<HTML> <META NAME="description" content="Institute of Cybernetics"> <META NAME="keywords" content="Georgia, Caucasus, "> <META http-equiv="Content-Type" content="text/html; charset=utf-8"> <TITLE>Institute of Cybernetics - Revaz Grigolia</TITLE> </head> <BODY BGCOLOR=#ffffee leftMargin=10 rightMargin=10 topMargin=5 MARGINWIDTH="0" MARGINHEIGHT="0"> <font face=" Sylfaen"> <hr><TABLE border=0 cellPadding=7 cellSpacing=0 width="100%"><TBODY><TR> <TD width="11%" vAlign=top><center><font size=-1><a href=index.html><br>Home</a></font></center></TD> <TD width="11%" vAlign=top><center><font size=-1><a href=ann.htm><br>Announcements</a></font></center></TD> <TD width="11%" vAlign=top><center><font size=-1><a href="reg.pdf" target="_blank"><br>Regulations</a></font></center></TD> <TD width="16%" vAlign=top><center><font size=-1><a href=aca.htm> <br>Academic Council</a></font></center></TD> <TD width="16%" vAlign=top><center><font size=-1><a href=str.htm>  <br>Structure & Staff</a></font></center></TD> <TD width="16%" vAlign=top><center><font size=-1><a href=rep.htm> <br>Annual report</a></font></center></TD> <TD width="19%" vAlign=top><center><font size=-1><a href=pro.htm> <br>International Projects</a></font></center></TD> </TR></TBODY></TABLE> <hr> <TABLE border=0 cellPadding=7 cellSpacing=0 width="100%"><TBODY> <TR><TD width="50%" vAlign=top><center><img alt="Revaz Grigolia" src="grigolia.jpg" border=0 width=400 height=300></center> </TD><TD width="50%" vAlign=center><center><font size=+2> <br><br>Revaz Grigolia<br><br>CV</font></center> </TD></TR></TBODY></TABLE> <TABLE border=0 cellPadding=7 cellSpacing=0 width="100%"><TBODY> <TR><TD width="50%" vAlign=top<p><b>1. POSITION: </b><br> Deputy director of the Institute of Cybernetics,<br> Head of logic group of the Institute of Cybernetics. <br> Associate Professor of Exact and Natural Sciences Faculty at Tbilisi State University.</p> <p><b>OFFICE ADDRESS: </b><br>Sandro Euli str., 5, 0186 Tbilisi, GEORGIA.<br> Tel: +995 32 304019, +995 32 307055, Fax: +995 32 305931, Mob.: +995 55 179 612<br> E-mail: <a href="mailto:grigolia@yahoo.com">grigolia@yahoo.com</a></p> <p><b>HOME ADDRESS: </b><br> G. Kikodze str., 12, 0105 Tbilisi, GEORGIA <br> Tel: +995 32 998853</p> <p><b>3. PERSONAL INFORMATION: </b> <ul><li>the place and the date of birth: GEORGIA, Senaki, 22 July 1947; <br> <li>nationality, citizenship: Georgian, citizen of Georgia; </li> <li>family status: married </li> &nbsp&nbsp<li>the wife: Tamar Nanukashvili</li> &nbsp&nbsp<li>the children: <ul><li>Gvantsa Grigolia - born in 1988,</li><li>Shota Grigolia - born in 1990.</li></ul></li></ul></p> <p><b>4. EDUCATION: </b> <ul><li>Graduated from Tbilisi State University, the department of Cybernetics and Applied Mathematics - graduation paper: "Many-valued Logics and their extensions" (1970); </li> <li>Graduated from the Post Graduated Course of Tbilisi State University in speciality mathematical logic and algebra (1973); </li> <li>PhD in Mathematics, 1976 : "Algebraic analysis of Lukasiewicz-Tarski n-valued logical systems", Moscow State pedagogical Univesity (Moscow State University - leading organization) (1976).</li> <li>Doctor of Sciences, 2006 :  Free algebras of non-classical logics , Tbilisi State University.</li></ul></p> <p><b>5. ACADEMIC ACTIVITY:</b> <ul><li>since 1973 works at the Institute of Cybernetics of Georgian Academy of Sciences; </li> <li>1973 - 1983 - junior researcher of the Institute; </li> <li>1983 - 1993 - Secretary general of the Institute of Cybernetics of Georgian Academy of Sciences;</li> <li>1993-1998 - Senior researcher of Department of Mathematical Logic of the Institute of Cybernetics;</li> <li>1998  2003 - Leading Researcher of Department of Mathematical Logic of the Institute of Cybernetics;</li> <li>2003  2005 - Senior Researcher of Department of Optimal Processes and Informatics of the Institute of Cybernetics.