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A

Index


Absurdity

In conceptual graph theory, Absurdity is the bottom-most type in the type hierarchy; it is the one type which is a subtype of everything else. As such, it contrasts with Entity.

Since Absurdity is a subtype of everything else in the type hierarchy, it inherits all of the properties from all other types. Therefore, it has conflicting properties, and hence nothing can exist which has the type Absurdity. Hence its name.


Actual parameter

Context

A term in programming language theory, as well as CG theory.

Conceptual graphs

Definition

A parameter to a lambda expression can either be an actual parameter or a formal parameter.

An actual parameter to a lambda expression is the specific concept that replaces the formal parameter when the lambda expression is used.

CG example

For example, in the following usage of a lambda expression:

  [Man: Socrates]<-([Man: ]->(Attr)->[Mortal])

"[Man: Socrates]" is the actual parameter which is substituted into the formal parameter "[Man: ]".

We see, then, that the notion "actual parameter" is complementary to the notion formal parameter.

Prolog+CG

Definition

In Prolog+CG, a predicate may have zero or more actual parameters. The actual parameters are the terms in parentheses after the functor when using (i.e., calling) the predicate.

Prolog+CG example

See formal parameter for an example.


Arc

Part of the terminology of graph theory. Arcs are the arrows (or lines) that connect nodes.


Argument

Context

A term in programming and in linguistics.

Definition: Programming

In Prolog, a rule or a fact may have zero or more arguments. The arguments are the terms enclosed in parentheses following the functor which is the name of the fact or rule.

For example:

patriarch(X) :- eq(X, Abraham).

Here, the variable X is the argument to the patriarch rule, and the arguments of the eq goal are X and Abraham.

Thus an argument can be both in the definition of a fact or rule (as in the definition of the patriarch rule) or in the usage of a fact or rule (as in the usage of the eq goal).

Sometimes, arguments are called parameters.

Definition: Linguistics

In linguistics, the arguments of a verb are those phrases which must necessarily be present in a clause for it to be semantically complete.

For example, the verb give requires three arguments:

  • A giver,
  • a taker, and
  • an object given

Thus in the sentence "John gave the book to Mary", there are three arguments of the verb:

  • John (the giver)
  • Mary (the taker)
  • the book (the object given)

Non-arguments

On the other hand, some phrases which might occur in such a sentence are not arguments of the verb, since they are not required to make a semantically complete clause. For example, in the sentence,

John gave the book to mary in the library.

The phrase in the library is not required for making a semantically complete clause. It is optional information. Thus, this phrase is a non-argument.


Arity

Context

A term in Prolog.

Definition

The arity of a structure is the number of arguments it takes.

For example, the arity of the following structure:

student(X,S)

is 2, since there are two arguments.

The arity of a structure can be 0, meaning it has no arguments. For example,

Abraham

is a structure with arity 0. A structure with arity 0 is also called an atomic constant (or simply "atom").


Aspect

Context

A term in linguistics.

Definition

Aspect is an inflectional or syntactic category of verbs which marks the internal temporal structure of the action. In other words, is the action completed or not? Does it happen all at once, or is it extended in time? Is it recurring (iterative) or ongoing?

The main categories which we find in languages are:

  • Perfective: Which means 'completed'
  • Imperfective: Which means 'non-completed'
  • Progressive: Which is 'on-going'
  • Perfect: Which is 'completed' like Perfective, but adds the notion of 'current relevance'

In English, the two major categories are 'Progressive' and 'Perfect'. Other Indo-European languages, however, have other categories.

Tense and aspect

Aspect is related to tense, but is distinct from this category (although the boundary is somewhat fluid). While aspect marks the internal temporal structure of the action, tense marks the temporal relationship between the time of the action and some reference time, usually the speaking-time. More information can be found in the glossary entry for tense.

Examples

As was just said, English has two major categories of aspect, perfect and progressive.

These two major categories of aspect can interact with all three tenses (and the categories of 'active', 'passive', 'indicative', and 'subjunctive') to form quite a few ways of expressing verbal ideas.

For example, "I am finishing my lunch" is in the present progressive tense and aspect, meaning the process of finishing my lunch is an on-going event that includes the present.

By contrast, "I have finished my lunch" is in the present perfect. It means that while the tense is present, the aspect is perfect, meaning that the action has been completed, but with current relevance.

Other examples include:

  • "I was finishing my lunch": Past progressive
  • "I had finished my lunch": Past perfect
  • "I will be finishing my lunch": Future progressive
  • "I will have finished my lunch": Future perfect
  • "I have been finishing my lunch": Present perfect progressive
  • "I had been finishing my lunch": Past perfect progressive
  • "I will have been finishing my lunch": Future perfect progressive

Atom (Atomic constant)

Context

A term in Prolog.

Definition

An atomic constant is a structure with arity 0.

For example, the following is an atomic constant:

Abraham

Atomic constants are also simply called atoms.


Axiom

An axiom is a proposition or statement which we decide to "take for granted", without proof. Axioms often form the foundation of our thinking; from the axioms, everything else should follow.

This is especially true of systems of logic and mathematics. For example, the theory of partial orders has three axioms. Everything else which we wish to know about partial orders follows from the three axioms.


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