Abstract Comparison Table

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Abstract comparison table

Subject be third domain of documentation be disjoint from be second domain of be first domain of have axiom

Attribute Qualities which we cannot or choose not to reify into subclasses of Object Quantity successorAttributeClosure successorAttributeClosure
(<=>
(instance ?ABS Abstract)
(not
(exists (?POINT)
(or
(located ?ABS ?POINT)
(existant ?ABS ?POINT)))))

Class domainSubclass Class generalizes Set. Classes, like Sets, are collections of things. Accordingly, the notion of membership is generalized as well - a member of a Class is an instance the Class. Classes can differ from Sets in two important respects. First, Classes that are not explicitly identified as Sets are not assumed to be extensional. That is, distinct Classes might well have exactly the same instances. Second, Classes typically have an associated `condition' that determines the instances of the Class. So, for example, the condition `human' determines the Class of Humans. Note that some Classes might satisfy their own condition (e.g., the Class of Abstract things is Abstract) and hence be instances of themselves Physical UnionFn UnionFn
(forall (?INT) (domain exhaustiveDecomposition ?INT Class))

Proposition Propositions are Abstract entities that express a complete thought or a set of such thoughts. As an example, the formula '(instance Yojo Cat)' expresses the Proposition that the entity named Yojo is an element of the Class of Cats. Note that propositions are not restricted to the content expressed by individual sentences of a Language. They may encompass the content expressed by theories, books, and even whole libraries. It is important to distinguish Propositions from the ContentBearingObjects that express them. A Proposition is a piece of information, e.g. that the cat is on the mat, but a ContentBearingObject is an Object that represents this information. A Proposition is an abstraction that may have multiple representations: strings, sounds, icons, etc. For example, the Proposition that the cat is on the mat is represented here as a string of graphical characters displayed on a monitor and/or printed on paper, but it can be represented by a sequence of sounds or by some non-latin alphabet or by some cryptographic form Physical realization relatedInternalConcept
(=>
(instance ?SENTENCE Sentence)
(exists (?PROP)
(and
(instance ?PROP Proposition)
(containsInformation ?SENTENCE ?PROP))))

Quantity Any specification of how many or how much of something there is. Accordingly, there are two subclasses of Quantity: Number (how many) and PhysicalQuantity (how much) Physical SubtractionFn SubtractionFn
(<=>
(instance ?ABS Abstract)
(not
(exists (?POINT)
(or
(located ?ABS ?POINT)
(existant ?ABS ?POINT)))))

Subject	be third domain of	documentation	be disjoint from	be second domain of	be first domain of	have axiom
Attribute		Qualities which we cannot or choose not to reify into subclasses of Object	Quantity	successorAttributeClosure	successorAttributeClosure	(<=> (instance ?ABS Abstract) (not (exists (?POINT) (or (located ?ABS ?POINT) (existant ?ABS ?POINT)))))
Class	domainSubclass	Class generalizes Set. Classes, like Sets, are collections of things. Accordingly, the notion of membership is generalized as well - a member of a Class is an instance the Class. Classes can differ from Sets in two important respects. First, Classes that are not explicitly identified as Sets are not assumed to be extensional. That is, distinct Classes might well have exactly the same instances. Second, Classes typically have an associated `condition' that determines the instances of the Class. So, for example, the condition `human' determines the Class of Humans. Note that some Classes might satisfy their own condition (e.g., the Class of Abstract things is Abstract) and hence be instances of themselves	Physical	UnionFn	UnionFn	(forall (?INT) (domain exhaustiveDecomposition ?INT Class))
Proposition		Propositions are Abstract entities that express a complete thought or a set of such thoughts. As an example, the formula '(instance Yojo Cat)' expresses the Proposition that the entity named Yojo is an element of the Class of Cats. Note that propositions are not restricted to the content expressed by individual sentences of a Language. They may encompass the content expressed by theories, books, and even whole libraries. It is important to distinguish Propositions from the ContentBearingObjects that express them. A Proposition is a piece of information, e.g. that the cat is on the mat, but a ContentBearingObject is an Object that represents this information. A Proposition is an abstraction that may have multiple representations: strings, sounds, icons, etc. For example, the Proposition that the cat is on the mat is represented here as a string of graphical characters displayed on a monitor and/or printed on paper, but it can be represented by a sequence of sounds or by some non-latin alphabet or by some cryptographic form	Physical	realization	relatedInternalConcept	(=> (instance ?SENTENCE Sentence) (exists (?PROP) (and (instance ?PROP Proposition) (containsInformation ?SENTENCE ?PROP))))
Quantity		Any specification of how many or how much of something there is. Accordingly, there are two subclasses of Quantity: Number (how many) and PhysicalQuantity (how much)	Physical	SubtractionFn	SubtractionFn	(<=> (instance ?ABS Abstract) (not (exists (?POINT) (or (located ?ABS ?POINT) (existant ?ABS ?POINT)))))

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