</li> <li>Since 2006 - Head of group of mathematical logic of the Institute of Cybernetics.</li></ul></p> <p><b>6. Participation in various scientific forums</b> <ul><li> Free and projective Heyting and monadic Heyting algebras , <b>14th Linz Seminar on  Fuzzy Set Theory, Non-classical Logics and their Applications </b>, September 7-11, 1992, Austria (Invited Speaker)</li> <li> Free MV-algebras , <b> International Seminar on  Order in Algebra and Logic with application </b>, III; February 9-12, 1993, Napoli University, Italy. <b>(Invited Speaker) </b></li> <li>  Free Algebras in Subvarieties of MV-algebras , <b>International Seminar on  Order in Algebra and Logic with application </b>, IV; February 8-11, 1994, Napoli University, Italy.</li> <li> Automorphism groups of free MV-algebras , <b>International Seminar on  Order in Algebra and Logic with application </b>, V; March 21-25, 1995, University of Oxford, England. (Invited Speaker)</b></li> <li>  Introduction in algebras of Intuitionistic logic , <b>Scool  Many-valued Loggics and their Applications </b>, October 7-12 , 1996, University of Salerno, Ravello, Italy. <b> (Invited Speaker)</b></li> <li> Projective MV-algebras and their automorphism groups , <b>International Seminar on  Order in Algebra and Logic with application </b>, VII; April 21-25, 1997, Marseille  Lumini, France. <b> (Invited Speaker)</b></li> <li>  MV-algebras with finite spectrum , <b>International workshop on  Many-valued Logics for Computer Sciences </b>, June 19  21, 1997, Patras, Greece. <b> (Invited Speaker)</b></li> <li> Monadic Fuzzy Logic , <b>International Workshop  Issues in non-classical logics </b>, 14-16 March, 2001, University of Milan, Italy. <b>(Invited Speaker)</b></li> <li> On one problem of Harvey Friedman , <b> International Conference on  Algebraic and Topological Methods in Non-Classical Logics </b>, July 7  11, 2003, Tbilisi, Georgia.</li> <li> Co-product of Heyting algebras , <b>International Conference on  Algebraic and Topological Methods in Non-Classical Logics </b>, July 15  18, 2005, Barselona, Spain.</li> <li> On projective MV-algebras , <b>International Conference on  Algebraic and Topological Methods in Non-Classical Logics.III </b>, August 04  13, 2007, Oxford, England</li> <li>  Monadic BL-algebras , <b> International Conference on Order, Algebra, and Logics,</b> Vanderbilt University, June 12-16, 2007, USA</li> <li> Monadic residuated algebras  ,<b>Workshop "Algebra and its applications"</b>, May 4-6, 2007, Ratnieki (Latvia) <b>(Invited Speaker) </b></li> <li> Modal and Temporal Logics , <b>Third Vienna Tbilisi Summer School in Logic and Language </b>, 24-28, September 2007, Tbilisi, Georgia <b> (Invited Speaker)</b></li> <li> On Medvedev s Logic , <b>Seventh International Tbilisi Symposium on Language, Logic and Computation</b>, Tbilisi, October 1-5, 2007, Georgia</li></ul></p> <p><b>7. Participation in grant projects </b> <ul><li>The grant of Cariplo Foundation organized by The Landau Network-Centro Volta, 2001.</li> <li>Georgian-U.S Bilateral Grants. Georgian Research and Development Foundation (GRDF) And U.S. Civilian Research and Development Foundation (CRDF),  Applications of Topology and Universal Algebra to Modal Logic , 2003-2004.</li> <li>Grant of Italian Ministry of Foreign Affairs for Institute of Cybernetics Georgian Academy of Sciences and Slerno and Napoli Universities (Italy), 2003-2004.</li> <li>The grant of Cariplo Foundation organized by The Landau Network-Centro Volta, 2005.</li> <li>Grants of Georgian Academy of Sciences, 1999-2005.