Publications

 

To appear

  1. G. Bezhanishvili, J. Lucero-Bryan. More on d-logics of subspaces of the rational numbers, Notre Dame Journal of Formal Logic.
  2. G. Bezhanishvili. De Vries algebras and compact regular frames, Applied Categorical Structures.
  3. G. Bezhanishvili, R. Jansana. Esakia style duality for implicative semilattices, Applied Categorical Structures.
  4. G. Bezhanishvili, J. Harding. Modal logics of Stone spaces, Order.
  5. M. Aiello, G. Bezhanishvili, I. Bloch, V. Goranko. Logic for physical space from antiquity to present days, Synthese.

2011

6.      G. Bezhanishvili, P. Morandi. Order-compactifications of totally ordered spaces: Revisited, Order, 28 (2011), pp. 577—592.

7.      G. Bezhanishvili, P. Morandi. Priestley rings and Priestley order-compactifications, Order, 28 (2011), pp. 399—413.

8.      G. Bezhanishvili, N. Bezhanishvili. An algebraic approach to canonical formulas: Modal case, Studia Logica, 99 (2011), pp. 93—125.

9.      G. Bezhanishvili, R. Jansana. Priestley style duality for distributive meet-semilattices, Studia Logica, 98 (2011), pp. 83—122.

10.  G. Bezhanishvili, R. Jansana. Generalized Priestley quasi-orders, Order, 28 (2011), pp. 201—220.

11.  G. Bezhanishvili, P. Morandi. One-point order-compactifications, Houston Journal of Mathematics, 37 (2011), pp. 699—713.

12.  G. Bezhanishvili, S. Ghilardi, M. Jibladze. An algebraic approach to subframe logics. Modal case, Notre Dame Journal of Formal Logic, 52 (2011), pp. 187—202.

13.  G. Bezhanishvili, D. Gabelaia. Connected modal logics, Archive for Mathematical Logic, 50 (2011), pp. 287—317.

14.  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. 16—29.

2010

15.  G. Bezhanishvili, N. Bezhanishvili, D. Gabelaia, A. Kurz. Bitopological duality for distributive lattices and Heyting algebras, Mathematical Structures in Computer Science, 20 (2010), pp. 359—393.

16.  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. 61—69.

17.  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. 135—155.

18.  G. Bezhanishvili, P. Morandi. Scattered and hereditarily irresolvable spaces in modal logic, Archive for Mathematical Logic, 49 (2010), pp. 343—365.

19.  G. Bezhanishvili. Stone duality and Gleason covers through de Vries duality, Topology and Its Applications, 157 (2010), pp. 1064—1080.

20.  G. Bezhanishvili, L. Esakia, D. Gabelaia. The modal logic of Stone spaces: Diamond as derivative, Review of Symbolic Logic, 3 (2010), pp. 26—40.

2009

  1. 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.
  2. G. Bezhanishvili, N. Bezhanishvili. An algebraic approach to canonical formulas: Intuitionistic case, Review of Symbolic Logic, 2 (2009), pp. 517—549.
  3. G. Bezhanishvili, P. Morandi. Profinite Heyting algebras and profinite completions of Heyting algebras, Georgian Mathematical Journal, 16 (2009), pp. 29—47.
  4. G. Bezhanishvili, J. Harding. The modal logic of b(N), Archive for Mathematical Logic, 48 (2009), pp. 231—242.
  5. G. Bezhanishvili. Zero-dimensional proximities and zero-dimensional compactifications, Topology and Its Applications, 156 (2009), pp. 1496—1504.
  6. 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.

 2008

  1. G. Bezhanishvili, J. Vosmaer. Comparison of MacNeille, canonical, and profinite completions, Order, 25 (2008), pp. 299—320.
  2. G. Bezhanishvili, N. Bezhanishvili. Profinite Heyting algebras, Order, 25 (2008), pp. 211—227.
  3. 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.
  4. G. Bezhanishvili, R. Mines, P. Morandi. Topo-canonical completions of closure algebras and Heyting algebras, Algebra Universalis, 58 (2008), pp. 1—34.

2007

  1. G. Bezhanishvili and S. Ghilardi. An algebraic approach to subframe logics. Intuitionistic case, Annals of Pure and Applied Logic, 147 (2007), pp. 84—100.
  2. J. Harding and G. Bezhanishvili. MacNeille completions of modal algebras, Houston Journal of Mathematics, 33 (2007), pp. 355—384.
  3. 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.

2006

  1. G. Bezhanishvili, M. Gehrke, R. Mines, P. Morandi. Profinite completions and canonical extensions of Heyting algebras, Order, 23 (2006), pp. 143—161.
  2. J. van Benthem, G. Bezhanishvili, B. ten Cate, D. Sarenac. Multimodal logics of products of topologies, Studia Logica, 84 (2006), pp. 369—392.

2005

  1. G. Bezhanishvili, R. Grigolia. Locally finite varieties of Heyting algebras, Algebra Universalis, 54 (2005), pp. 465—473.
  2. G. Bezhanishvili, L. Esakia, D. Gabelaia. Some results on modal axiomatization and definability for topological spaces, Studia Logica, 81 (2005), pp. 325—355.
  3. 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.
  4. 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.

2004

  1. J. Harding, G. Bezhanishvili. MacNeille completions of Heyting algebras, Houston Journal of Mathematics, 30 (2004), pp. 937—952.
  2. 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.

2003

  1. M. Aiello, J. van Benthem, G. Bezhanishvili. Reasoning about space: the modal way, Journal of Logic and Computation, 13 (2003), pp. 889—920.
  2. J. van Benthem, G. Bezhanishvili, M. Gehrke. Euclidean hierarchy in modal logic, Studia Logica, 75 (2003), pp. 327—345.
  3. G. Bezhanishvili, R. Mines, P. Morandi. Scattered, Hausdorff-reducible, and hereditarily irresolvable spaces, Topology and Its Applications, 132 (2003), pp. 291—306.

2002

  1. G. Bezhanishvili, J. Harding. Functional monadic Heyting algebras, Algebra Universalis, 48 (2002), pp. 1—10.
  2. G. Bezhanishvili, R. Mines, P. Morandi. The Priestley separation axiom for scattered spaces, Order, 19 (2002), pp. 1—10.

2001

  1. G. Bezhanishvili. Locally finite varieties, Algebra Universalis, 46 (2001), pp. 531—548.
  2. G. Bezhanishvili. Glivenko type theorems for intuitionistic modal logics, Studia Logica, 67 (2001), pp. 89—109.
  3. 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.

2000

  1. G. Bezhanishvili. Varieties of monadic Heyting algebras. Part III, Studia Logica, 64 (2000), pp. 215—256.
  2. 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.

1999

  1. G. Bezhanishvili. Varieties of monadic Heyting algebras. Part II: Duality theory, Studia Logica, 62 (1999), pp. 21—48.

1998

  1. G. Bezhanishvili. Varieties of monadic Heyting algebras. Part I, Studia Logica, 61 (1998), pp. 367—402.

1997

  1. 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.
  2. 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.
  3. 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.