Giorgi Japaridze

Research and Publications

 Description: C:\Users\gjaparid\Desktop\thinker.jpg

NOTE: Before 1994 the English spelling of my name was "Dzhaparidze", the result of a two-step transliteration Georgian -> Russian -> English, while the current "Japaridze" is a direct transliteration from Georgian into English. Don't get confused if you need to look up my name in some earlier literature.

Main Contributions to Science

Provability and interpretability logics

(1985-1998)

·       While a student,  introduced polymodal provability logic GLP, and proved its arithmetical completeness. This contained a solution of an open problem on the logic of w-provability raised by George Boolos a decade earlier (1985-1988).

·       Introduced logic D and proved its arithmetical completeness (1987).

·       Extended Solovay's theorems from propositional level to the one-variable predicate level, and introduced the corresponding sound and complete logic GLq (1987). 

·       Introduced the concepts of cointerpretability, tolerance and cotolerance (1992-1993).

·       Proved that cointerpretability is equivalent to S1-conservativity and tolerance is equivalent to P1-consistency. This was an answer to the long-standing open problem regarding the metamathematical meaning of S1-conservativity (1992-1993). 

·       Introduced modal logics for tolerance and proved their arithmetical completeness (1993).

·       Introduced a modal logic for the arithmetical hierarchy and proved its arithmetical completeness (1994).

Game semantics and the theory of interactive computation

(1997-present)

·       Introduced the Logic of Tasks (2000-2002). It later became a part of computability logic on one hand, and a part of abstract game semantics on the other hand.

·       Introduced and started elaborating Computability Logic. This is work with a beginning but no end. An ambitious program and platform for redeveloping logic as a formal theory of (interactive) computability, as opposed to the formal theory of truth that it has more traditionally been (2003-2007).

·       Proved the soundness and completeness of intuitionistic logic with respect to the semantics of computability logic, thus corroborating Kolmogorov's (1932) well known yet rather abstract thesis, according to which intuitionistic logic is a logic of problems (2006-2007).

·       Introduced Abstract Resource Semantics (2006). 

Proof theory and deep inference

(2006-present)

Complexity theory

(2010-present)

