interpretability

The concept of interpretability is one in mathematical logic. Assume T and S are formal theories. Slightly simplified, T is said to be interpretable in S iff the language of T can be translated into the language of S in such a way that S proves the translation of every theorem of T. Of course, there are some natural conditions on admissible translations here, such as the necessity for a translation to preserve the logical structure of formulas. This concept, together with weak interpretability, was introduced by Alfred Tarski in 1953. Three other related concepts are cointerpretability, logical tolerance, and cotolerance, introduced by Giorgi Japaridze in 1992-1993. See also Interpretability logic.

References

A.Tarski, A.Mostovski and R.M.Robinson, Undecidable Theories. North-Holland, Amsterdam, 1953.
G.Japaridze and D. de Jongh, The logic of provability. Handbook of Proof Theory. S.Buss, ed. Elsevier, 1998, pp. 476-546.

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