 'universal parser' - ie. A system of
translation between different logical representations of concepts.
High-level logical representations (ie data models) can be considered
as methods of logical communication. Thus, the aim is the
construction of an Upper Ontology capable of encompassing all other
ontologies (ie a general purpose representation of the domain
'knowledge' which enables the translation between all other more
specific ontologies (ie general purpose ontology merging).
Previously, I designed the skeleton out-line of the Upper Ontology
('Top Level Domain Model of the Mathematico-Cognition Reality Theory',
Marc Geddes, First correct version: 4th Dec, 2007, everything-list).
This is MCRT (the Mathematico-Cognition Reality Theory). It appears
that the process of data modeling can be separated into three general
types: Mathematical (Software Development - or SD), Teleological (The
creation of value systems - ie. Story Narration - or SN) and Physical
(Virtual Reality - or VR). The initial aim then, is the elaboration
of MCRT, the development of the triple-aspect ontology and the study
of the relationships between SD, SN and VR ontologies.
Initial Knowledge Base: MCRT Ontology
MCRT Upper Ontology provides a skeleton structure for the proposed
Upper Ontology . This paper provides the beginnings of the
specification of MCRT Upper Ontology.
MCRT is an Upper Ontology, an abstract top-level representation of
'reality' at the highest possible level of description.
Knowledge Domains
Sub-domains of reality are areas of 'Concept Space'(CS) classified by
three KR axes.
1st Axis: Physics, Teleology, Mathematics
2nd Axis: Platonic, Cognition, Artifact
3rd Axis: Independent, Relative, Mediating
A brief description of each axis follows. The meaning of each domain
is then elaborated on through references to known fields and examples.
1st Axis:
Physics (PHY): Domains related to material entities. Concerned with
space and geometry - or the classification of whether things are
'Solid' or 'Empty'.
Teleology (TEL): Domains related to goal directed entities. Concerned
with values - or the classification of whether things are 'Good' or
'Bad' relative to agents.
Mathematics (MAT): Domains related to knowledge itself (meta-data).
Concerned with logical implications - or the classification of
models of reality as 'True' or 'False'.
2nd Axis:
Platonic (PLA): Domains related to abstract universal entities. These
are entities which are postulated to be eternal and unchanging, and
cannot be located in any finite region of reality (they are
abstract). This is simply anything which is 'abstract', 'constant',
and 'applicable to any region of reality'.
Cognition (COG): Domains related to systems. Systems have three main
characteristics: (i) Input, (ii)
Processing, (iii) Output. Simply, the term means 'system' in the most
general sense.
Artifact (ART): Domains related to particular things. An artifact is
an instantiated object, a particular instance of something with
particular attributes and behaviours. This is close to the meaning of
'object' in the sense of OOP (Object Oriented Programming).
3rd Axis:
Independent (IND): Domains related to intrinsic properties.
Properties of things in themselves, without reference to external
objects. An 'element' in the most general sense of the term.
Relative (REL): Domains related to functional (external) properties.
The relation or effect something has on things external to itself. A
'function' or 'action' in the most general sense of these terms.
Mediating (MED): Domains related to signifying (semantic) properties.
How something is represented or 'appears' to something else. An
'icon', 'signal' or 'means of communication' in the most general sense
of the term.
Reference: The third axis is similar to the ontological classification
scheme of Charles Pierce, hence, the same names have been used.
However the definitions given here are not identical to Pierces.
The following summarizes the concepts that each axis attempts to
capture.
1st Axis:
PHY - Geometry
TEL - Value
MAT - Implication
2nd Axis:
PLA - Universal (Abstraction)
COG - System (Process)
ART - Particular (Object)
3rd Axis:
IND - Comprising (is made of)
REL - Acting (functions as)
MED - Signifying (appears as)
The names and areas of knowledge referenced by pairs of the 1st and
2nd axes are as follows:
Mathematico-Platonic: Pure mathematics
Mathematico-Cognition: Intelligence/Mind
Mathematico-Artifact: Software
Teleo-Platonic: Moral Ideals
Teleo-Cognition: Agents/Society
Teleo-Artifact: Memes/Culture
Physico-Platonic: Laws of Physics
Physico-Cognition: Physical Interactions
Physico-Artifact: Concrete objects
Classification of IT related knowledge domains by the MCRT
The three KR axes combine to generate 27 'fundamental knowledge
domains'. The 27 knowledge domains resulting from the combination of
these axes is described as follows. Examples are given of known
fields (often information technology (IT) related) which fit the
classifications. Maintaining and developing an effective general
purpose knowledge base implies investigating the ontological
categories of all these fields.