</li></ul></p> <p><b>8. PEDAGOGICAL ACTIVITY:</b> <ul><li> 1971 -1973 conducts practical studies with the students at the Department of Cybernetics and Applied Mathematics of Tbilisi State University; </li> <li>1983 - 1985 - lectures on Mathematical Logic at Tbilisi State University and since 1986 at Tbilisi State Pedagogical University; </li> <li>since 1994 - lectures on Descrete Mathematics at the Department of Applied Mathematics and Informatics of Tbilisi State University. </li> <li>2005 - lectures on Mathematical Logic for student and Ph.D students at Milan University (Italy) </li> <li>2006 - associate professor of Tbilisi State University.</li></ul></p> <p><b>9. AREA OF RESEARCH :</b> <ul><li>Modal Logic (Including Provability Logic),</li><li>Intuitionistic Logic,</li><li> Algebraic Logic,</li><li>Many-valued Logics, Fuzzy Logic.</li></ul></p> <p align=justify><b>10. SUMMARY OF SCIENTIFIC PAPERS:</b><br>The algebraic semantics of n-valued Lukasiewizc-Tarski logical systems is constructed, on base of which the axiomatic of that logical systems is obtained. n-generated free MV-algebras, corresponding to n- valued Lukasiewicz logics, is described. The criterion of finitely generatability of Heyting algebras and Closure algebras is given. Free algebras, free products, projective algebras are described in varieties, the algebras of which form models of such known non-classical logics as Lewis modal system, Grzegorchic system, bi-modal system, Godel logic of provability, Intuitionistic logic, many-valued logic of Lukasiewicz and their extensions.</p> <p><b>11. INVITED SPEAKER</b> <ul><li><b> Free and projective Heyting and monadic Heyting algebras </b>, 14th Linz Seminar on Fuzzy Set Theory, Non-classical Logics and their Applications, September 7-11, 1992</li> <li><b> Free MV-algebras </b>, International Seminar on  ORDER IN ALGEBRA AND LOGIC WITH APPLICATION , III; February 9-12, 1993, Napoli University.</li> <li><b> Free Algebras in Subvarieties of MV-algebras </b>, International Seminar on  ORDER IN ALGEBRA AND LOGIC WITH APPLICATION , IV; February 8-11, 1994, Napoli University.</li> <li><b> Automorphism groups of free MV-algebras </b>, International Seminar on  ORDER IN ALGEBRA AND LOGIC WITH APPLICATION , V; 21-25 March, 1995, University of Oxford.</li> <li><b> Introduction in algebras of Intuitionistic logic </b>, Scool  Many-valued Loggics and their Applications , 7-12 October , 1996, University of Salerno, Ravello.</li> <li><b> Projective MV-algebras and their automorphism groups </b>, International Seminar on  ORDER IN ALGEBRA AND LOGIC WITH APPLICATION , VII; 21-25 April, 1997, Marseille  Lumini, France.</li> <li><b> Monadic Fuzzy Logic </b>, International Workshop  Issues in non-classical logics , 14-16 March, 2001, University of Milan.</li> <li><b> Monadic residuated algebras  </b>, Workshop "Algebra and its applications", May, 4-6, 2007, Ratnieki (Latvia)</li> <li><b> Modal and Temporal Logics </b>, Third Vienna Tbilisi Summer School in Logic and Language , 24-28, September 2007, Tbilisi, Georgia.</li></ul></p> <p><b>12. VISITING POSITIONS</b> <ul><li>1994 Visiting Professor of Napoli University</li> <li>1997 Visiting Professor of Napoli University</li> <li>2004 Visiting Professor of Napoli University</li></ul></p> <p><b>11. SELECTED PUBLICATIONS: </b> <ul><li>1.<i>"Algebraic analysis of Lukasiewicz-Tarski n-valued logical systems"</i>, Selected papers on Lukasiewicz Sentential Calculi, Wroclaw, 81-91 (1977).</li> <li>2.<i>"Free algebras of non-classical logics"</i> (in Russian), Metsniereba Press, Tbilisi, 1987.</li> <li>3. (with V.K. Finn) <i>"Nonsense logic and their algebraic properties"</i>, THEORIA, vol. LIX(1993), Part 1-3, pp.203- 273.</li> <li>4. <i>"Free and projective Heyting and monadic Heyting algebras"</i>, Non-classical Logics and their applications to fuzzy subsets (Ed. Ulrich Hole and Erich Peter Klement), 1995, 33-52.</li> <li>5. (with A. Di Nola and G.Panti), <i>"Finitely generated free MV-algebras and their automorphism groups"</i>, Studia Logica, vol. 61(1998), N 1, 65-78.