Лични средства
Вие сте тук: Начало Преподаватели Математическа логика и приложенията й проф. д.м.н. Димитър Вакарелов

проф. д.м.н. Димитър Вакарелов

Димитър Иванов Вакарелов

Професор, Катедра Математическа логика и приложенията й

dvak@fmi.uni-sofia.bg

Служебен телефон: 8161-596

Кабинет: ФМИ-510

Лична страница

Научни интереси

  • Математическа логика
  • Некласически логики

Научни проекти

Проект № MИ 1510/2005  "Приложни логики и топологични структури" с фонд "Научни изследвания" към Министерството за образование и наука

Преподавателска дейност

Зимен семестър 2006 - 2007

  • Математическа логика, спец. информатика, хорариум 3+1
  • Модална логика за магистри, 3+1

 

Летен семестър 2006 - 2007

  • Логически основи на информационните системи, спец. информатика, хорариум 3+0
  • Некласически логики за изкуствен интелект, спец. информатика, хорариум 3+0
  • Математическа логика, спец. информатика, хорариум 3+1

Приемно време

четвъртък   13-14  к. 523 ФМИ

Публикации


[1] L. Maksimova and D. Vakarelov, Representation theorem for
generalized Post algebras of order $\omega +$. Bull. Acad. Polon.
Sci. Ser. Math. Phis., 22(1974), 757-764.

[2] L. Maksimova and D. Vakarelov, Semantics for $\omega +$-valued
predicate Calculi, Bull. Acad. Polon. Sci. Ser. Math. Phis.,
22(1974), 765-771.

[3] Representation theorem for semi-Boolean algebras and semantics
for HB-predicate logic, Acad. Polon. Sci. Ser. Math. Phis.,
22(1974), 1087-1095.

[4] Theory of negation in certain logical systems. Algebraic and
semantical approach. Ph.D. dissertation, University of Warsaw,
1976.

[5] Models for constructive logic with strong negation. V Balkan
Mathematical Congress, Beograd, 1976, abstracts, pp 298.

[6] Generalized Nelson lattices, IV Vsesojuznaja Konferencija po
matematicheskoj logike, Kishinev  1976, abstracts, pp 298. (in
Russian)

[7] Lattices related to Post algebras and their applications to
some logical systems. Studia Logica, 36(1977), 89-107.

[8] Notes on Constructive logic with strong negation, Studia
Logica, 36(1977), 110-125.

[9] M. Mircheva and D. Vakarelov, Modal Post algebras and
many-valued modal logics, Comptes rendus de l'Academie Bulg. des
sci. 33, 5, (1980), 591-593.

 [10] Simple examples of incomplete logics, Comptes rendus de l'Academie Bulg. des sci.
33,5, (1980), 103-118.

[11] Intuitionistic modal logics incompatible with the law of
excluded middle, Studia Logica, XL, 2, 1981, 103-111.

[12] Filtration theorem for dinamic algebras with tests and
inverse operator, Lecture Notes in Computer Science No 148, 1983.

[13] T. Tinchev and D. Vakarelov, Propositional Dynamic Logic with
least fixed points which are programs, In: Summer School on
mathematical logic and its applications, abstracts, Publishing
hous of the Bulgrian Acad. of Sci., Sofia, 1983, 64-67.

[14] T. Tinchev and D. Vakarelov, Propositional Dynamic Logic with
Counters and stacks, in: Lecture Notes in Computer Science No 208,
1985.

[15] T. Tinchev and D. Vakarelov, Propositional Dynamic logic with
Counters, In: Mathematical Theory of programming, Novosibirsk,
1985, 50-57.


[16] Abstract characterization of some  knowledge representation
systems and the logic NIL  of  nondeterministic information,  in:
AIMSA'87  Artificial  Intelligence   II, Methodology,   Systems,
Applications, Ph. Jorrand and V. Sgurev ed., North-Holland, 1987.


