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MWN Compendium: Defining an "Idea" using Mathematics (Partitions and Chains) and the Five Predicables of Classical Logic


This "Compendium" is a new type of dictionary that defines Ideas in terms of Set Relationships. The Set Relationships correspond to the five Predicables of Classical Logic.

A. Select an Idea to define.

You can select any of the following Ideas, which are sorted by Context. To get started, try "pizza", "wine", or "dog" for more complete datasets.

Contracts
; ;

Loans
;

Equipment Leases
;

Receivables Purchase Agreements
;

NDAs
;

Insurance
;

Uniform Commercial Code
;
Grammar
; ;

Living Thing
; ;

Cooking
; ; ; ; ;

Pizza
; ; ; ; ; ; ; ; ; ;

Wine
; ; ; ; ; ; ; ; ; ; ;

Music
; ;

Exercise
;

Karate
;

Kung Fu
; ; ;

History

Other


Alternatively, search to see if an Idea is in the database.

Type in an Idea:

B. Definitions

Definition of the Idea: Dog (context: Animal)

Definition = Cover plus Differences
[Predicable: Difference]

A "dog" is a Mammal (i.e., a Cover Set) that has the following set of distinctive Properties or Differences from other members of the class of Mammal : Barks; Lives on land; Four legs; Domesticated; Omnivore;

A "Difference" is one of the five Predicables of Classical Logic.

Properties
(Subsets of Attributes)
[Predicable: Property]



Examples
(Subsets of Objects)
[Predicable: Species]


Covers
(Supersets of Objects)
[Predicable: Genus]





Properties (Subset of Attributes) [Predicable: Property]

"Dog" has the following Properties: Barks; Lives on land; Four legs; Domesticated; Omnivorous;

Examples (Subset of Objects) [Predicable: Species]

The following are Examples of "Dog": Black Lab; German shepherd; Pitbull; Poodle; Mongrel; Lucy; Leo;

Cover Sets (Superset of Objects) [Predicable: Genus]

The following are Cover Sets of "Dog"; i.e., Dog is a Species of: Substance; Tangible Substance; Living thing; Vertebrate; Mammal;

Accidents or Accidental Properties (Superset of Attributes) [Predicable: Accident]

The following are Accidental Properties of "Dog", i.e., every Dog has some value for each of the classes of Attributes listed below. The specific value of the Accidental Property, however, varies from one example of Dog to another.
Class of Attribute Number of Equivalence Classes Equivalence Class Order Values
Color 3 1 Brown
Color 0 2 Black
Color 0 3 White
Size 3 1 Small
Size 0 2 Medium
Size 0 3 Large
Breed 6 1 Lab
Breed 0 2 German Shepard
Breed 0 3 Pitbull
Breed 0 4 Dalmatian
Breed 0 5 Poodle
Breed 0 6 Blend

Notes:
1. Set theory: This Compendium is constructed in accordance with the rules of Set Theory. As a result, we can incorporate the definitions directly into any software application that uses Set Theory as a basis for Natural Language Generation.

2. Sources: The sources of the data for the Idea "Dog" include: Common knowledge;