Interpretability
In the following article, Interpretability will be addressed from different perspectives in order to provide a comprehensive and detailed analysis on the topic. Its origins, evolution, impact on society and possible future implications will be explored. Throughout these pages, we will seek to provide the reader with a complete and updated vision of Interpretability, shedding light on its most relevant aspects and providing a clear and objective overview. Without a doubt, this article will serve as a source of knowledge and reflection for those interested in entering the world of Interpretability.
In mathematical logic, interpretability is a relation between formal theories that expresses the possibility of interpreting or translating one into the other.
Informal definition
Assume T and S are formal theories. Slightly simplified, T is said to be interpretable in S if and only if 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 1992–93.
See also
References
- Japaridze, G., and De Jongh, D. (1998) "The logic of provability" in Buss, S., ed., Handbook of Proof Theory. North-Holland: 476–546.
- Alfred Tarski, Andrzej Mostowski, and Raphael Robinson (1953) Undecidable Theories. North-Holland.
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