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T

Index


Tense

Context

A term in linguistics

Definition

Tense is an inflectional category of verbs which marks the time of the action with respect to some reference point in time, usually the speaking-time. The meaning of "tense" is also extended to any syntactic or morphemic device which marks this category.

Examples

For example, "I love" is present (at the time of speaking), "I loved" is past (before the time of speaking), while in English, the auxiliary "will" is often used to indicate future ("I will love").

Tense and aspect

Tense is different from aspect. While tense marks the relation between the time of the action and some reference time, aspect marks the internal temporal structure of the action. See the definition of aspect for more information.


Term

Context

A term in Prolog.

Definition

The term "term" is a generic name given to any kind of Prolog+CG data.

The most useful terms are structures.


Transitivity

Definition

The notion of transitivity is a very general notion that applies to many relationships. A relationship can be transitive, which simply means that two entities from a set are related if they are both related to a common, mediating entity from the same set.

Examples

Taking an example from the natural numbers, since "2 ≤ 5" and "5 ≤ 6", it follows that "2 ≤ 6". This is because "≤" on the natural numbers is a partial order, and partial orders are transitive.

Another example, this time from the world of types: Since "Elephant ≤ Mammal" and "Mammal ≤ Animal", it follows that "Elephant ≤ Animal", where "≤" means "is a subtype of". This is because the subtype-relation is also a partial order, and partial orders are transitive.

Transitivity is a general concept

Transitivity is not just a property of partial orders. The equality relation "=" is also transitive. For natural numbers, the "less than" ("<") relation is transitive. For types, the "proper subtype" relation ("<") is transitive.

For example, since "Elephant < Mammal" and "Mammal < Animal", it follows that "Elephant < Animal".

Note how this is different from the "≤" subtype-relation. The proper subtype-relation "<" allows us to infer more than the "≤" subtype-relation, namely that the types involved are proper subtypes, i.e., that they are not identical.

In this particular example, there difference, since "Elephant", "Mammal", and "Animal" are all distinct types. But if we knew only that "Elephant ≤ Mammal" and that "Mammal ≤ Animal", and nothing else, then we could not be sure that these types were not identical. Specifying the relationships with the "<" proper subtype-relation removes this doubt.

Axiom

Transitivy can be defined as an axiom. This axiom must refer to a set S of entities, a relation R on S, and three members A,B,C of S:

For all members A,B,C of S:

If

   A R B   (i.e., A is related to B)

and

   B R C   (i.e., B is related to C)

then

   A R C

.


Type

Definition

A type consists of two things:

  1. A name, and
  2. A definition of a group of entities with similar traits.

Example

For example, "Bus" is a name which we give to the group of individuals which is defined as "A vehicle on wheels for transporting several persons at once". Here "Bus" is the name, and the definition is the sentence that was just given.

Related terminology

Types are the subject of study of ontology. When types are organized in a type-hierarchy, they are related as subtypes and supertypes. Types inherit from zero or more supertypes. Type-hierarchies can be thought of (and depicted) as lattices. Type-hierarchies and lattices support multiple inheritance. The subtype-relation and supertype-relation are partial orders. Partial orders are transitive, as are the "proper subtype-relation" and "proper supertype-relation". Two special types are Entity and Absurdity. Types can be defined in a number of ways. One of them is "By reference to supertypes with differentiae". While types are abstract groups of entities, the entities themselves are instances of the types.


Type hierarchy

Context

A term in ontology, CG theory, and Prolog+CG.

Definition: Ontology

A type-hierarchy is also called an ontology, and is the product of the study of a domain of existence, with an enumeration and categorization of all of the entities that exist in that domain of existence.

Type-hierarchies are usually specified in terms of a lattice.

Definition: CG theory

A type-hierarchy in CG theory is a concept of type TypeHierarchy whose referent is a conceptual graph which specifies a number of type labels, a partial order over the type labels, and the monadic lambda expressions which define the type labels.

Definition: Prolog+CG

A type-hierarchy in Prolog+CG consists of a series of type-rules. A type-rule has the following syntax:

Supertype > Subtype, Subtype, ...,
            Subtype.

Examples

For example, the following is a type-hierarchy in Prolog+CG.

Entity > Physical, Abstract.
Physical > Object, Process, Property.
Object > Animate, Inanimate.
Animate > HumanBeing, Animal, Plant.
Property > Juvenile, Adult, Gender.
Gender > Male, Female.
HumanBeing > Man, Woman, Boy, Girl.
Adult > Man, Woman.
Juvenile > Boy, Girl.
Male > Man, Boy.
Female > Woman, Girl.


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