Philosophy:Weak interpretability
From HandWiki
In mathematical logic, weak interpretability is a notion of translation of logical theories, introduced together with interpretability by Alfred Tarski in 1953. Let T and S be 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.
A generalization of weak interpretability, tolerance, was introduced by Giorgi Japaridze in 1992.
See also
References
- Undecidable theories, Studies in Logic and the Foundations of Mathematics, Amsterdam: North-Holland Publishing Company, 1953. Written in collaboration with Andrzej Mostowski and Raphael M. Robinson.
- "A generalized notion of weak interpretability and the corresponding modal logic", Annals of Pure and Applied Logic 61 (1-2): 113–160, 1993, doi:10.1016/0168-0072(93)90201-N.
- "The logic of linear tolerance", Studia Logica 51 (2): 249–277, 1992, doi:10.1007/BF00370116
- "The logic of provability", Handbook of Proof Theory, Stud. Logic Found. Math., 137, Amsterdam: North-Holland, 1998, pp. 475–546, doi:10.1016/S0049-237X(98)80022-0
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