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.
Tarski, Alfred (1953), Undecidable theories, Studies in Logic and the Foundations of Mathematics, Amsterdam: North-Holland Publishing Company, MR 0058532. Written in collaboration with Andrzej Mostowski and Raphael M. Robinson.
Dzhaparidze, Giorgie (1993), "A generalized notion of weak interpretability and the corresponding modal logic", Annals of Pure and Applied Logic, 61 (1–2): 113–160, doi:10.1016/0168-0072(93)90201-N, MR 1218658.
Dzhaparidze, Giorgie (1992), "The logic of linear tolerance", Studia Logica, 51 (2): 249–277, doi:10.1007/BF00370116, MR 1185914
Japaridze, Giorgi; de Jongh, Dick (1998), "The logic of provability", in Buss, Samuel R. (ed.), Handbook of Proof Theory, Stud. Logic Found. Math., vol. 137, Amsterdam: North-Holland, pp. 475–546, doi:10.1016/S0049-237X(98)80022-0, MR 1640331
December 01, 2023
weak, interpretability, mathematical, logic, weak, interpretability, notion, translation, logical, theories, introduced, together, with, interpretability, alfred, tarski, 1953, formal, theories, slightly, simplified, said, weakly, interpretable, only, language. 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 editInterpretability logicReferences editTarski Alfred 1953 Undecidable theories Studies in Logic and the Foundations of Mathematics Amsterdam North Holland Publishing Company MR 0058532 Written in collaboration with Andrzej Mostowski and Raphael M Robinson Dzhaparidze Giorgie 1993 A generalized notion of weak interpretability and the corresponding modal logic Annals of Pure and Applied Logic 61 1 2 113 160 doi 10 1016 0168 0072 93 90201 N MR 1218658 Dzhaparidze Giorgie 1992 The logic of linear tolerance Studia Logica 51 2 249 277 doi 10 1007 BF00370116 MR 1185914 Japaridze Giorgi de Jongh Dick 1998 The logic of provability in Buss Samuel R ed Handbook of Proof Theory Stud Logic Found Math vol 137 Amsterdam North Holland pp 475 546 doi 10 1016 S0049 237X 98 80022 0 MR 1640331 Retrieved from https en wikipedia org w index php title Weak interpretability amp oldid 1170901182, wikipedia, wiki, book, books, library,