Publications

  1. G.Japaridze,
    Introduction to clarithmetic III
    Annals of Pure and Applied Logic (to appear)
           Official journal version        Online preprint         
  2. G.Japaridze,
    The taming of recurrences in computability logic through cirquent calculus, Part II
    Archive for Mathematical Logic   52 (2013),  pp. 213-259.
           Official journal version        Online preprint        Author’s official copy
  3. G.Japaridze,
    The taming of recurrences in computability logic through cirquent calculus, Part I
    Archive for Mathematical Logic  52 (2013),  pp. 173-212.   
           Official journal version        Online preprint        Author’s official copy
  4. G.Japaridze,
    A new face of the branching recurrence of computability logic
    Applied Mathematics Letters 25 (2012), pp. 1585-1589.
           Official journal version        Online preprint
  5. G.Japaridze,
    A logical basis for constructive systems
    Journal of Logic and Computation  22 (2012), pp. 605-642.  
            Official journal version (free access)       
  6. G.Japaridze,
    Separating the basic logics of the basic recurrences
    Annals of Pure and Applied Logic 163 (2012), pp. 377-389.
           Official journal version        Online preprint
  7. G.Japaridze,
    Introduction to clarithmetic I
    Information and Computation 209 (2011), pp. 1312-1354.
           Official journal version        Online preprint
  8. G.Japaridze,
    From formulas to cirquents in computability logic
    Loical Methods is Computer Science 7 (2011),  Issue 2 , Paper 1, pp. 1-55.  
            Official journal version (free access)        
  9. G.Japaridze,
    Toggling operators in computability logic
    Theoretical Computer Science 412 (2011), pp. 971-1004.
            Official journal version        Online preprint
  10. G.Japaridze,
    Towards applied theories based on computability logic
    Journal of Symbolic Logic 75 (2010), pp. 565-601.
            Official journal version         Online preprint 
  11. G.Japaridze,
    Many concepts and two logics of algorithmic reduction
    Studia Logica 91 (2009), No.1,  pp. 1-24.
            Official journal version         Online preprint 
  12. G.Japaridze,
    In the beginning was game semantics
    Games: Unifying Logic, Language and Philosophy. O. Majer, A.-V. Pietarinen and T. Tulenheimo, eds. Springer 2009, pp. 249-350.  
            Official book version         Online preprint 
  13. G.Japaridze,
    Sequential operators in computability logic
    Information and Computation 206 (2008), No.12, pp. 1443-1475.  
            Official journal version        Online preprint 
  14. G.Japaridze,
    Cirquent calculus deepened
    Journal of Logic and Computation 18 (2008), No.6, pp. 983-1028. 
            Official journal version (free access)        
  15. G.Japaridze,
    The intuitionistic fragment of computability logic at the propositional level
    Annals of Pure and Applied Logic 147 (2007), No.3, pp. 187-227. 
            Official journal version          Online preprint 
  16. G.Japaridze,
    The logic of interactive Turing reduction
    Journal of Symbolic Logic 72 (2007), No.1, pp. 243-276.
            Official journal version         Online preprint
  17. G.Japaridze,
    Intuitionistic computability logic
    Acta Cybernetica 18 (2007), No. 1, pp. 77-113.
            Official journal version           Online preprint
  18. G.Japaridze,
    From truth to computability II
    Theoretical Computer Science 379 (2007), pp. 20-52.
               Official journal version   Online preprint 
  19. G.Japaridze,
    From truth to computability I
    Theoretical Computer Science 357 (2006), pp. 100-135.
               Official journal version   Online preprint
  20. G.Japaridze,
    Introduction to cirquent calculus and abstract resource semantics
    Journal of Logic and Computation 16 (2006), No.4, pp. 489-532.
            Official journal version       Online preprint
  21. G.Japaridze,
