This may be a formal hierarchy, or they may be vague, overlapping terms, or a combination of both.

Later still, abstraction was manifest in more purely formal terms, such as color, freedom from objective context, and a reduction of form to basic geometric designs.

Using terms from formal language theory, the precise mathematical definition of this concept is as follows: Let S and T be two finite sets, called the source and target alphabets, respectively.

* Semantics encoding of formal language A in formal language B is a method of representing all terms ( e. g. programs or descriptions ) of language A using language B.

In every day terms, the imam for Sunni Muslims is the one who leads Islamic formal ( Fard ) prayers, even in locations besides the mosque, whenever prayers are done in a group of two or more with one person leading ( imam ) and the others follow by copying his ritual actions of worship.

In general terms, a calculus is a formal system that consists of a set of syntactic expressions ( well-formed formulæ or wffs ), a distinguished subset of these expressions ( axioms ), plus a set of formal rules that define a specific binary relation, intended to be interpreted as logical equivalence, on the space of expressions.

Tegmark writes that " abstract mathematics is so general that any Theory Of Everything ( TOE ) that is definable in purely formal terms ( independent of vague human terminology ) is also a mathematical structure.

The terms Neogene System ( formal ) and upper Tertiary System ( informal ) describe the rocks deposited during the Neogene Period.

Like other theories, the theory of probability is a representation of probabilistic concepts in formal terms — that is, in terms that can be considered separately from their meaning.

These formal terms are manipulated by the rules of mathematics and logic, and any results are interpreted or translated back into the problem domain.

where n is a natural number, the coefficients are elements of R, and X is a formal symbol, whose powers X < sup > i </ sup > are just placeholders for the corresponding coefficients a < sub > i </ sub >, so that the given formal expression is just a way to encode the sequence, where there is an n such that a < sub > i </ sub > = 0 for all i > n. Two polynomials sharing the same value of n are considered equal if and only if the sequences of their coefficients are equal ; furthermore any polynomial is equal to any polynomial with greater value of n obtained from it by adding terms in front whose coefficient is zero.

Thus each polynomial is actually equal to the sum of the terms used in its formal expression, if such a term a < sub > i </ sub > X < sup > i </ sup > is interpreted as a polynomial that has zero coefficients at all powers of X other than X < sup > i </ sup >.

Prolog has its roots in first-order logic, a formal logic, and unlike many other programming languages, Prolog is declarative: the program logic is expressed in terms of relations, represented as facts and rules.

The terms ' Paleogene System ' ( formal ) and ' lower Tertiary System ' ( informal ) are applied to the rocks deposited during the ' Paleogene Period '.

When the terms formal parameter and actual parameter are used, they generally correspond with the definitions used in computer science.

In less formal terms, a polymath ( or polymathic person ) may simply be someone who is very knowledgeable.

The relational model was the first database model to be described in formal mathematical terms.

Numerous slang terms pass into informal mainstream speech, and sometimes into formal speech, though this may involve a change in meaning or usage.

A more formal definition of a finite sequence with terms in a set S is a function from

In formal terms, the worldsheet in these theories is a non-orientable surface.

The collection, structuring and recovery of linked data are enabled by technologies that provide a formal description of concepts, terms, and relationships within a given knowledge domain.

The group conducting the review is not holding formal hearings.

So far as the existing body of formal principle and procedure is concerned, categorical novelties are not to be anticipated in Jewish-Gentile relationships ; ;

It is not implied that formal principles and procedures are so firmly entrenched within the public order of the world community or even of free commonwealths that they will control in all circumstances involving Jews and Gentiles during coming years.

The formal position of Americans who identify themselves with one or more of the several identities of the Jewish symbol is already clear ; ;

The third Act of Faust 2, is a formal celebration of the union between the Germanic and the classic, between the spirit of Euripides and that of romantic drama.

There is no formal equivalence to the supervisory ranks ; ;

A second major point of this essay is to examine the formal arrangements for the elections.

Whereas Bultmann's `` center '' position is structurally inconsistent and is therefore indefensible on formal grounds alone, the general position of the `` right '', as represented, say, by Karl Barth, involves the rejection or at least qualification of the demand for demythologization and so is invalidated on the material grounds we have just considered.

With the Prior Analytics, Aristotle is credited with the earliest study of formal logic, and his conception of it was the dominant form of Western logic until 19th century advances in mathematical logic.

The formal ceremony at which the Awards of Merit are presented is one of the most prominent award ceremonies in the world, and is televised live in more than 100 countries annually.

The difference is not a formal one taxonomically and there are numerous exceptions to this rule.

A trial de novo is usually available for review of informal proceedings conducted by some minor judicial tribunals in proceedings that do not provide all the procedural attributes of a formal judicial trial.

After an appeal is heard, the " mandate " is a formal notice of a decision by a court of appeal ; this notice is transmitted to the trial court and, when filed by the clerk of the trial court, constitutes the final judgment on the case, unless the appeal court has directed further proceedings in the trial court.

Arraignment is a formal reading of a criminal complaint in the presence of the defendant to inform the defendant of the charges against him or her.

Affirming the consequent, sometimes called converse error, is a formal fallacy, committed by reasoning in the form:

This force is used in the formal definition of the ampere, which states that it is " the constant current that will produce an attractive force of 2 × 10 < sup >– 7 </ sup > newton per metre of length between two straight, parallel conductors of infinite length and negligible circular cross section placed one metre apart in a vacuum ".

While there is no generally accepted formal definition of " algorithm ," an informal definition could be " a set of rules that precisely defines a sequence of operations.

That notion is central for explaining how formal systems come into being starting from a small set of axioms and rules.

Written in prose but much closer to the high-level language of a computer program, the following is the more formal coding of the algorithm in pseudocode or pidgin code:

When language is used, prayer may take the form of a hymn, incantation, formal creed, or a spontaneous utterance in the praying person.

He views the word ' hymn ' as suggesting " outpourings of emotion " while he sees them as " eulogies, formal and rhetorical statements of praise " honoring Aten and the royal couple.