Closed Loop Interval Ontology
       The Digital Integration of Conceptual Form


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Project under development
Evolving and coalescing

Guiding motivation
Why we do this

Objectives and strategy
Reconciliation and integration

Reconciliation of perspectives
Holistic view on alternatives

What is truth?
How do we know?

What is a concept?
Definitions and alternatives

How meaning is created

Universal Hierarchy
Spectrum of levels

A Universal Foundation
The closed loop ensemble contains
all primary definitions

Dimensions of set theory

Venn diagrams
Topology of sets

Objects in Boolean Algebra
How are they constructed?

Core vocabulary
Primary terms

Core terms on the strip
Closed Loop framework

Hierarchical models

Digital geometry
Euclid in digital space

The digital integration
of conceptual form

Compositional semantics

Closed loop interval ontology
How it works

Cognitive science
The integrated science of mind

What does it mean?

Formal systematic definitions
Core terms

Data structures
Constructive elements
and building blocks

Preserving data under transformation

Steady-state cosmology
In the beginning

Semantic ontology
Domain and universal

From other sources

Venn diagrams
Topology of sets

We are generalizing the notion of container and interval in terms of boundaries.

If possible, we want to ground all analytic structure in the topology of the Closed Loop, mapping from serial/linear sequential forms into the holistic all-at-once everything-at-the-same-time framework of the loop.

So a question arises.

How can we define the contents of a Venn diagram with its continuous circle-based boundary, so as to distinguish "what is IN the set" (inside the circle) and "what is NOT IN the set" (outside the circle)?

The answer is -- this structure is hierarchical.

Is the hierarchical model isomorphic to the Venn diagram? We are studying the meaning of isomorphic - along with other related concepts that might be grounded together as a "family" -- such as identity, equality, similarity.

Set, venn diagram, dimensionality, boundary
What is a container?
Venn diagrams and dimensionality

Set, venn diagram, dimensionality, boundary

Set, venn diagram, dimensionality, boundary

Define the concept of set in terms of boundary and its objects in terms of dimensionality

(abstract object, concrete object)

At a minimum, a set has a boundary -- things IN the set, and things NOT IN the set

Can that be specified by dimensionality?

Yes, as long as the objects are defined in terms of dimensionality

Abstract objects are defined in terms of dimensionality, and then a mapping/correlation is established by the abstract object (the word, the symbol) and the concrete object ("the actual thing" it is pointing to))

Venn diagrams

What is a container?

We want to generalize the notion of container based on boundaries, and following the ideal and intuitive definitions of Venn diagrams.

Are Venn diagrams hierarchical in every case?

  • Containers
  • HTML tables -- rows [tr] "table row" and columns [td] intersect to form cells, which contain something -- td -- "table data"?
  • Boundaries
  • Circles
  • Boxes
  • Matrix (matrices)
  • Row / column intersection = cell

In computer science, a container is a class, a data structure, or an abstract data type (ADT) whose instances are collections of other objects.

In other words, they store objects in an organized way that follows specific access rules. The size of the container depends on the number of objects (elements) it contains. Underlying (inherited) implementations of various container types may vary in size and complexity, and provide flexibility in choosing the right implementation for any given scenario.

Function and properties

Containers can be characterized by the following three properties:

  • access, that is the way of accessing the objects of the container. In the case of arrays, access is done with the array index. In the case of stacks, access is done according to the LIFO (last in, first out) order and in the case of queues it is done according to the FIFO (first in, first out) order;
  • storage, that is the way of storing the objects of the container;
  • traversal, that is the way of traversing the objects of the container.

Container classes are expected to implement methods to do the following:

  • create an empty container (constructor);
  • insert objects into the container;
  • delete objects from the container;
  • delete all the objects in the container (clear);
  • access the objects in the container;
  • access the number of objects in the container (count).

  • Container (abstract data type), a class or data structure that is a collection of other objects
  • Container (type theory), abstractions that represent collection types in a uniform way
  • Container (virtualization), a server virtualization method
  • Container file format for storing related data together, such as audio and video data


Venn diagrams and dimensionality

We want to connect the construction of meaning and "making a point" to interpretation and representation by Venn diagrams -- such that "the point" that that we are arguing is defined as (contained within) an "n-dimensional envelope" can be fully represented by the overlap of Venn diagrams. Is that really feasible?

I'll have to explore that one facet at a time, but it looks promising.