Solid State Physics (PHY, ART, IND)
Examples: Chemical Engineering, Electrical Engineering, Circuits, Nano-
Technology
Engineering (PHY, ART, REL)
Examples: Mechanical Engineering, Telecommunications-Internet,
Networks, Computer Engineering-Personal Computers, Super Computers
Virtual Reality (PHY, ART, MED)
Examples: Human-Computer Interaction, User Interfaces-Graphical User
Interface
Sociology (TEL, ART, IND)
Examples: Group Dynamics
Political Science (TEL, ART, REL)
Examples: Democracy, Humanism, Socialism, Libertarianism
Arts (TELE, ART, MED)
Examples: Science Fiction, Fantasy, Computer Games
Software (MAT, ART, IND)
Examples: Unix-Linux, Windows
Software Engineering (MAT, ART, REL)
Examples: Architecture, Design Pattern, Quality Assurance
DP Modeling (MAT, ART, MED)
Examples: Programming Language-Java, Ruby, LISP, Object Oriented
Technology - UML, Databases - ERD, SQL
Chemistry (PHY, COG, IND)
Examples: Organic Chemistry
Thermodynamics (PHY, COG, REL)
Examples: Robotics, Applied Mechanics
Data Communications (PHY, COG, MED)
Example: Physical Perception - Vision, Acoustics
Social Psychology (TEL, COG, IND)
Examples: Evolutionary Psychology
Decision Theory (TEL, COG, REL)
Examples: Economics, Game Theory
Communication (TEL, COG, MED)
Examples: Linguistics, Semiotics
Symbolic Logic (MAT, COG, IND)
Example: Predicate Logic, Propositional Logic
Probability Theory (MAT, COG, REL)
Example: Bayesian Inference - Bayesian Networks, Bayes Theorem
Reflective Reasoning (MAT, COG, MED)
Example: Ontology Merging, Analogy formation
Particle Physics (PHY, PLA, IND)
Example: Standard Model.
Mechanics (PHY, PLA, REL)
Examples: Lagrangian Mechanics, Newton Mechanics, Quantum Mechanics,
Hamiltonian Mechanics)
Field Theory (PHY, PLA, MED)
Examples: Relatively, Geometry
Virtue Ethics (TEL, PLA, IND)
Example: Aristotlean Eudamonic Ethics
Morality (TEL, PLA, REL)
Examples: Utilitarianism, Consequentialism
Aesthetics (TEL, PLA, MED)
Example: Kant
Discrete Math (MAT, PLA, IND)
Examples: Complexity Theory-P=NP, Computability Theory-Finite State
Machines, Combinatorics, Graph Theory
Algebra (MAT, PLA, REL)
Examples: Fields, Groups, Rings, Relations-Functions
Analysis (MAT, PLA, MED)
Examples: Sets - Axiom of Choice, Differentiation, Integration, Number
Theory, Continuum Hypotheses, Category Theory
Ontological Primatives
Each of the 27 fundamental knowledge domains, has associated
ontological primatives ('Prims'), as described below. Preliminary
definitions and examples (instances) of each 'Prim' are given below.
The idea is that the whole of reality is 'built' from combinations of
and elaborations upon these fundamental 'Prims'. These 'Prims' are
the 'ontological elements' (building blocks) of reality.
