Other Concepts of Interpretation
There are other uses of the term "interpretation" that are commonly used, which do not refer to the assignment of meanings to formal languages.
In model theory, a structure A is said to interpret a structure B if there is a definable subset D of A, and definable relations and functions on D, such that B is isomorphic to the structure with domain D and these functions and relations. In some settings, it is not the domain D that is used, but rather D modulo an equivalence relation definable in A. For additional information, see Interpretation (model theory).
A theory T is said to interpret another theory S if there is a finite extension by definitions T′ of T such that S is contained in T′.
Read more about this topic: Interpretation (logic)
Famous quotes containing the word concepts:
“It is impossible to dissociate language from science or science from language, because every natural science always involves three things: the sequence of phenomena on which the science is based; the abstract concepts which call these phenomena to mind; and the words in which the concepts are expressed. To call forth a concept, a word is needed; to portray a phenomenon, a concept is needed. All three mirror one and the same reality.”
—Antoine Lavoisier (1743–1794)