    Computability logic: a formal theory of interaction
    Interactive Computation: The New Paradigm. D.Goldin, S.Smolka and P.Wegner, eds. Springer Verlag, Berlin 2006, pp. 183-223.
               Official book version      Online preprint
  22. G.Japaridze,
    Propositional computability logic II
    ACM Transactions on Computational Logic 7 (2006), No. 2, pp. 331-362.
            Official journal version       Online preprint
  23. G.Japaridze,
    Propositional computability logic I
    ACM Transactions on Computational Logic 7 (2006) No.2, pp. 302-330.
            Official journal version        Online preprint
  24. G.Japaridze,
    The simplest completeness proof in computability logic
    Vriendboek ofwel Liber Amicorum ter gelegenheid van het afscheid van Dick de Jongh. Institute for Logic, Language and Computation, University of Amsterdam, 2004. 7 pages.
  25. G.Japaridze,
    A basic completeness theorem of CL.
    Bulletin of the Georgian Academy of Sciences 169 (2004), No.1, pp. 34-36.
  26. G.Japaridze,
    A basic soundness theorem of CL.
    Bulletin of the Georgian Academy of Sciences 168 (2003), No.3, pp. 215-218.
  27. G.Japaridze,
    Introduction to computability logic
    Annals of Pure and Applied Logic, vol. 123 (2003), p. 1-99.
            Official journal version        Online preprint
  28. G.Japaridze,
    Some preliminary results on computability logic
    Proceedings of Kalmar Workshop on Logic and Computer Science. Szeged, Hungary, 2003. 15 pages.
  29. G.Japaridze,
    What is the real logic of games after all?
    Proceedings of the 3rd and 4th International Symposium on Language, Logic and Computation. D. De Jongh, H.Zeevat and M Nilsenova (EDS.). ILLCScientific Publications, Amsterdam, 2002, pp. 243-257.
  30. G.Japaridze,
    Preliminary results on the basic predicate logic of racefree games.
    Bulletin of the Georgian Academy of Sciences 165 (2002), No. 2, pp. 256-259.
  31. G.Japaridze,
    Preliminary results on the basic propositional logic of racefree games.
    Bulletin of the Georgian Academy of Sciences 165 (2002), No. 1, pp. 26-29.
  32. G.Japaridze,
    The logic of tasks.
    Annals of Pure and Applied Logic 117 (2002), pp. 263-295
            Official journal version         Online preprint 
  33. G.Japaridze,
    A decidable substructural predicate logic with a natural semantics.
    4th Tbilisi Symposium on Language, Logic and Computation (abstracts) ILLC, University of Amsterdam / CLLS, Tbilisi State University, 2001, 5 pages.
  34. G.Japaridze,
    A task semantics for the language of linear logic
    Bulletin of the Georgian Academy of Sciences 163, No. 1 (2001), pp. 5-7.
  35. G.Japaridze,
    The propositional logic of elementary tasks
    Notre Dame Journal of Formal Logic 41 (2000), No. 2, pp. 171-183.
            Official journal version      Online preprint
  36. G.Japaridze,
    A decidable first order epistemic logic
    Proceedings of the Georgian Academy of Sciences No. 1-2 (2000), pp. 81-95.
  37. G.Japaridze and D.DeJongh
    The logic of provability.
    Handbook of Proof Theory, S.Buss, ed., North-Holland, 1998, pp. 475-545.
            Official book version      Online preprint
  38. G.Japaridze,
    A constructive game semantics for the language of linear logic.
    Annals of Pure and Applied Logic 85 (1997), No. 2, pp. 87-156.
            Official journal version       Online preprint
  39. G.Japaridze,
    A simple proof of arithmetical completeness for Pi-1 conservativity logic.
    Notre Dame Journal of Formal Logic 35 (1994), No. 3. pp. 346-354.
            Official journal version       Online preprint
  40. G.Japaridze,
    The logic of the arithmetical hierarchy.
    Annals of Pure and Applied Logic 66 (1994), No. 2, pp. 89-112.
  41. G.Japaridze,
    A generalized notion of weak interpretability and the corresponding modal logic.
    Annals of Pure and Applied Logic 61 (1993), No. 1-2, pp. 113-160.
  42. G.Japaridze,
    The logic of linear tolerance.
