Introduction to “The Principles of Ternary Logic”
First principles of a Ternary Logic implementation
Ontology (in the philosophical sense) is a study of the nature of being, existence, or reality, as well as the basic categories of being and their relations. At one end of the spectrum (the very heavy end) of ontological inquiry is the collection of shared mental events which constitute the discourse of understanding in which we contend that entitles are said to “exist”.
This dialog will necessarily leave these existential considerations to the philosophers, and will focus on the more limited subject of the categorization of being and their relations, and how entities can be grouped within a hierarchy.
This discourse on the symbolic expression of being (as opposed to the nature of being) is confined to a strictly narrow viewpoint for exploring the categorical aspects of being, the definitions of ordinal relations, changes in entities and causation relations, and the temporal concepts necessary to describe the models of real-world entities.
Wikipedia defines Ontology (as an information science) as formally representing knowledge as a set of concepts within a domain, using a shared vocabulary to denote the types, properties and inter-relationships of those concepts.
Ontologies are the structural framework for organizing information. The creation of domain ontologies is also fundamental to the definition and use of an enterprise architecture framework.
This starts with the most basic definitions of form, to establish the formalized expression of categorical being. This is essentially a discourse on the intrinsic properties, discriminating attributes, and generalized principles of family, to create a taxonomy as a quantified (or scoped) systematic of categorical being expressing the concepts of Extension and Intension, along with a library of predicates establishing the formalization of relationship.
It then builds on these basic definitions of form, which establishes classification and the abstraction of categorical being, to create concepts and expressions of relation, dependency, possession and ownership.
From this systematic of definition, characterization and classification, the relation and dependency generalizations can lead to concepts of change and the building of abstract expressions for cause and effect, consequence and agency structures, and finally leading to the establishment of the temporal relations and expressions for parametric change.
In order to implement these organizing structures into an active systematic which is itself changing, as in an artificial intelligence system, the very concept of “ontological definition” cannot remain static, even the very definitions of relation and dependency themselves.
In an artificial intelligence systematic, ontological structure must remain dynamic, as even the definition of “definition” is a fluid concept, being relative only to the intelligent agent (as it changes), and not to a common perspective. This requires a symbolic structure which maintains a clear separation between the existence of a thing, and the definition of a thing. As first principles, a “thing”, in the implementation of the Ternary Logic, is a “referent”. And this symbolic structure must be expressive within the realm of adaptive systems.
Adaptive systems must first and foremost be based on a rigorous methodology of abstraction of information, always from the particular toward the general. The representation of this information and its abstractions must always be codified explicitly, as opposed to being represented implicitly in algorithms.
Adaptive system representations cannot function under a true-false or present-absent binary logic, but at its most fundamental level must embrace a true-false-indeterminate or present-absent-ambiguous Ternary Logic.
Adaptive systems must be equally adept at expressions at all levels of Typology (typically defined as levels of scale: nominal, ordinal, interval and ratio). Adaptive systems must also provide for situations where expressions have inter-mixed levels of typology. The systematic should strive toward a consistent and unified model of typological construction.
Adaptive systems should have an element structure that is sufficiently diverse to allow dynamic interaction among elements with no defined rigid interaction. The element structure should allow many nonlinear interactions, and the behaviors of some elements should demonstrate feedback or recurrency.
The systematic must allow for partial constructs at every level, from atomic specifications in expressions up to an incremental development of the whole system.
Additionally, every level of the systematic must work with ambiguity, incompleteness (partial constructs and fragmentary evidence), inconsistency, and “information independent” constraints (constraints imposed by the implementation of the symbolic structure).
GO TO THE PRINCIPLES OF TERNARY LOGIC
GO TO TOP OF PAGE
Copyright © 2019 All rights reserved