Collection (MAT, PLA, IND): A related collection of finite elements
Example: Network
Relation (MAT, PLA, REL): Abstract relation (including mathematical
functions)
Example: Less Than
Category (MAT, PLA, MED): The limits of an infinite series
Example: 5 (Number)
Deduction (MAT, COG, IND): Deterministic reasoning steps
Example: Syllogism
Pattern (MAT, COG, REL): Probabilistic prediction
Example: Sequence
Reflection (MAT, COG, MED): Semantic similarity
Example: Analogy
Code (MAT, ART, IND): System (hardware) command
Example: Assembler (Low-Level Language)
Design (MAT, ART, REL): Class (object oriented) model
Example: Java (Programming Language)
Analysis (MAT, ART, MED): Logical (Data) model
Example: UML (System Model)
Characteristic (TEL, PLA, IND): Personality trait
Example: Untrustworthy
Skill (TEL, PLA, REL): Agent Ability
Example: Lock-Picking
Style (TEL, PLA, MED): Aesthetic Preference
Example: Victorian
Goal-Setter (TEL, COG, IND): System defined by internal preferences
(goals)
Example: Olympic Games
Decision-Maker (TEL, COG, REL): System defined by external choices
Example: Parliament
Communicator (TEL, COG, MED): System defined by semantics of icons
produced
Example: Person (Sentient)
Role (TEL, ART, IND): Actor
Example: Film Star
Meme (TEL, ART, REL): Philosophy of social organization
Example: Democracy
Message (TEL, ART, MED): Transmission of values via icons
Example: Story
Symmetry (PHY, PLA, IND): Spatial forms
Example: Circle
Force (PHY, PLA, REL): Spatial relations (least action principles)
Example: Gravity
Field (PHY, PLA, MED): Spatial measuring system
Example: Grid
Transformation (PHY, COG, IND): Physical System - Internals
Example: Eclipse
Interaction (PHY, COG, REL): Physical System - External effects
Example: Punch
Signal (PHY, COG, MED): Physical System - Information exchange
Example: Sound Wave
Material (PHY, ART, IND): Physical solid defined by internal
properties (intrinsic element)
Example: Wood
Structure (PHY, ART, REL): Physical solid defined by how it is used by
agents (functional object)
Example: Bridge
Presentation (PHY, ART, MED): Physical Icon
Example: Picture
Relationship to other methods of data modeling
Since MCRT represents the outline of a completely general type of data
modeling, the relationship between MCRT and other forms of data
modeling will be considered.
MCRT and Unified Modeling Language (UML)
There are 3 generic types of UML techniques: State Models, Behavior
Models and State Change Models.
State Models - Static views of a domain, constituting class diagrams.
Comparable to MCRT ontology as a whole.
Behavior Models - Models specialized for dealing with systems.
(Dynamic processes with input and output). State Chart Diagrams focus
on state transitions, Sequence and Activity Diagrams focus on time
ordering and data flow, respectively, and Use Case Diagrams focus on
overall functional behavior. These are all associated with the
'Cognition' (COG) level of MCRT.
MCRT and Relational Schema such as Entity Relationship Diagrams (ERD)
The terminology used in relational database technology is motivated by
pure mathematical relations. Pure relational databases lack
additional specialized techniques for dealing with dynamic systems.
Thus, relational schema such as ERD's effectively only deal with the
'Artifact' level of MCRT.
The 'Internal View' of ERD's corresponds to meta-data about the
database itself. It corresponds to the Mathematico-Artifact level of
MCRT.
MCRT ERD
Mathematico-Artifact Internal View
MCRT and Software Architectures
By considering knowledge domains as representing actual classes in an
object oriented software architecture, relations between MCRT and
software architectures can be discussed.
Model-Controller-View (MCV) architecture
Model - Models of objects external to the computer system (analogous
to the 'Conceptual' view in relational modeling).
View - Particular presentation of some aspects of a model to a user
(or the system itself).
Control - Models of internal objects representing the computer system
itself ('Reflective schema') analogous to the 'Internal' view in
relational modeling).
In MCRT, the domains on the Mathematico-Cognition (MAT, COG) level
correspond to the 'Control' classes of MCV.
MCRT MCV
Mathematico-Cognition Control
Hierarchical Levels of Reality
A most important feature of MCRT is that reality is hierarchical. MCRT
assumes that the 'concept space' representing reality is a hierarchy.
The more general concepts subsume (include and supercede) the more
specific. There are levels of abstraction.
The hierarchical ordering of the elements of the axes, from most
general to least general, is as follows:
1st axis:
1st Mathematics (MAT)
2nd Teleology (TEL)
3rd Physics (PHY)
2nd axis:
1st Platonic (PLA)
2nd Cognition (COG)
3 rd Artifact (ART)
3rd axis:
1st Mediating (MED)
2nd Relative (REL)
3rd Independent (IND)
If the scheme is correct, it is to be expected that fields of
knowledge classified as domains lower in the ontological hierarchy
should be subsumed by fields of knowledge classified as domains higher
in the ontological hierarchy.
For example, Category Theory should be a more powerful type of
mathematics than Algebraic Fields, since Algebraic Fields are
classified at a lower level of ontological abstraction (Mathematics-
Platonic-Relative) than Category Theory (Mathematics-Platonic-
Mediating). In turn, Algebraic Fields should be a more powerful
mathematics than Combinatorics, since Combinatorics (Mathematics-
Platonic-Independent) is classified at a lower level of ontological
abstraction than Algebraic Fields (Mathematics-Platonic-Relative).