[17] S4 and S5 together - S4+5. In the proc. of LMPS'87, Moskow,
USSR, 1987, abstracts, vol. 5, part 3, pp 271-274.

[18] T. Tinchev and D. Vakarelov, Propositional Dynamic Logic with
recursive programs, In: Banach Center Publications, vol. 21, 1998,
419-426, PWN, Warsaw, 1988.

[19] Modal  characterizations  of  the  classes  of  finite  and
infinite quasi-ordered sets. In: Heyting'88:  Mathematical  Logic,
P. Petkov ed., Plenum Press,pp 373-397, 1989.

[20]  Consistency, Completeness and Negation. In: Paraconsistent
Logic. Essays on the Inconsistent. Gr. Priest, R. Routley and J.
Norman Eds. Analitica, Philosophia Verlag, Munhen, 1989.

[21] Intuitive semantics for some three-valued logics connected
with information, contrariety and subcontrariety, Studia Logica,
XLVIII, 4, 1989, 565-575.

[22] Modal Logics for reasoning about arrows: Arrow logics, In the
Proceedings of 9-th International Congress of Logic, Methodology
and Philosophy of Science, Section 5 Philosophical Logic, August
7-14, 1991


[23] Modal logics for knowledge representation systems, LNCS 363,
1989, 257-277, Theoretical Computer Science, 90(1991) 433-456.

[24] A modal logic for similarity relations in  Pawlak  knowledge
representation systems, Fundamenta Informaticae, XV(1991),61-79.

[25]  Logical  analysis  of  positive  and  negative   similarity
relations  in  property  systems.  In:  WOKFAI'91,   First   World
Conference  on the Fundamentals of  Artificial  Intelligence,  1-5
July 1991, Paris, France, Proceedings ed. Mishel De Glas  and  Dov
Gabbay, pp 491-499.

[26]  Rough  polyadic  modal logics,  Journal  of  Applied  Non-
Classical Logics, vol. 1, 1(1991), 9-35.

[27] A modal theory of arrows. Arrow logics  I.  Invited  lecture
in: D. Pearce and  G.  Wagner  (Eds.)  "Logics  in  AI",  European
Workshop JELIA'92, Berlin, Germany, September 1992, LNAI  No  633,
pp 1-24. Updated version is published under the title ``Modal
Logics of Arrows" in M. de Rijke (ed.) Advances in Intensional
Logic, 137-171,, Kluwer Academic Publishers, Dordrecht, 1997.

[28] Consequence relations and Information Systems. In:
``Intelligent Decision Support, Handbook of Applications and
Advances in Rough Sets Theory", Ed. R. Slowinski, 391-400, Kluwer
academic Publishers, 1992.


[29] Inductive Modal  Logics,  Fundamenta  Informaticae  16(1992)
383-405.

[30]  A  Modal  Logic  for  Cyclic  Repeating.  Information   and
Computation, vol 101, No 1 November 1992, 103-122

[31] Arrow logics with cylindric operators, Abstract,
1992-European Summer Meeting of the  ASL. Journal of Symbolic
logic, vol 58, No 3, 1993, 1135-1136.

[32] Modal rules of Intersection, Abstract, 1994-European Summer
Meeting of ASL, p. 126, In the Bulletin of Symbolic Logic, vol. 1,
No 2, 1995, 264-265.

[33] A modal logic for set relations, Abstract, 10-th
International Congress of Logic, Methodology and Philosophy of
Science, 1995, Florence, Italy, p. 183.

[34] Logic in Central and Eastern Europe: Balkan Region. Invited
lecture at the 10-th International Congress of Logic Methodology
and Philosophy of Science, 1995, Florence, Italy. In: ``Logic and
Scientific methods, vol 1 of the 10-th International congress of
Logic Methodology and Philosophy of Science, Florence, August
1995, pp 485-4495. Kluwer Academic Publishers, 1997.