    Studia Logica 51 (1992), No. 2, pp. 249-277.
          Official journal version    Online preprint
  43. G.Japaridze,
    Predicate provability logic with non-modalized quantifiers.
    Studia Logica 50 (1991), No. 1, pp. 149-160.
          Official journal version    Online preprint
  44. G.Japaridze,
    Semidecidable fragments of first order provability logic.
    Semantical Analysis of Non-classical Logics. Tbilisi, Metsniereba, 1991, pp. 63-79
  45. G.Japaridze,
    The logic of generalized weak interpretability.
    Bulletin of the Academy of Sciences of the Georgian SSR 143 (1991), No. 3, pp. 233-235.
  46. G.Japaridze,
    The propositional logic of truth and provability.
    Logic and Philosophic Essays. Moscow, 1991, pp. 43-52 (Russian).
  47. G.Japaridze,
    Decidable and enumerable predicate logics of provability.
    Studia Logica 49 (1990), No. 1, pp. 7-21.
          Official journal version    Online preprint
  48. S.Artemov and G.Japaridze,
    Finite Kripke models and predicate logics of provability.
    Journal of Symbolic Logic 55 (1990), No. 3, pp. 1090-1098.
         Official journal version    Online preprint
  49. G.Japaridze,
    Provability logic with modalities for arithmetical complexities.
    Bulletin of the Academy of Sciences of the Georgian SSR 138 (1990), No. 3, pp. 481-484.
  50. G.Japaridze,
    On predicate provability logics of nonenumerable theories.
    Suslin Mathematical Readings. Saratov, 1989, p. 84 (Russian).
  51. G.Japaridze,
    The polymodal logic of provability.
    Intensional Logics and Logical Structure of Theories. Metsniereba, Tbilisi, 1988, pp. 16-48 (Russian).
  52. G.Japaridze,
    The arithmetical completeness of provability logic with quantifier modalities.
    Bulletin of the Academy of Sciences of the Georgian SSR 132 (1988), No. 2, pp. 265-268.
  53. G.Japaridze,
    Quantifiers over realizations in provability logic.
    Semiotical Aspects of Formalization of the Intellectual Activity. Moscow, 1988, pp. 81-83 (Russian).
  54. G.Japaridze,
    Quantifier modalities in provability logic.
    Proceedings of the 9th All Union Conference on Mathematical Logic. Leningrad, 1988, p. 51 (Russian).
  55. S.Artemov and G.Japaridze,
    On effective predicate logics of provability.
    Doklady AN SSSR (now Dokady Mathematics) 297 (1987), No. 3, pp. 521-523 (Russian).
    English translation in: Soviet Math. Doklady 36, pp.478-480.
  56. G.Japaridze,
    Generalized provability principles and modal logic.
    Proceedings of the 8th International Congress on Logic, Methodology and Philosophy of Science. Moscow, 1987, volume 5, Part 1, pp. 32-34.
  57. G.Japaridze and L.Mchedlishvili,
    Gottlob Frege: Begriffshrift
    Methods for Research in Logic, Metsniereba, Tbilisi, 1987, pp. 83-151 (Russian).
  58. G.Japaridze,
    Proof theory and some modal systems.
    Methods of Logic Research. Tbilisi, Metsniereba, 1986, pp. 39-47 (Russian).
  59. G.Japaridze,
    Modal logical means of studying provability
    Autoreferat of the candidate's thesis. Moscow State University, Moscow, 1986, 20 pages.
  60. G.Japaridze,
    Some modal systems with provability interpretation of the necessity operator.
    Logic and Methods of Analysis of the Scientific Knowledge. Moscow, 1986, pp. 18-19 (Russian).
  61. G.Japaridze,
    GL as the intersection of truth provability logics.
    Proceedings of the 8th All Union Conference on Mathematical Logic. Moscow, 1986, p. 58 (Russian).
  62. G.Japaridze,
    Provability principles and extensions of arithmetic.
    Nonstandard Semantics of Nonclassical Logics. Moscow, 1986, pp. 89-98 (Russian).
  63. G.Japaridze,
    Necessity as provability.
    Izvestia (Annals) of the Academy of Sciences of the Georgian SSR (Philosophy and Psychology), 1986, No. 3, pp. 34-44 (Russian).
  64. G.Japaridze,
    N-provability reflected in a modal logic with infinitely many modal operators.
    Proceedings of the 4th Soviet-Finnish Symposium on Logic. Tbilisi, 1985, pp. 56-57 (Russian).