</li> <li>6. (with G. Bezhanishvili) <i>"Locally tabular extensions of MIPC"</i>, Proceedings of Uppsala Symposium ", Advances in Modal Logic'98" vol. 2, Csli Publications, Stanford, California, 101-120 (2001)</li> <li>7. (with A. Di Nola) <i> Projective MV-algebras and their automorphism groups </i> , Mutiple valued Logic , vol. 8, issue 6, 2002.</li> <li>8. (with A. Di Nola) <i> MV-algebras in duality with labeled root systems </i>, Discrete Mathematics, 243 (2002) 79-90. <li>9. (with A. Di Nola) <i> On Monadic MV-algebras </i>, APAL, Vol. 128, Issues 1-3 (August 2004), pp. 125-139. <li>10. (with A. Di Nola) <i> Pro-finite MV-spaces </i>, Discrete Mathematics , Vol. 283, Issues 1-3 (6 June 2004), pp. 61-69.</li> <li>11. (with L.P. Belluce and A. Lettieri) <i> Representations of monadic MV-algebras </i>, Studia Logica, vol. 81, Issue October 15th, 2005, pp. 125-144.</li> <li>12. <i>Co-products of three-element Heyting algebras</i>, Bulletin of Georgian Academy of Sciences, vol. 172, N. 2, 2005.</li> <li>13. <i>Monadic BL-algebras</i>, Georgian Mathematical Journal, vol. 13 (2006), No. 2.</li> <li>14. <i>Co-products of Heyting algebras</i>, Proceedings of A. Razmadze Mathematical Institute, vol. 140 (2006), 83-89.</li> <li>15. (with A. Di Nola and A. Lettieri), <i> Projective MV-algebras </i>, International Journal of Approximate Reasoning, v. 47 (2008), pp. 323-332; Available online 4 July, 2007.</li></ul></p> </TD><TD width="50%" vAlign=top><p><b>1. , ,  :</b><br>   </p> <p><b>2. , , , -:</b><br>0186, ,   ., 5,  <br> : +995 32 304019, +995 32 307055, : +995 32 305931, .: +995 55 179 612<br> -: <a href="mailto:grigolia@yahoo.com">grigolia@yahoo.com</a></p> <p><b>3.  :</b> 22  1947</p> <p><b>4. :</b> <ul><li>  ,     ,         (1970);</li> <li>         (1970-1973);</li> <li>  :  - n-     ,    ( -  ) (1976).</li> <li>  :      ,   . (2006)</li></ul></p> <p><b>5.   (   )</b> <ul><li>1998  2003         ;</li> <li>2003- - 2006 -          ;</li> <li>2006-     I ;   </li> <li>2006-   .   .</li></ul></p> <p><b>6.   , :</b> <ul><li>1. L. P. Belluce, R. Grigolia, A. Lettieri, <i>"Representations of monadic MV-algebras"</i>, Studia Logica, vol. 81 (2005), October 15, 123-144.</li> <li>2. G. Bezhanishvili and R. Grigolia, <i> Locally Tabular Extensions of MIPC </i>, Proceedings of Uppsala Symposium ", Advances in Modal Logic'98" , vol. 2, Csli Publications, Stanford, California, 101-120 (2001).</li> <li>3. G. Bezhanishvili and R. Grigolia, <i> Subalgebras of free cyclic Heyting algebras </i>, Proceedings of Institute of Cybernetics, vol. 1, N 1-2, 2000.</li> <li>4. G. Bezhanishvili, R. Grigolia, <i> Locally finite Heyting algebras </i>, Algebra Universalis, Vol. 54, (December 2005), Nu. 4, pp. 465-473.</li> <li>5. A. Di Nola , R. Grigolia, G. Panti, Finitely generated free MV-algebras and their auto-morphism groups, Studia Logica, vol.61, N1, 65-78(1998).</li> <li>6. A. Di Nola, R. Grigolia, A. Lettieri, V.Loia, <i> Cellular logic based automata </i>, Proceedings of Institute of Cybernetics, vol. 2, N 1-2, 2002.</li> <li>7. A. Di Nola and R. Grigolia, <i> Projective MV-Algebras and Their Automorphism Groups </i>, J. of Mult.-Valued Logic & Soft Computing., Vol. 9, (2003), pp. 291-317.</li> <li>8. A. Di Nola, R. Grigolia, <i> MV-algebras in duality with labeled root systems </i>, Discrete mathematics, 243 (2002), 79-90.</li> <li>9. A. Di Nola, R. Grigolia, <i> On Monadic MV-algebras </i>, APAL, vol. 128, Issues 1-3 (August 2004), pp. 125-139.</li> <li>10. Grigolia, <i> Pro-finite MV-spaces </i>, Discrete Mathematics , Vol. 283, Issues 1-3 (6 June 2004), pp. 61-69. <li>11. A. Di Nola, R. Grigolia, <i> Free BL-algebras </i>, Proceedings of the Institute of Cybernetics, Vol. 3, N1-2 (2004), pp.22-31.</li> <li>12. R. Grigolia, <i> Free and projective Heyting and monadic Heyting algebars </i>, Non-classical Logics and their applications to fuzzy subsets (Ed.U. Hole and E.P.Klement), Kluwer Acad. Publ.,33-52 (1995).</li> <li>13. R. Grigolia, <i> Free Heyting algebras and their automorphism groups </i>, Proceedings of Institute of Cybernetics, vol. 2, N 1-2, 2002.</li> <li>14. R. Grigolia, <i> Co-products of Heyting algebras </i>, Proceedings of A. Razmadze Mathematical Institute, vol. 140 (2006), 83-89.</li> <li>15. R. Grigolia, <i> Co-products of three-element Heyting algebras </i>, Bulletin of Georgian Academy of Sciences, vol. 172, N. 2, 2005.</li> <li>16. R. Grigolia (with A. Di Nola and A. Lettieri), <i> Projective MV-algebras </i>, International Journal of Approximate Reasoning, v. 47 (2008), pp. 323-332; Available online 4 July, 2007.</li></ul></p> <p><b>7.     </b> <ul><li> Free and projective Heyting and monadic Heyting algebras , <b>14th Linz Seminar on  Fuzzy Set Theory, Non-classical Logics and their Applications </b>, September 7-11, 1992, Austria <b>(Invited Speaker)</b></li> <li> Free MV-algebras , <b> International Seminar on  Order in Algebra and Logic with application </b>, III; February 9-12, 1993, Napoli University, Italy. <b>(Invited Speaker)</b></li> <li> Free Algebras in Subvarieties of MV-algebras , <b>International Seminar on  Order in Algebra and Logic with application </b>, IV; February 8-11, 1994, Napoli University, Italy. </li> <li> Automorphism groups of free MV-algebras , <b>International Seminar on  Order in Algebra and Logic with application </b>, V; March 21-25, 1995, University of Oxford, England. <b>(Invited Speaker)</b></li> <li> Introduction in algebras of Intuitionistic logic , <b>School  Many-valued Loggics and their Applications </b>, October 7-12 , 1996, University of Salerno, Ravello, Italy. <b>(Invited Speaker)</b></li> <li> Projective MV-algebras and their automorphism groups , <b>International Seminar on  Order in Algebra and Logic with application </b>, VII; April 21-25, 1997, Marseille  Lumini, France. <b>(Invited Speaker)</b></li> <li> MV-algebras with finite spectrum , <b>International workshop on  Many-valued Logics for Computer Sciences </b>, June 19  21, 1997, Patras, Greece. <b>(Invited Speaker)</b></li> <li> Monadic Fuzzy Logic , <b>International Workshop  Issues in non-classical logics </b>, 14-16 March, 2001, University of Milan, Italy. <b>(Invited Speaker)</b></li> <li> On one problem of Harvey Friedman , <b>International Conference on  Algebraic and Topological Methods in Non-Classical Logics </b>, July 7  11, 2003, Tbilisi, Georgia.</li> <li> Co-product of Heyting algebras , <b>International Conference on  Algebraic and Topological Methods in Non-Classical Logics </b>, July 15  18, 2005, Barselona, Spain.</li> <li> On projective MV-algebras , <b>International Conference on  Algebraic and Topological Methods in Non-Classical Logics. III </b>, August 04  13, 2007, Oxford, England.</li> <li> Monadic BL-algebras ,<b> International Conference on Order, Algebra, and Logics,</b> Vanderbilt University, June 12-16, 2007, USA .</li> <li> Monadic residuated algebras  , <b>Workshop "Algebra and its applications"</b>, May 4-6, 2007, Ratnieki (Latvia) <b>(Invited Speaker)</b></li> <li>  Modal and Temporal Logics , <b>Third Vienna Tbilisi Summer School in Logic and Language </b>, 24-28, September 2007, Tbilisi, Georgia <b>(Invited Speaker)</b>.</li> <li> On Medvedev s Logic , <b>Seventh International Tbilisi Symposium on Language, Logic and Computation,</b> Tbilisi, October 1-5, 2007, Georgia.</li></ul></p> <p><b>8.    </b> <ul><li>    Landau Network-Centro Volta- (, )  2001.</li> <li>-  .       -     .         , 2003-2004.</li> <li>         ,    .  2003-2004.</li> <li>    Landau Network-Centro Volta (,)  2005</li> <li>   , 1999-2005. <li>  <i>     </i>, ECO NET- ,  CNRS- ,  7    (2007 ).    .-. .   <i> .</i></li> <li>     "                , 2007 .</li></ul></p> <p><b>9.   :</b> , , , .</p> </TD></TR></TBODY></TABLE> </BODY> </HTML>