Interpretations and Models
Formal languages are entirely syntactic in nature but may be given semantics that give meaning to the elements of the language. For instance, in mathematical logic, the set of possible formulas of a particular logic is a formal language, and an interpretation assigns a meaning to each of the formulas—usually, a truth value.
The study of interpretations of formal languages is called formal semantics. In mathematical logic, this is often done in terms of model theory. In model theory, the terms that occur in a formula are interpreted as mathematical structures, and fixed compositional interpretation rules determine how the truth value of the formula can be derived from the interpretation of its terms; a model for a formula is an interpretation of terms such that the formula becomes true.
Read more about this topic: Formal Language, Applications, Formal Theories, Systems and Proofs
Famous quotes containing the word models:
“The parents who wish to lead a quiet life I would say: Tell your children that they are very naughty—much naughtier than most children; point to the young people of some acquaintances as models of perfection, and impress your own children with a deep sense of their own inferiority. You carry so many more guns than they do that they cannot fight you. This is called moral influence and it will enable you to bounce them as much as you please.”
—Samuel Butler (1835–1902)