Giorgi Japaridze
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Giorgi Japaridze is a logician, at Villanova University in Villanova, Pennsylvania. In the past his contributions were primarily into the areas of provability logic and interpretability logic. Currently he is best known for his work on computability logic (CL).
Technically CL is a game logic: it understands interactive computational problems as games played by a machine against the environment, their computability as existence of a machine that always wins the game, logical operators as operations on computational problems, and validity of a logical formula as being a scheme of "always computable" problems.
Classical logic, intuitionistic logic, and linear logic (in a broad sense), turn out to be three natural fragments of CL. The classical concept of truth is a special case of computability, -- computability restricted to problems of zero interactivity degree. Correspondingly, classical logic is a special fragment of CL. One of the main intuitions associated with intuitionistic logic is that it must be a logic of problems (Kolmogorov 1932); this is exactly what CL is, but in a more expressive language than intuitionistic logic. And one of the main claims of linear logic is that it is a logic of resources. Reversing of the roles of the machine and its environment turns computational problems into computational resources, which makes CL a logic of resources, only, again, in a more expressive language than that of linear logic, and based on an intuitively convincing and mathematically strict resource semantics.
[edit] References
- G. Japaridze, Introduction to computability logic. Annals of Pure and Applied Logic 123 (2003), pages 1-99.
- G.Japaridze and D.DeJongh, The logic of provability. In: Handbook of Proof Theory, S.Buss, ed., North-Holland, 1998, pages 475-545.
- L.D. Beklemishev, J.J. Joosten and M. Vervoort, "A finitary treatment of the closed fragment of Japaridze's provability logic". Journal of Logic and Computation 15(4) (2005), pages 447-463.
- G. Boolos, The analytical completeness of Japaridze's polymodal logics. Annals of Pure and Applied Logic 61 (1993), pages 95-111.
