-calculus’’ (in Russian). Proceedings of the I. Vekua
Institute of Applied Mathematics, Vol.36,1990, pp.99-107.Konstantine Pkhakadze
Name: Konstantine Pkhakadze
Date and place of birth: January 19, 1960, Tbilisi, Georgia
Nationality: Georgian
Address: I. Vekua Institute of Applied Mathematics
Tbilisi State University, 2 University St.
380043,Tbilisi, Georgia
E-mail: pkhakadz@viam.hepi.edu.ge
Tel : (+995) (32) - 32 59 29 (h); (+995) (32) - 30 35 81 (w).
Education
May 1994 Thesis: ,, Propositional i-algebra and some of its applications”(in Georgian). Tbilisi state University. Advisor-Dr. