'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 [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---