Weak interpretability

Weak interpretability is a special case of the concept of tolerance introduced by Giorgi Japaridze in 1992.

Assume T and S are formal theories. Slightly simplified, T is said to be weakly interpretable in S if, and only if, the language of T can be translated into the language of S in such a way that the translation of every theorem of T is consistent with S. 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 interpretability, was introduced by Alfred Tarski in 1953.

See also Interpretability logic.

References

* A.Tarski, A.Mostovski and R.M.Robinson, Undecidable Theories. North-Holland, Amsterdam, 1953.
* [http://www.csc.villanova.edu/~japaridz/ G.Japaridze] , "A generalized notion of weak interpretability and the corresponding logic". Annals of Pure and Applied Logic 61 (1993), pp. 113-160.
* [http://www.csc.villanova.edu/~japaridz/ G.Japaridze] , "The logic of linear tolerance". Studia Logica 51 (1992), pp. 249-277.
* [http://www.csc.villanova.edu/~japaridz/ G.Japaridze] and D. de Jongh, "The logic of provability". Handbook of Proof Theory. S.Buss, ed. Elsevier, 1998, pp. 476-546.