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The concept of interpretability is one in mathematical logic. Assume T and S are formal theories. Slightly simplified, T is said to be interpretable in S iff 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 1992-1993. See also Interpretability logic.

References

• A.Tarski, A.Mostovski and R.M.Robinson, Undecidable Theories. North-Holland, Amsterdam, 1953.
• G.Japaridze and D. de Jongh, The logic of provability. Handbook of Proof Theory. S.Buss, ed. Elsevier, 1998, pp. 476-546.

External links

• Giorgi Japaridze: Homepage
• Giorgi Japaridze: Research and Publications

Monday, I've done my exam Information Theory. Didn't go well. I thought I'd studied enough, but the exam was very hard with large time-consuming question. Nobody was done on time, but I've hardly completed half of it. So I think I'll fail for that one, but let's hope for the best.

Next one is friday, speech processing. Harder than I thought. Large parts of the course handle signal processing and statistics, my two big problems of the second year. I'll do my best ;-)

I also had contact with Dirk Steel about my internship at Siemens. I allready have to start monday! Just a week quality time with my lovely girlfriend isn't possible :-( We'll be together now friday after my exam and her thesis defence. I've cancelled VTK Weekend for me. Saturday, I have a BBQ with people from student representation boards all over Flanders. Let's hope I can spend a large part of my sunday with my sweetheart...