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:
“Science is a dynamic undertaking directed to lowering the degree of the empiricism involved in solving problems; or, if you prefer, science is a process of fabricating a web of interconnected concepts and conceptual schemes arising from experiments and observations and fruitful of further experiments and observations.”
—James Conant (1893–1978)