In logic, mathematics, computer science, and linguistics, a formal language is a set of strings whose symbols are taken from a set called "alphabet".
The alphabet of a formal language consists of symbols that concatenate into strings (also called "words"). Words that belong to a particular formal language are sometimes called well-formed words. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar.
A pictogram (also pictogramme, pictograph, or simply picto) is a graphical symbol that conveys meaning through its visual resemblance to a physical object. Pictograms are used in systems of writing and visual communication. A pictography is a writing system which uses pictograms. Some pictograms, such as hazard pictograms, may be elements of formal languages.
In the field of prehistoric art, the term "pictograph" has a different definition, and specifically refers to art painted on rock surfaces. Pictographs are contrasted with petroglyphs, which are carved or incised.
In formal languages, terminal and nonterminal symbols are parts of the vocabulary under a formal grammar. Vocabulary is a finite, nonempty set of symbols. Terminal symbols are symbols that cannot be replaced by other symbols of the vocabulary. Nonterminal symbols are symbols that can be replaced by other symbols of the vocabulary by the production rules under the same formal grammar.
A formal grammar defines a formal language over the vocabulary of the grammar.
In formal systems particularly mathematical logic, a function symbol is a non-logical symbol which represents a function or mapping on the domain of discourse, though, formally, does not need to represent anything at all. Function symbols are a basic component in formal languages to form terms. Specifically, if the symbol is a function symbol, then given any constant symbol representing an object in the language, also represents an object in the language. Similarly, if is some term in the language, is also a term. As such, the interpretation of a function symbol must be defined over the whole domain of discourse. Function symbols are a primitive notion, and are therefore not defined in terms of other, more basic concepts.
In typed logic, F is a functional symbol with domain type T and codomain type U if, given any symbol X representing an object of type T, F(X) is a symbol representing an object of type U.One can similarly define function symbols of more than one variable, analogous to functions of more than one variable; a function symbol in zero variables is simply a constant symbol.