[35] Many-dimensional Arrow Logics. Journal of Applied
Non-Classical Logics, vol.  6, No 4 (1996), 303-345

[36] Many-dimensional  arrow  structures.  Arrow  logics  II. in:
M. Marx, L. Pplos and  M.  Masuch  (Eds.),  "Arrow  Logic  and
Multi-Modal Logic", pp 141-187.  Studies  in  Logic  Language  and
Information, Stanford, California, 1996.

[37] Hyper Arrow logics, Abstract, Logic Colloquium'96, Donostia,
san Sebastian, July 9-15, 1996, p. 155.

[38] Balbiani, F., L. Farinas del Cerro, T. Tinchev, D. Vakarelov,
Modal Logics for Incidence  Geometries,  Journal  of Logic  and
Computation, vol 7, No 1 (1997) 59-78.

[39] Hyper Arrow Structures. Arrow Logics III. In: M.Kracht, M. de
Rijjke, H. Wansing and M. Zakharyaschev Eds.  "Advances  in  Modal
Logic'96", pp 253-273. Studies in Logic, Language and Information,
Stanford, California, 1997.

[40] Proximity  Modal  Logics,  In  the  Proceedings  of  the
11-th Amsterdam  Colloquioum,  December  17-20,   1997,   pp.
301-306. Amsterdam.

[41] Ana Deneva and Dimiter Vakarelov, Modal Logics  for  Local
and Global Similarity Relations, Fundamenta Informaticae, vol  31,
No 3,4, (1997), 295-304.


[42]  Information Systems, Similarity Relations  and Modal Logics,
in:E. Orlowska (ed.) "Incomplete Information:  Rough Set
Analysis",  pp.  492-550  Studies  in  Fuzziness   and   Soft
Computing, Phisica-Verlag Heidelberg New York, 1998.

\newpage
[43] Applied Modal Logic: Modal Logics  in  Information  Science.
Doktoral Dissertation, 1996. Published in  the  ILLC-publications,
University of Amsterdam, 1998.


[44] Georgi  Dimov  and  Dimiter  Vakarelov,  On  Scott
consequence systems, Fundamenta Informaticae 33(1998), 43-70.

[45] Valentin Goranko and Dimiter Vakarelov,  Hyperboolean
Algebras and Hyperboolean Modal Logic, Verslagreeks  van  die
Departement Wiskunde, RAU, No 1/1998. Also:  in    Journal  of
Applied Non-Classical Logic, v.9, No 2-3(1999), 345-368.

[46] Valentin Goranko and Dimiter Vakarelov, Modal Logic and
Universal Algebra.  I.  Modal Axiomatizations of structures.
Verslagreeks  van  die  Departement Wiskunde, RAU, No 1/1998. In
the Proc. of AiML'98.

[47] P. Balbiani and D. Vakarelov, Iteration-free PDL with
Intersection: a Complete axiomatization, Fundamenta Informaticae
33 (1998) 1-22.

[48] Demri, S., Orlowska, E., Vakarelov, D. Indiscernibility and
complementarity relations in information systems. In Gerbrandy,
J., Marx, M., de Rijke, M., Venema, Y. (Eds.): JFAK: Esays
dedicated to Johan van Benthem on the ocasion of his 50-th
Birthday. Amserdam University Press (1999),

http://turing.wins.uva.nl/j50/cdrom/contribs/demri/index.html.


[49] V. Goranko and D. Vakarelov, Sahlqvist formulas Unleashed in
Polyadic Modal languages, in: Advances in Modal Logic'2000,
Leipzig, October 4-7, 2000.

[50] V. Goranko and D. Vakarelov, Sahlqvist Formulas in Hybrid
Polyadic Modal logics. Journal of Logic and Computation, vol. 11,
No 5, pp 737-754, 2001.

[51] P. Balbiani and D. Vakarelov, A modal Logic for
Indiscernibility and Complementarity in Information Systems.
Fundamenta Informaticae 45(2001) 173-194.

