1. A language with explicit and precise rules for its syntax and semantics. Examples include programming languages and also logics such as predicate calculus. Thus formal languages contrast with natural languages such as English whose rules, evolving as they do with use, fall short of being either a complete or a precise definition of the syntax, much less the semantics, of the language.

2. A finite or infinite set of strings, considered in isolation from any possible meaning the strings or the symbols in them may have. If A is any set, an A-language (or language over A) is any set of A-words (see word). A is referred to as the alphabet of such a language.