Definition:

A formal language L over an alphabet Σ is just a subset of Σ*, that is, a set of words over that alphabet.

Discussion

Formal languages are entirely syntactic in nature but may be given semantics that give meaning to the elements of the language. Formal languages are useful in logic because they have formulas that can be interpreted as expressing logical truths. An interpretation of a formal language is the assignment of meanings to its symbols and formulas.

Model theory is the theory of interpretations of formal languages. The study of interpretations is called formal semantics. Giving an interpretation is synonymous with constructing a model. A model of a formula of a formal language is an interpretation of the language for which the formula comes out to be true.

Some links:

  1. Formal semantics
  2. Interpretation (logic)
  3. Model theory
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