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How Data are Classified: Categorical Data01:11

How Data are Classified: Categorical Data

A variable, usually notated by capital letters such as X and Y, is a characteristic or measurement that can be determined for each member of a population. Data are the actual values of variables. They may be numbers, or they may be words. Datum is a single value.
Data are classified based on whether they are measurable or not. Categorical data cannot be measured; instead, it can be divided into categories. For example, if Y denotes a person's party affiliation, some examples of Y include...
Taxonomy01:31

Taxonomy

Taxonomy is the science of defining and naming groups of biological organisms based on shared characteristics. It uses a hierarchy of increasingly inclusive categories with Latin names. The smallest units of taxonomy, species and genus, are used to assign a formal, taxonomic name to each species in a system. This classification system, referred to as binomial nomenclature, was formalized by Carolus Linnaeus in the 18th century.
Hierarchy of Taxonomy
The hierarchy that Carolus Linnaeus first...
Classification of Systems-I01:26

Classification of Systems-I

Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
Schemata01:17

Schemata

A schema is a mental construct that organizes related concepts, allowing the brain to process information efficiently. Upon activation, schemata facilitate assumptions about people or objects.
Two types of schemata are:
How Data are Classified: Numerical Data00:59

How Data are Classified: Numerical Data

Data that are countable or measurable in specific units are called numerical or quantitative data. Quantitative data are always numbers. Quantitative data are the result of counting or measuring the attributes of a population. Amount of money, pulse rate, weight, number of people living in a town, and number of students who opt for statistics are examples of quantitative data.
Quantitative data may be either discrete or continuous. All quantitative data that take on only specific numerical...
Natural and Artificial Concepts01:24

Natural and Artificial Concepts

In psychology, concepts can be divided into two categories: natural and artificial. Natural concepts are formed through direct or indirect experiences. For example, consider the concept of snow. If you live in a place with regular snowfall, such as Essex Junction, Vermont, you know snow through direct experiences. You’ve seen it fall, touched it, shoveled it, and played in it. You recognize its texture, appearance, and even its smell. In contrast, if you live on an island like Saint Vincent in...

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Related Experiment Video

Updated: May 25, 2026

Creating Objects and Object Categories for Studying Perception and Perceptual Learning
14:38

Creating Objects and Object Categories for Studying Perception and Perceptual Learning

Published on: November 2, 2012

Ologs: a categorical framework for knowledge representation.

David I Spivak1, Robert E Kent

  • 1Mathematics Department, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America. dspivak@math.mit.edu

Plos One
|February 4, 2012
PubMed
Summary
This summary is machine-generated.

We introduce the ontology log (olog), a mathematically grounded knowledge representation model. Ologs offer a user-friendly, rigorously formulated alternative to traditional systems, enabling network integration for diverse world-views.

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Evidence-based Knowledge Synthesis and Hypothesis Validation: Navigating Biomedical Knowledge Bases via Explainable AI and Agentic Systems
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Evidence-based Knowledge Synthesis and Hypothesis Validation: Navigating Biomedical Knowledge Bases via Explainable AI and Agentic Systems

Published on: June 13, 2025

Related Experiment Videos

Last Updated: May 25, 2026

Creating Objects and Object Categories for Studying Perception and Perceptual Learning
14:38

Creating Objects and Object Categories for Studying Perception and Perceptual Learning

Published on: November 2, 2012

Evidence-based Knowledge Synthesis and Hypothesis Validation: Navigating Biomedical Knowledge Bases via Explainable AI and Agentic Systems
05:47

Evidence-based Knowledge Synthesis and Hypothesis Validation: Navigating Biomedical Knowledge Bases via Explainable AI and Agentic Systems

Published on: June 13, 2025

Area of Science:

  • Formal mathematics
  • Computer Science
  • Knowledge Representation

Background:

  • Traditional knowledge representation (KR) models like semantic networks lack rigorous formulation and cross-comparison capabilities.
  • Relational database schemas are difficult to create and modify, hindering user accessibility.
  • Existing KR systems present challenges in integrating local and global perspectives.

Purpose of the Study:

  • Introduce the ontology log (olog), a novel category-theoretic model for KR.
  • Demonstrate the mathematical rigor, user-friendliness, and data repository capabilities of ologs.
  • Explore ologs' potential for network integration and information flow.

Main Methods:

  • Developed a category-theoretic framework for ologs, emphasizing formal mathematical grounding.
  • Illustrated olog construction and application with numerous examples.
  • Utilized functors for aligning and connecting ologs into larger networks.

Main Results:

  • Ologs provide a rigorously formulated and cross-comparable KR model, surpassing limitations of semantic networks.
  • Ologs function as user-friendly data repositories, easier to author and reconfigure than database schemas.
  • Demonstrated that primitive recursive functions can be described by ologs.
  • Showcased olog network integration using functors for information flow and world-view unification.

Conclusions:

  • Ologs represent a significant advancement in knowledge representation, offering a blend of formal rigor and user-friendliness.
  • The category-theoretic foundation of ologs enables robust integration and information sharing across diverse knowledge domains.
  • Ologs present a promising avenue for future research in artificial intelligence and data management.