Dissertations

  1. G.Japaridze,
    Modal-logical Means of Studying Provability.
    Ph.D. Thesis. Moscow State University, Moscow, 1987, 118 pages (Russian).
  2. G.Japaridze,
    The Logic of Resources and Tasks.
    PhD Thesis. University of Pennsylvania, Philadelphia, 1998, 145 pages.

Research Grants

(Principal Investigator without co-PIs)

  1. Outstanding Foreign Experts Program grant (China)
  2. Summer Research Fellowship and Grant from Villanova University
  3. Summer Research Fellowship and Grant from Villanova University
  4. NSF grant CCR-0208816 (Theory of Computing Program)
  5. Summer Research Fellowship from Villanova University

Major Citations

[Other authors’ papers focused on one of the following 4 brainchildren of mine:

GLP (1985),  Logic of Tasks (2002),  Computability Logic (2003),  Cirquent Calculus (2006)]

 

  1. M.Bauer,
     “A PSPACE-complete first order fragment of computability logic”.
    ACM Transactions on Computational Logic (to appear).
  2. L.Beklemishev and  D.Gabelaia,
    “    Topological completeness of provability logic GLP”.
    Annals of Pure and Applied Logic (to appear)
  3. M.Qu, J.Luan, D.Zhu and M.Du,
     “On the toggling-branching recurrence of computability logic”.
    Journal of Computer Science and Technology 28  (2013), pp. 278-284.
  4. W.Xu and S.Liu,
     “The parallel versus branching recurrences in computability logic”.
    Notre Dame Journal of Formal Logic 54  (2013), pp. 61-78.
  5. C.Yu and W.Zhou,
     “Hierarchy organization model based on the logic of tasks”.
    Applied Mechanics and Materials 310  (2013), pp. 644-649.
  6. W.Zhang, L.Zeng and S.Li,
     “Coordinative relationship model for groups organization based on the description logic of tasks”.
    Computer Engineering and Science 35:1  (2013).
  7. H.Kwon,
     “Expressing algorithms as concise as possible via computability logic”.
    arXiv:1305.2004 (2013).
  8. W.Xu and S.Liu,
     “The countable versus uncountable branching recurrences in computability logic”.
    Journal of Applied Logic 10 (2012), pp. 431-446. 
  9. W.Xu and S.Liu,
     “Soundness and completeness of the cirquent calculus system CL6 for computability logic”.
    Logic Journal of the IGPL 20  (2012), pp. 317-330.
  10. W.Xu and S.Liu,
     “Cirquent calculus system CL8S versus calculus of structures system SKSg for propositional logic”.
    In:     Quantitative Logic and Soft Computing. Guojun Wang, Bin Zhao and Yongming Li, eds. Singapore, World Scientific, 2012,   pp. 144-149.
  11. F.N. Pakhomov,
     “Undecidability of the elementary theory of the semilattice of GLP-words”.
    Matematicheskii Sbornik  203 (2012), pp. 141-160.
  12. D. Fernαndez-Duque and J.J.Joosten,
     “Well-orders in the transfinite Japaridze algebra”.
    arXiv:1212.3468 (2012).
  13. D. Fernαndez-Duque and J.J.Joosten,
     “Well-founded orders on the transfinite Japaridze algebra II”.
    arXiv:1204.4743 (2012)
  14. W.Zhang, L.Zeng, H.Zhang and S.Li,
     “Collaboration in digital games: An approach to the description logic of tasks”.
    Journal of Computer Research and Development   49:7 (2012).
  15. L.Beklemishev,
    “    A simplified proof of arithmetical completeness theorem for provability logic GLP”.
    Proceedings of the Steklov Institute of Mathematics  274 (2011),  pp. 25-33.
  16. L.Beklemishev,
    “    Ordinal completeness of bimodal provability logic GLB”.
    Lecture Notes in Computer Science  6618 (2011),  pp. 1-15.
  17. D.S.Shamkanov,
    “Interpolation properties for provability logics GL and GLP    ”    .
    Proceedings of the Steklov Institute of Mathematics 274 (2011),  pp. 303-316.
  18. L.Min, Y.Liu and X.Chen,
    “    Analysis of deterministic finite automata in computability logic”.
    Journal of Chongqing University of Posts and Telecommunications (Natural Science Edition)   23:6 (2011), pp. 80-82.
  19. X.Ma,
    “    On theorems in system CL4 of computability logic”.
    Journal of Xi’an Institute of Posts and Telecommunications      16:5 (2011), pp. 80-82.
  20. I.Mezhirov and N.Vereshchagin,
    “    On abstract resource semantics and computability logic”    .
    Journal of Computer and Systems Sciences 76 (2010), pp. 356-372.
  21. L.Beklemishev,
    “    Kripke semantics for provability logic GLP”.
    Annals of Pure and Applied Logic 161, 756–774 (2010).
  22. L.Beklemishev, G. Bezhanishvili and T. Icar,
    “    On topological models of GLP”.
    Ways of proof theory, Ontos Mathematical Logic, 2, eds. R. Schindler, Ontos Verlag, Frankfurt, 2010, pp. 133–153.
  23. L.Beklemishev,
    “    On the Craig interpolation and the fixed point properties of GLP”.
    In: Proofs, Categories and Computations. S. Feferman et al., eds., College Publications 2010.  pp. 49-60.
  24. W.Xu and S.Liu,
    “    Deduction theorem for symmetric cirquent calculus”.
    Advances in Intelligent and Soft Computing 82 (2010),  pp. 121-126.
  25. W.Zhang, L.Zeng, H.Zhang and S.Li,
    “    Task planning based on the description logic of tasks in joint operation scenarios”.
    Journal of Software 21 (2010), pp.140−148.
  26. W.Xu and S.Liu,
    “    Knowledge representation and reasoning rased on computability logic”.
    Journal of Jilin University 47 (2009), pp. 1230-1236.
  27. L.Beklemishev,
    “    On GLP-spaces”.
    Manusript, Steklov Institute of Mathematics, 2009. 
  28. I. Shapirovsky,
    "PSPACE-decidability of Japaridze's polymodal logic".
    Advances in Modal Logic 7 (2008), pp. 289-304.
  29. L.Beklemishev,
    “    A simplified proof of arithmetical completeness theorem for provability logic GLP”.
    Proceedings of the Steklov Institute of Mathematics  274 (2011),  pp. 25-33.
  30. N.Vereshchagin,
    "Japaridze's computability logic and intuitionistic propositional calculus".
    Moscow State University preprint (Russian), 2006.
  31. G.Wang and W.Xu,
    "Theorems in the logic of tasks".
    Fuzzy Systems and Mathematics     20（2006), No.6, pp. 15-20.
  32. H.Zhang and S.Li,
    "The description logic of tasks: from theory to practice".
    Chinese Journal of Computers     29（2006), No.3, pp. 488-494.

  33. 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 (2005), No 4, pp. 447-463.
  34. G.Wang and W.Xu,
    "From the logic of facts to the logic of tasks".
    Fuzzy Systems and Mathematics     18（2004), No.1, pp. 1-8.
  35. G. Boolos,
    "The analytical completeness of Japaridze's polymodal logics".
    Annals of Pure and Applied Logic 61 (1993), pp. 95-111.

