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 , introduced by Giorgi Japaridze in 1992–93.
See also[]
- Interpretation (logic)
- Interpretation (model theory)
- Interpretability logic
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.
 | This logic-related article is a stub. You can help Wikipedia by . |
- Proof theory
- Logic stubs