[52] Vakarelov, D. Duntsch, I., and Bennett, B. A note on
proximity spaces and connection based mereology. In C. Welty and
B. Smith (Eds), Proceedings of the 2nd International Conference on
Formal Ontology in Information Systems (FOIS'01) 139-150, ACM.

[53] Vakarelov, D., Dimov, G., and Bennett, B. A proximity
approach to some region based theories of space. Journal of
Applied Non-Classical Logics, 12 (2002), 527-559.

[54] Modal definability in languages with a finite number of
propositional variables and a new extension of the Sahlqvist's
class. Advances in Modal Logic, vol 4, (2002) 499-518.

[55] V. Goranko, U. Hustadt, R. Schmidt, and D. Vakarelov, SCAN is
complete for all Sahlqvist formulae, Proc. of RelMICS'03, 2003,
in: LNCS No 3051, Springer, pp 149, 162.

[56] I. Duentsch and D. Vakarelov, Region-based theory of discrete
spaces: A proximity approach. Invited lecture in Fourth
International Conference JIM'2003, September 3-6, 2003, Metz,
France, Knowledge Discovery and Discrete Mathematics, at http:
//www.cosc.brocku.ca/Department/Research/TR/cs0304.pdf to appear
in Discrette Applied Mathematics.

[57] On a generalization of the Ackermann's Lemma for computing
first-order equivalents of modal formulas. Abstract. TARSKI
Workshop, March 11-13, 2003, Toulouse.

 [58] P. Balbiani and D. Vakarelov, Dynamic Extension of Arrow
Logic. Annals of Pure and Applied Logic, vol. 127 (1-3) (2004),
1-5.

[59] Exstended Sahlqvist Formulas and Solving Equations in Modal
Algebras, Abstract, 12-th International Congress of Logic
Methodology and Philosophy of Science, August 7-13, 2003, Oviedo,
Spain, p 33 in the Program.

\newpage
[60] Orlowska, E., D. Vakarelov, Lattice based Modal logics and
Modal algebras. Invited Lecture, 12-th International Congress of
Logic, Methodology and Philosophy of Science, August 7-13, 2003,
Oviedo, Spain, p. 33 in the Program. To appear in the Proceedings.


[61] G. Dimov and D. Vakarelov, Construction of all locally
compact extensions of Tychonoff spaces by means of non-symmetrical
proximities. Abstract, Proc. of the International Mathematical
Congress MASSEE'03, Borovets, September 15-21, 2003, Bulgaria.

[62]  P. Balbiani and D. Vakarelov, Dynamic Extension of Arrow
Logic.  Annals of Pure and Applied Logic 127 (2004), 1-15.


[63]  I. Duntsch, E. Orlowska, A. Radzikowska and D. Vakarelov.
Relational representation theorem of some lattice-based
structures. Journal of Relational Methods in Computer Science,
vol. 1, 2004, 132-160.

[64]  D. Vakarelov and G. Dimov, Topological representation of
precontact algebras. Invited lecture in  ReLMiCS'05, St.
Catharines, Canada, February 22-26, 2005, Extended abstract in the
Proc. pp. 269-271.

[65] W. MacCaull, D. Vakarelov, Lattice-based paraconsistent
logic. ReLMiCS'05, St. Catharines, Canada, February 22-26, 2005,
Extended abstract in the Proc. pp. 155-162.


[66] A modal Characterization of indiscernibility and similarity
relations in  Pawlak's information systems, In: LNAI 3641, 2005,
pp 12-22.

[67]  Nelson's negation on the base of weaker versions of
intuitionistic negation, Studia Logica, vol. 80,  2005, pp.
393-430.

[68] W. Conradie, V. Goranko, D. Vakarelov. Elementary Canonical
Formulae: a survey on syntactic, algorithmic and model-theoretic
aspects. In: Advances in Modal Logic, vol. 5. Kings College London
Pub. 2005, pp. 17-51.