  36. K. Ignatiev,
    "    The closed fragment of Japaridze's polymodal logic and the logic of Sigma-1 conservativity".
    ITLI Prepublication Series for Mathematical Logic and Foundations, X-92-02, University of Amsterdam, 1992.

  37. K. Ignatiev,
    "    Japaridze's polymodal logic: arithmetical completeness, fixed point property, Craig's property".
    ITLI Prepublication Series for Mathematical Logic and Foundations, X-90-13, University of Amsterdam, 1990.

 

Technical Reports and Unpublished Papers

  1. On the system CL12 of computability logic. arXiv:203.0103.  2012. 46 pages.
  2. The taming of recurrences in computability logic through cirquent calculus, Part II. arXiv:1106.3705.  2011. 36 pages.
  3. The taming of recurrences in computability logic through cirquent calculus, Part I. arXiv:1105.3853.  2011. 31 pages.
  4. A new face of the branching recurrence of computability logic. arXiv:1102.1054.  2011. 6 pages.
  5. Introduction to clarithmetic III. arXiv:1008.0770. 10 pages.
  6. Introduction to clarithmetic II. arXiv:1004.3236. 2010. 28 pages.
  7. Introduction to clarithmetic I. arXiv:1003.4719. 2010. 52 pages.
  8. A logical basis for constructive systems. arXiv:1003.0425. 2010. 30 pages.
  9. Separating the basic logics of the basic recurrences. arXiv:1007.1324. 2010. 18 pages.
  10. From formulas to cirquents in computability logic. arXiv:0906.2154. 2009. 42 pages.
  11. Toggling operators in computability logic. arXiv:0904.3469. 2009. 43 pages.
  12. Ptarithmetic. arXiv:0902.2969. 2009. 103 pages.
  13. Towards applied theories based on computability logic.  arXiv:0805.3521. 2008. 30 pages.
  14. Sequential operators in computability logic. arXiv:0712.1345, 2007. 40 pages.
  15. Cirquent calculus deepened. arXiv:0709.1308, 2007.  40 pages
  16. Many concepts and two logics of algorithmic reduction. arXiv:0706.0103, 2007. 15 pages.
  17. The intuitionistic fragment of computability logic at the propositional level. arXiv:cs.LO/0602011, 2006. 59 pages.
  18. The logic of interactive Turing reduction. arXiv:cs.LO/0512100, 2005. 38 pages.
  19. In the beginning was game semantics. arXiv:cs.LO/0507045, 2005. 76 pages.
  20. Introduction to cirquent calculus and abstract resource semantics. arXiv:math.LO/0506553, 2005. 50 pages.
  21. Intuitionistic computability logic. arXiv:cs.LO/0411008, 2004. 25 pages.
  22. From truth to computability II. arXiv:cs.LO/0501031, 2005. 34 pages.
  23. From truth to computability I. arXiv:cs.LO/0407054, 2004. 64 pages.
  24. Computability logic: a formal theory of interaction. arXiv:cs.LO/0404024, 2004. 26 pages.
  25. Propositional computability logic II. arXiv:cs.LO/0406037, 2004. 25 pages.
  26. Propositional computability logic I. arXiv:cs.LO/0404023, 2004. 22 pages.
  27. A formalism for resource-oriented planning. IRCS Technical Reports 98-01 (1998), 38 pages.
  28. A decidable predicate logic of knowledge. IRCS Technical Reports 96-06 (1996), 20 pages.
  29. (With D.DeJongh) The logic of provability. ILLC Prepublication Series for Mathematical Logic and Foundations ML-1997-01.
  30. Effective truth. In: ILLC Prepublication Series for Mathematical Logic and Foundations ML-93-15 (1993), 25 pages.
  31. The logic of tolerance. ILLC Prepublication Series for Mathematical Logic and Foundations, X-1991-08.
  32. Determinism and freedom of will. This philosophical paper, written in Georgian, brought me the highest annual prize for student research in Georgia called "Medal from the Academy of Sciences of Georgian SSR" in 1982. I have never tried to publish the manuscript, although I regard it as the most important of my works. I am thinking of getting back to that exciting field in the (perhaps not very near) future and writing a book.

Computability Logic on the Web:

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