Indeed, this is exactly what we find. Category Theory is believed to
be a more general type of math than ordinary algebra, which in turn is
known to have superceded the ancient field of Combinatorics. Thus, it
appears that the fields of mathematics can indeed be arranged
hierarchically.
The fields of knowledge classified at higher levels of the ontological
hierarchy indeed appear to supercede the fields of knowledge
classified at lower levels of the ontological hierarchy, establishing
that knowledge can be hierarchically organized. Checking the
postulated ontological hierarchy with respect to the examples of
classified fields of knowledge given earlier seems to establish the
consistency of the scheme.
Bayesian reasoning is not sufficient to fully capture rationality
Contrary to claims that 'Bayes is the secret of universe' among logic
aficionados (circa 2008), MCRT classification offers the intriguing
suggestion that Bayesian reasoning cannot possibly be a fully general
method of rationality. Observe the classification scheme shown.
Bayesian reasoning is a field of knowledge classified as Mathematics-
Cognition-Relative (MAT, COG, REL). This field indeed subsumes the
types of rationality classified as Mathematics-Cognition-Independent
(MAT, COG, REL), such as Predicate and Propositional Logic (see above
examples of fields of knowledge and hierarchical ordering of KR axes),
establishing that Bayes is more powerful than these earlier methods.
However, Bayes only deals with *Relative* reasoning and should itself
be superceded by the fields of knowledge classified as Mathematics-
Cognition-Mediating (MAT, COG, MED). These fields of knowledge deal
with reflective reasoning, and include ontology merging and analogy
generation. Thus, based on MCRT, we anticipate that ontology merging
and analogy generation are more powerful methods of rationality than
Bayes.
Conclusion: MCRT - The 'Universal Parser'
Recall that the basic theory motivating MCRT is two-fold:
(i) Ontology (data models) are the 'language of logic'.
(ii) A method of general purpose reality modeling is equivalent to a
'universal parser'
Given only these two assumptions, it follows that a fully general
method of reality modeling can be entirely achieved with the design of
an 'Upper Ontology' (a general data modeling scheme for all
knowledge). An upper ontology is capable of modeling any concept
within reality, since anything can be logically represented
(communicated) with a logical classification (ontology). Ontology
(data modeling) is a method of *communication* enabling the
translation of any coherent logical representation of a concept in
some particular knowledge domain, into a representation in another
particular logical domain.
In this paper I presented a preliminary description of the ontological
categories required to actually implement a general purpose system of
reality modeling. I attempted to classify IT related fields using the
MCRT ontology. I found that MCRT is a scheme which is consistent,
clear and original. It appears to be in principle capable of
classifying all knowledge. Based on the patterns of classification, I
found the surprising implication that Bayesian Reasoning may not be
the complete form of rationality that logic experts believe it is.
Instead, it appears that ontology merging and analogy formation may be
beyond the scope of Bayes, and my prediction that this will prove to
be so constitutes a logically testable hypothesis of MCRT. I provided
brief preliminary descriptions of 27 fundamental ontological
primatives, with examples.
The curious point warranting deep meditation is that a
representational ('Mediating') knowledge domain appears to reside at
the highest level of abstraction - this is the 'Category' (see MCRT
classification scheme - The domain Mathematics-Platonic-Mediating
(Category) is at the top of the abstraction hierarchy. If the Tegmark
hypothesis that reality is at root mathematical, is entertained, some
surprising implications follow. Mathematics is a representation, and
mathematical categories are 'representations of representations'. A
double abstraction 'twice removed' from the substance. But where is
the substance? Like the old concept if the aether, it is not clear
that any substance is needed. It appears that the whole of reality is
at root nothing more than a *representation of a representation*.
There is no substance *apart* from the representation. It is *all*,
at root, a logical communication.
Consider that MCRT is itself knowledge, which can be classified and
represented by a general purpose DP-Modeling scheme. MCRT (at least
its representation) is itself classified under 'Mathematics-Artifact-
Mediating' (see MCRT classification scheme). This enables MCRT to
model itself and understand its own operation. This verifies that
MCRT is indeed a viable ontology for general purpose reality
modeling.
--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups "Everything List" group.
To post to this group, send email to everything-list.domain.name.hidden
To unsubscribe from this group, send email to everything-list-unsubscribe.domain.name.hidden
For more options, visit this group at
http://groups.google.com/group/everything-list?hl=en
-~----------~----~----~----~------~----~------~--~---
Received on Sat Mar 22 2008 - 02:49:26 PDT