[69] On a generalization of Ackermann Lemma for computing
first-order equivalents of modal formulas. Logic Colloquium'2005,
July 28- August 3, 2005, Athens, Greece, Abstracts, p. 123.

[70]A Modal Characterization of Indiscernibility and Similarity
Relations in Pawlak's Information Systems. Invite paper in:  Rough
Sets, Fuzzy Sets, Data Mining, and Granular Computing, 10th
International Conference RSFDGrC-2005, Rgina, Canada,
August/September 2005, Proceedings, Part I. LNAI No 3641, 12-22,
Springer.

[71] Modal definability, solving equations in modal algebras and a
generalizations of Ackermann Lemma. 5-th Panhellenic Logic
Symposium, July 25-28, 2005, Athens, Greece, Proceedings, pp.
182-189.

[72] On a generalizations of Ackermann Lemma for computing
first-order equivalents of modal formulas.  Logic Collquium 2005,
July 28 - August 3, Athens, Greece, Abstracts, page 123.

[73] Solving recursive equations in complete modal algebras with
applications to modal definability. In: "Pioneers of Bulgarian
Mathematics", International Conference dedicated to Nikola
Obrechkoff and Lubomir Tschakaloff, Sofia, July 8-10, 2006,
Abstracts.

[74] Nonclassical Negation in the Works of Helena Rasiowa and
Their Impact  on the Theory of Negation. Studia Logica, vol 84, No
1, 2006, 105-127.

[75] V. Goranko, D. Vakarelov, Elementary Canonical Formulae:
Extending Sahlqvist Theorem. Annals of Pure and Applied Logic,
vol. 141, 1-2, 2006, 180-217.

[76] W. Conradie, V. Goranko, D. Vakarelov, Algorithmic
Correspondence and Completeness in Modal Logic, I. The Core
Algoritm SQEMA.  Logical Methods in Computer Science, vol 2 (1:5),
2006, 1-26.

\newpage
[77] Willem Conradie; Valentin Goranko; Dimiter Vakarelov.
Algorithmic Correspondence and Completeness in Modal Logic. II.
Polyadic and Hybrid Extensions of the Algorithm SQEMA. Journal of
Logic and Computation 2006; doi: 10.1093/logcom/exl026.

[78]G. Dimov and D. Vakarelov, Topological representations of
precontact algebras. LNCS No 3929, 2006, 1-16, Springer.

[79] W. MacCaul, D. Vakarelov, Lattice-based Paraconsistent Logic.
LNCS No 3929, 2006, 173-187. Springer.


[80]D. Georgiev, T. Tinchev, D. Vakarelov, SQEMA - an algorithm
for computing first-order correspondents in modal logic: a
computer realization. In: "Pioneers of Bulgarian Mathematics",
International Conference dedicated to Nikola Obrechkoff and
Lubomir Tschakaloff, Sofia, July 8-10, 2006, Abstracts.

[81] G. Dimov and D. Vakarelov. Contact Algebras and Region-based
Theory of Space: A Proximity Approach. I. Fundamenta Informaticae,
74 (2006), 209-249.

[82] G. Dimov and D. Vakarelov. Contact Algebras and Region-based
Theory of Space: A Proximity Approach. II. Fundamenta
Informaticae, 74, (2006), 251-282.

[83] Region-Based Theory of Space: Algebras of Regions,
Representation Theory, and Logics. Invited paper in: Mathematical
Problems from Applied Logic. New Logics for the XXIst Century. II.
Edited by Dov M. Gabbay et al. International Mathematical Series.
Springer. To appear in 2007.

[84] Ph. Balbiani, T. Tinchev and D. Vakarelov, Dynamic logic of
region-based theory of discrete  spaces. To appear in the Journal
of Non-Classical Logic, 2007.

[85] Ph. Balbiani, D. Vakarelov,  Arrow logic with arbitrary
intersections: applications to Pawlak's information systems.
Fundamenta Informaticae, to appear in 2007.