Publications

Edited Volumes

  1. Leo Esakia. Heyting algebras: Duality theory, Translated by A. Evseev. Edited by G. Bezhanishvili and W. Holliday, Trends in Logic, Volume 50, Springer, 2019.
  2. Advances in modal logic, Volume 12 (2018), College Publications London, 2018, Editors: G. Bezhanishvili, G. D’Agostino, G. Metcalfe, T. Studer.
  3. Leo Esakia on duality in modal and intuitionistic logics, Outstanding Contributions to Logic, Springer, 2014. Editor: G. Bezhanishvili.
  4. Revised selected papers of the 9th international Tbilisi symposium on logic, language, and computation (TbiLLC 2011), Lecture Notes in Computer Science 7758, Springer, 2013. Editors: G. Bezhanishvili, S. Loebner, V. Marra, F. Richter.
  5. Special issue of Studia Logica dedicated to the memory of Leo Esakia. Studia Logica, Vol. 100, No. 1-2 (2012). Editors: L. Beklemishev, G. Bezhanishvili, D. Mundici, Y. Venema.

Handbook Chapter

  1. J. van Benthem, G. Bezhanishvili. Modal logics of space, Handbook of Spatial Logics, M. Aiello, J. van Benthem, I. Pratt-Hartman, editors. Springer, 2007, pp. 217-297.

Journal Publications

  1. G. Bezhanishvili, P. J. Morandi, B. Olberding. An extension of de Vries duality to normal and locally compact Hausdorff spaces, Journal of Pure and Applied Algebra, 224 (2020), pp. 703-724.
  2. G. Bezhanishvili, D. Gabelaia, J. Harding, M. Jibladze. Compact Hausdorff spaces with relations and Gleason spaces, Applied Categorical Structures 27 (2019), pp. 663-686.
  3. G. Bezhanishvili, L. Carai. Characterization of metrizable Esakia spaces via some forbidden configurations, Algebra Universalis, 80 (2019), paper 42, 18 pages.
  4. G. Bezhanishvili, N. Bezhanishvili, T. Santoli, Y. Venema. A strict implication calculus for compact Hausdorff spaces, Annals of Pure and Applied Logic, 170 (2019), paper 102714, 29 pages.
  5. G. Bezhanishvili, W. Holliday. A semantic hierarchy for intuitionistic logic, Indagationes Mathematicae, 30 (2019), pp. 403-469.
  6. G. Bezhanishvili, N. Bezhanishvili, J. Lucero-Bryan, J. van Mill. On modal logics arising from scattered locally compact Hausdorff spaces, Annals of Pure and Applied Logic, 170 (2019), pp. 558-577.
  7. G. Bezhanishvili, P. J. Morandi, B. Olberding. An extension of de Vries duality to completely regular spaces and compactifications, Topology and Its Applications, 257 (2019), pp. 85-105.
  8. G. Bezhanishvili, N. Bezhanishvili, J. Ilin. Subframization and stabilization for superintuitionistic logics, Journal of Logic and Computation, 29 (2019), pp. 1-35.
  9. G. Bezhanishvili, N. Bezhanishvili, J. Lucero-Bryan, J. van Mill. A new proof of the McKinsey-Tarski Theorem, Studia Logica, 106 (2018), pp. 1291-1311.
  10. G. Bezhanishvili, N. Bezhanishvili, J. Ilin. Stable modal logics, Review of Symbolic Logic, 11 (2018), pp. 436-469.
  11. G. Bezhanishvili, J. Harding, J. Ilin, F. Lauridsen. MacNeille transferability and stable classes of Heyting algebras, Algebra Universalis, 79 (2018), paper 55, 21 pages.
  12. G. Bezhanishvili, P. J. Morandi, B. Olberding. Canonical extensions of bounded archimedean vector lattices, Algebra Universalis, 79 (2018), paper 12, 17 pages.
  13. G. Bezhanishvili, N. Bezhanishvili, J. Lucero-Bryan, J. van Mill. Tychonoff HED-spaces and Zemanian extensions of S4.3, Review of Symbolic Logic, 11 (2018), pp. 115-132.
  14. G. Bezhanishvili, P. J. Morandi, B. Olberding. Pierce sheaves and commutative idempotent generated algebras, Fundamenta Mathematicae, 240 (2018), pp. 105-136.
  15. G. Bezhanishvili, N. Bezhanishvili, J. Lucero-Bryan, J. van Mill. Krull dimension in modal logic, Journal of Symbolic Logic, 82 (2017), pp. 1356-1386.
  16. G. Bezhanishvili, P. J. Morandi. Proximity biframes and Nachbin spaces, Applied Categorical Structures, 25 (2017), pp. 1077-1095.
  17. G. Bezhanishvili, T. Moraschini, J. Raftery. Epimorphisms in varieties of residuated structures, Journal of Algebra, 492 (2017), pp. 185-211.
  18. G. Bezhanishvili, N. Bezhanishvili, S. Sourabh, Y. Venema. Irreducible equivalence relations, Gleason spaces, and de Vries duality, Applied Categorical Structures, 25 (2017), pp. 381-401.
  19. G. Bezhanishvili, N. Bezhanishvili. Locally finite reducts of Heyting algebras and canonical formulas, Notre Dame Journal of Formal Logic, 58 (2017), pp. 21-45.
  20. G. Bezhanishvili, P. J. Morandi, B. Olberding. A functorial approach to Dedekind completions and the representation of vector lattices and l-algebras by normal functions, Theory and Applications of Categories, 31 (2016), pp. 1095-1133.
  21. G. Bezhanishvili, N. Bezhanishvili, J. Ilin. Cofinal stable logics, Studia Logica, 104 (2016), pp. 1287-1317.
  22. G. Bezhanishvili, J. Harding. Compact Hausdorff Heyting algebras, Algebra Universalis, 76 (2016), pp. 301-304.
  23. G. Bezhanishvili. Forbidden configurations and subframe varieties, Algebra Universalis, 76 (2016), pp. 237-243.
  24. G. Bezhanishvili, J. Harding. On the proof that compact Hausdorff Boolean algebras are powersets, Order, 33 (2016), pp. 263-268.
  25. G. Bezhanishvili, D. Gabelaia, M. Jibladze. Spectra of compact regular frames, Theory and Applications of Categories, 31 (2016), pp. 365-383.
  26. G. Bezhanishvili, N. Bezhanishvili, R. Iemhoff. Stable canonical rules, Journal of Symbolic Logic, 81 (2016), pp. 284-315.
  27. G. Bezhanishvili, D. Pengelley. What does `less than or equal’ really mean?, American Mathematical Monthly, 122 (2015), pp. 983-989.
  28. G. Bezhanishvili, D. Gabelaia, M. Jibladze, P. J. Morandi. Profinite topological spaces, Theory and Applications of Categories, 30 (2015), pp. 1841-1863.
  29. G. Bezhanishvili, N. Bezhanishvili, J. Lucero-Bryan, J. van Mill. S4.3 and hereditarily extremally disconnected spaces, Georgian Mathematical Journal, 22 (2015), pp. 469-475.
  30. G. Bezhanishvili, P. J. Morandi. Proximity biframes and compactifications of completely regular ordered spaces, Theory and Applications of Categories, 30 (2015), pp. 1469-1500.
  31. G. Bezhanishvili, N. Bezhanishvili, J. Harding. Modal operators on compact regular frames and de Vries algebras, Applied Categorical Structures, 23 (2015), pp. 365-379.
  32. G. Bezhanishvili, D. Gabelaia, J. Lucero-Bryan. Topological completeness of logics above S4, Journal of Symbolic Logic, 80 (2015), pp. 520-566.
  33. G. Bezhanishvili, V. Marra, P. J. Morandi, B. Olberding. De Vries powers: A generalization of Boolean powers for compact Hausdorff spaces, Journal of Pure and Applied Algebra, 219 (2015), pp. 3958-3991.
  34. G. Bezhanishvili, V. Marra, P. J. Morandi, B. Olberding. Idempotent generated algebras and Boolean powers of commutative rings, Algebra Universalis, 73 (2015), pp. 183-204.
  35. G. Bezhanishvili, D. Gabelaia, J. Lucero-Bryan. Modal logics of metric spaces, Review of Symbolic Logic, 8 (2015), pp. 178-191.
  36. G. Bezhanishvili, N. Bezhanishvili, J. Harding. Modal compact Hausdorff spaces, Journal of Logic and Computation, 25 (2015), pp. 1-35.
  37. G. Bezhanishvili, J. Harding. Stable compactifications of frames, Cah. Topol. Geom. Differ. Categ., 55 (2014), pp. 37–65.
  38. G. Bezhanishvili, J. Harding. Proximity frames and regularization, Applied Categorical Structures, 22 (2014), pp. 43-78.
  39. G. Bezhanishvili. Lattice subordinations and Priestley duality, Algebra Universalis, 70 (2013), pp. 359-377.
  40. G. Bezhanishvili, D. Gabelaia, M. Jibladze. Funayama’s theorem revisited, Algebra Universalis, 70 (2013), pp. 271-286.
  41. G. Bezhanishvili, P. J. Morandi, B. Olberding. Bounded Archimedean l-algebras and Gelfand-Neumark-Stone duality, Theory and Applications of Categories, 28 (2013), pp. 435-475.
  42. G. Bezhanishvili, R. Jansana. Esakia style duality for implicative semilattices, Applied Categorical Structures, 21 (2013), pp. 181-208.
  43. G. Bezhanishvili, P. J. Morandi, B. Olberding. Dedekind completions of bounded Archimedean l-algebras, Journal of Algebra and Its Applications, 12 (2013), 1250139, 16 pp.
  44. G. Bezhanishvili, N. Bezhanishvili. Canonical formulas for wK4, Review of Symbolic Logic, 5 (2012), pp. 731-762.
  45. G. Bezhanishvili. De Vries algebras and compact regular frames, Applied Categorical Structures, 20 (2012), pp. 569-582.
  46. G. Bezhanishvili, J. Lucero-Bryan. More on d-logics of subspaces of the rational numbers, Notre Dame Journal of Formal Logic, 53 (2012), pp. 319-345.
  47. G. Bezhanishvili, J. Lucero-Bryan. Subspaces of Q whose d-logics do not have the FMP, Archive for Mathematical Logic, 51 (2012), pp. 661-670.
  48. M. Aiello, G. Bezhanishvili, I. Bloch, V. Goranko. Logic for physical space from antiquity to present days, Synthese, 186 (2012), pp. 619-632.
  49. G. Bezhanishvili, J. Harding. Modal logics of Stone spaces, Order, 29 (2012), pp. 271-292.
  50. G. Bezhanishvili, P. Morandi. Order-compactifications of totally ordered spaces: Revisited, Order, 28 (2011), pp. 577592.
  51. G. Bezhanishvili, P. Morandi. Priestley rings and Priestley order-compactifications, Order, 28 (2011), pp. 399413.
  52. G. Bezhanishvili, N. Bezhanishvili. An algebraic approach to canonical formulas: Modal case, Studia Logica, 99 (2011), pp. 93-125.
  53. G. Bezhanishvili, R. Jansana. Priestley style duality for distributive meet-semilattices, Studia Logica, 98 (2011), pp. 83122.
  54. G. Bezhanishvili, R. Jansana. Generalized Priestley quasi-orders, Order, 28 (2011), pp. 201220.
  55. G. Bezhanishvili, P. Morandi. One-point order-compactifications, Houston Journal of Mathematics, 37 (2011), pp. 699-713.
  56. G. Bezhanishvili, S. Ghilardi, M. Jibladze. An algebraic approach to subframe logics. Modal case, Notre Dame Journal of Formal Logic, 52 (2011), pp. 187202.
  57. G. Bezhanishvili, D. Gabelaia. Connected modal logics, Archive for Mathematical Logic, 50 (2011), pp. 287317.
  58. G. Bezhanishvili, N. Bezhanishvili, D. Gabelaia, A. Kurz. Bitopological duality for distributive lattices and Heyting algebras, Mathematical Structures in Computer Science, 20 (2010), pp. 359393.
  59. G. Bezhanishvili, P. Morandi. Scattered and hereditarily irresolvable spaces in modal logic, Archive for Mathematical Logic, 49 (2010), pp. 343365.
  60. G. Bezhanishvili. Stone duality and Gleason covers through de Vries duality, Topology and Its Applications, 157 (2010), pp. 10641080.
  61. G. Bezhanishvili, L. Esakia, D. Gabelaia. The modal logic of Stone spaces: Diamond as derivative, Review of Symbolic Logic, 3 (2010), pp. 2640.
  62. G. Bezhanishvili. The universal modality, the center of a Heyting algebra, and the Blok-Esakia theorem, Annals of Pure and Applied Logic, 161 (2009), pp. 253-267.
  63. G. Bezhanishvili, N. Bezhanishvili. An algebraic approach to canonical formulas: Intuitionistic case, Review of Symbolic Logic, 2 (2009), pp. 517-549.
  64. G. Bezhanishvili, P. Morandi. Profinite Heyting algebras and profinite completions of Heyting algebras, Georgian Mathematical Journal, 16 (2009), pp. 29-47.
  65. G. Bezhanishvili, J. Harding. The modal logic of b(N), Archive for Mathematical Logic, 48 (2009), pp. 231-242.
  66. G. Bezhanishvili. Zero-dimensional proximities and zero-dimensional compactifications, Topology and Its Applications, 156 (2009), pp. 1496-1504.
  67. G. Bezhanishvili, J. Vosmaer. Comparison of MacNeille, canonical, and profinite completions, Order, 25 (2008), pp. 299-320.
  68. G. Bezhanishvili, N. Bezhanishvili. Profinite Heyting algebras, Order, 25 (2008), pp. 211-227.
  69. G. Bezhanishvili, N. Bezhanishvili, D. de Jongh. The Kuznetsov-Gerciu and Rieger-Nishimura logics: the boundaries of the finite model property, Logic and Logical Philosophy, 17 (2008), pp. 73-110.
  70. G. Bezhanishvili, R. Mines, P. Morandi. Topo-canonical completions of closure algebras and Heyting algebras, Algebra Universalis, 58 (2008), pp. 1-34.
  71. G. Bezhanishvili and S. Ghilardi. An algebraic approach to subframe logics. Intuitionistic case, Annals of Pure and Applied Logic, 147 (2007), pp. 84-100.
  72. J. Harding and G. Bezhanishvili. MacNeille completions of modal algebras, Houston Journal of Mathematics, 33 (2007), pp. 355-384.
  73. G. Bezhanishvili, M. Gehrke, R. Mines, P. Morandi. Profinite completions and canonical extensions of Heyting algebras, Order, 23 (2006), pp. 143-161.
  74. J. van Benthem, G. Bezhanishvili, B. ten Cate, D. Sarenac. Multimodal logics of products of topologies, Studia Logica, 84 (2006), pp. 369-392.
  75. G. Bezhanishvili, R. Grigolia. Locally finite varieties of Heyting algebras, Algebra Universalis, 54 (2005), pp. 465-473.
  76. G. Bezhanishvili, L. Esakia, D. Gabelaia. Some results on modal axiomatization and definability for topological spaces, Studia Logica, 81 (2005), pp. 325-355.
  77. G. Bezhanishvili, M. Gehrke. Completeness of S4 with respect to the real line: revisited, Annals of Pure and Applied Logic, 131 (2005), pp. 287-301.
  78. J. Harding, G. Bezhanishvili. MacNeille completions of Heyting algebras, Houston Journal of Mathematics, 30 (2004), pp. 937-952.
  79. M. Aiello, J. van Benthem, G. Bezhanishvili. Reasoning about space: the modal way, Journal of Logic and Computation, 13 (2003), pp. 889-920.
  80. J. van Benthem, G. Bezhanishvili, M. Gehrke. Euclidean hierarchy in modal logic, Studia Logica, 75 (2003), pp. 327-345.
  81. G. Bezhanishvili, R. Mines, P. Morandi. Scattered, Hausdorff-reducible, and hereditarily irresolvable spaces, Topology and Its Applications, 132 (2003), pp. 291-306.
  82. G. Bezhanishvili, J. Harding. Functional monadic Heyting algebras, Algebra Universalis, 48 (2002), pp. 1-10.
  83. G. Bezhanishvili, R. Mines, P. Morandi. The Priestley separation axiom for scattered spaces, Order, 19 (2002), pp. 1-10.
  84. G. Bezhanishvili. Locally finite varieties, Algebra Universalis, 46 (2001), pp. 531-548.
  85. G. Bezhanishvili. Glivenko type theorems for intuitionistic modal logics, Studia Logica, 67 (2001), pp. 89-109.
  86. G. Bezhanishvili. Varieties of monadic Heyting algebras. Part III, Studia Logica, 64 (2000), pp. 215-256.
  87. G. Bezhanishvili. Varieties of monadic Heyting algebras. Part II: Duality theory, Studia Logica, 62 (1999), pp. 21-48.
  88. G. Bezhanishvili. Varieties of monadic Heyting algebras. Part I, Studia Logica, 61 (1998), pp. 367-402.

Special Volumes and Proceedings

  1. G. Bezhanishvili, W. Holliday. Locales, nuclei, and Dragalin frames, Advances in Modal Logic. Volume 11. Lev Beklemishev, Stephane Demri, and Andras Mate, editors. College Publications, 2016, pp. 177-196.
  2. G. Bezhanishvili, N. Bezhanishvili. An algebraic approach to filtrations for superintuitionistic logics, Liber Amicorum Alberti. A tribute to Albert Visser. Jan van Eijck, Rosalie Iemhoff, and Joost Joosten, editors. College Publications, 2016, pp. 47-56.
  3. G. Bezhanishvili, L. Esakia, D. Gabelaia. Spectral and T0-spaces in d-semantics, Lecture Notes in Artificial Intelligence. N. Bezhanishvili, S. Loebner, K. Schwabe, and L. Spada, editors. Springer, 2011, pp. 1629.
  4. G. Bezhanishvili, L. Esakia, D. Gabelaia. K4.Grz and hereditarily irresolvable spaces, Proofs, Categories and Computations. Essays in honor of Grigori Mints. Solomon Feferman, Wilfried Sieg,  Vladik Kreinovich, Vladimir Lifschitz, and Ruy de Queiroz, editors. College Publications, 2010, pp. 6169.
  5. L. Beklemishev, G. Bezhanishvili, T. Icard. On topological models of GLP, Ways of Proof Theory. Essays in honor of Wolfram Pohlers. Ralf Schindler, editor. Ontos Verlag, 2010, pp. 135155.
  6. G. Bezhanishvili, M. Gehrke, J. Harding, C. Walker, E. Walker. Varieties of algebras in fuzzy set theory, Logical, Algebraic, and Probabilistic Aspects of Triangular Norms, E. Klement and R. Mesiar, editors. Elsevier, 2005, pp. 321-344.
  7. G. Bezhanishvili, L. Esakia, D. Gabelaia. Modal logics of submaximal and nodec spaces, Collection of Essays Dedicated to Dick de Jongh on Occasion of His 65th Birthday, J. van Benthem, F. Veltman, A. Troelstra, A. Visser, editors. 2004, pp. 1-13.
  8. G. Bezhanishvili, R. Grigolia. Locally tabular extensions of MIPC, Advances in Modal Logic, Volume 2, M. Zakharyaschev, K. Segerberg, M. de Rijke, and H. Wansing, editors. CSLI, Stanford, 2001, pp. 101-120.
  9. G. Bezhanishvili, R. Grigolia. Subalgebras and homomorphic images of the Rieger-Nishimura lattice, Proceedings of the Institute of Cybernetics of the Georgian Academy of Sciences, Vol. 1, N1, 2000, pp. 9-16.
  10. G. Bezhanishvili. Some results in monadic Heyting algebras, The Tbilisi Symposium on Logic, Language, and Computation. Selected papers. October 1995, Gudauri, Georgia. J. Ginzburg, Z. Khasidashvili, C. Vogel, J. Levy, and E. Valduvi, editors. CSLI, Stanford, 1997, pp. 251-261.
  11. G. Bezhanishvili, M. Zakharyaschev. Logics over MIPC, Proceedings of Sequent Calculus and Kripke Semantics for Non-Classical Logics, RIMS Kokyuroku 1021, Kyoto University, 1997, pp. 86-95.
  12. G. Bezhanishvili. Modal intuitionistic logics and superintuitionistic predicate logics: correspondence theory, Proceedings of New Aspects of Non-Classical Logics and Their Kripke Semantics, RIMS Kokyuroku 1010, Kyoto University, 1997, pp. 1-6.
  13. G. Bezhanishvili. Monadic extentions of linear intermediate propositional logics, Logic, Methodology, and Philosophy of Science, Moscow-Obninsk, RGNF Press, 1995, Vol.II, pp. 3-6 (Russian).

Math Education publications

  1. J. Barnett, G. Bezhanishvili, J. Lodder, D. Pengelley. Teaching discrete mathematics entirely from primary historical sources, PRIMUS: Problems, Resources and Issues in Mathematics Undergraduate Studies, 26 (2016), pp. 657-675.
  2. J. Barnett, G. Bezhanishvili, H. Leung, J. Lodder, D. Pengelley, I. Pivkina, D. Ranjan, M. Zack, Primary historical sources in the classroom: Discrete mathematics and computer science, Loci: Convergence (July 2013), DOI: 10.4169/loci003984.
  3. G. Bezhanishvili, W. Fussner, An introduction to symbolic logic, Loci: Convergence (July 2013), DOI: 10.4169/loci003990.
  4. G. Bezhanishvili, E. Landreth, An introduction to elementary set theory, Loci: Convergence (July 2013), DOI: 10.4169/loci003991.
  5. J. Barnett, G. Bezhanishvili, H. Leung, J. Lodder, D. Pengelley, D. Ranjan. Historical projects in discrete mathematics and computer science, Resources for Teaching Discrete Mathematics, B. Hopkins, editor. MAA, 2009, pp. 165-274.

Preprints

  1. G. Bezhanishvili, R. Jansana. Duality for distributive and implicative semi-lattices, Preprints of University of Barcelona Research Group in Non-Classical Logics, 2008.
  2. G. Bezhanishvili, M. Gehrke. A new proof of completeness of S4 with respect to the real line, ILLC Prepublication Series, Technical Report PP-2002-06, University of Amsterdam, 2002.
  3. G. Bezhanishvili. Splitting monadic Heyting algebras, Report # IS-RR-97-0044F, JAIST, 1997.

Ph.D. Thesis

  1. G. Bezhanishvili. An Algebraic Approach to Intuitionistic Modal Logics Over MIPC, Ph.D. Thesis (167 pages), Tokyo Institute of Technology, 1998.

Master’s Thesis

  1. G. Bezhanishvili. On the Variety of Monadic Heyting Algebras, Master’s thesis (24 pages), Tbilisi State University, 1992 (Georgian).