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Formal system, an abstract means of generating inferences in a formal language; Formal language, comprising the symbolic "words" or "sentences" of a formal system; Formal grammar, a grammar describing a formal language; Colloquialism, the linguistic style used for informal communication
A formal system (also called a logical calculus, or a logical system) consists of a formal language together with a deductive apparatus (also called a deductive system). The deductive apparatus may consist of a set of transformation rules , which may be interpreted as valid rules of inference, or a set of axioms , or have both.
Formal language, which is a set of well-formed formulas, which are strings of symbols from an alphabet, formed by a formal grammar (consisting of production rules or formation rules). Deductive system , deductive apparatus, or proof system , which has rules of inference that take axioms and infers theorems , both of which are part of the formal ...
Formal verification is the use of software tools to prove properties of a formal specification, or to prove that a formal model of a system implementation satisfies its specification. Once a formal specification has been developed, the specification may be used as the basis for proving properties of the specification, and by inference ...
A formal grammar describes which strings from an alphabet of a formal language are valid according to the language's syntax. A grammar does not describe the meaning of the strings or what can be done with them in whatever context—only their form. A formal grammar is defined as a set of production rules for such strings in a formal language.
Formal definitions, first devised in the early 19th century, are given below. Informally, a function f assigns an output f ( x ) to every input x . We say that the function has a limit L at an input p , if f ( x ) gets closer and closer to L as x moves closer and closer to p .
Formal semantics is a subfield of logic, linguistics, and the philosophy of language. The discipline of semantics studies the meaning of language. Formal semantics uses formal tools from the fields of symbolic logic and mathematics to give precise theories of the meaning of natural language expressions.
A formality is an established procedure or set of specific behaviors and utterances, conceptually similar to a ritual although typically secular and less involved. A formality may be as simple as a handshake upon making new acquaintances in Western culture to the carefully defined procedure of bows, handshakes, formal greetings, and business card exchanges that may mark two businessmen being ...