His interest in the formal study of religion waned when he was sixteen and he substituted for it an interest in Asian affairs.

His works contain the earliest known formal study of logic, which was incorporated in the late 19th century into modern formal logic.

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.

amator, " lover ") is generally considered a person attached to a particular pursuit, study, or science, without pay and often without formal training.

The formal study of architecture in academic institutions played a pivotal role in the development of the profession as a whole, serving as a focal point for advances in architectural technology and theory.

Significant amounts of energy and time were devoted to support and foster formal study of the balalaika, from which highly skilled ensemble groups such as the Osipov State Balalaika Orchestra emerged.

It was increasingly recognized as a formal division of theological study during the 20th century.

The study of mathematical proof is particularly important in logic, and has applications to automated theorem proving and formal verification of software.

Hence for both logic and mathematics, the different formal categories are the objects of study, not the sensible objects themselves.

After this formal education, Elizabeth spent the next nine years tending to domestic duties, but with her lively mind, energy and vigour, the prospect of a solely domestic existence would not satisfy her, so she continued to study Latin and arithmetic in the mornings and also read widely.

Formalist film theory is a theory of film study that is focused on the formal, or technical, elements of a film: i. e., the lighting, scoring, sound and set design, use of color, shot composition, and editing.

The mathematical roots of the idea of fractals have been traced through a formal path of published works, starting in the 17th century with notions of recursion, then moving through increasingly rigorous mathematical treatment of the concept to the study of continuous but not differentiable functions in the 19th century, and on to the coining of the word fractal in the 20th century with a subsequent burgeoning of interest in fractals and computer-based modelling in the 21st century.

Despite the formal disapproval of religious authority, the segregation of women in Muslim societies and the strong emphasis on male virility leads adolescent males and unmarried young men to seek sexual outlets with boys younger than themselves — in one study in Morocco, with boys in the age-range 7 to 13.

The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics.

The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems.

The mathematical field of category theory uses many formal axiomatic methods, and includes the study of categorical logic, but category theory is not ordinarily considered a subfield of mathematical logic.

Objects of study in model theory are models for formal languages which are structures that give meaning to the sentences of these formal languages.

Natural language is distinguished from constructed languages and formal languages such as computer-programming languages or the " languages " used in the study of formal logic, especially mathematical logic.

The formal design and study of type systems is known as type theory.

A formal academic study of the Patterson film was conducted by Dmitri Donskoy, Chief of the Dept.

* Cone ( formal languages ), an abstract family of languages that contains the languages with a regular grammar

A formal grammar of this type consists of:

A formal grammar defines ( or generates ) a formal language, which is a ( usually infinite ) set of finite-length sequences of symbols ( i. e. strings ) that may be constructed by applying production rules to another sequence of symbols which initially contains just the start symbol.

Such a grammar defines the formal language: all words consisting solely of terminal symbols which can be reached by a derivation from the start symbol.

His formal education was limited: he suffered from psychological disorders including a fear of crowds, and although admitted to high school after attending eight years of grammar school ( Long Valley School, whence dates the earliest known photo of him ), he never went to high school.

A context-sensitive grammar ( CSG ) is a formal grammar in which the left-hand sides and right-hand sides of any production rules may be surrounded by a context of terminal and nonterminal symbols.

A formal language that can be described by a context-sensitive grammar is called a context-sensitive language.

A formal grammar G

In theoretical computer science, a context-sensitive language is a formal language that can be defined by a context-sensitive grammar.

In formal language theory, a context-free grammar ( CFG )

is a formal grammar in which every production rule is of the form

A formal grammar is considered " context free " when its production rules can be applied regardless of the context of a nonterminal.

The formalism of context-free grammars was developed in the mid-1950s by Noam Chomsky, and also their classification as a special type of formal grammar ( which he called phrase-structure grammars ).

In formal language theory, a context-free language is a language generated by some context-free grammar.

He received the formal Christian education standard for his day: he studied grammar from age twelve to fourteen ( 390-392 ), rhetoric and humanities from fifteen to twenty ( 393-397 ) and finally theology and biblical studies ( 398-402 ).

In formal language theory, a context-free grammar is said to be in Chomsky normal form if all of its production rules are of the form:

A formal grammar is in Chomsky reduced form if all of its production rules are of the form:

A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar, also called its formation rule.

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.

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: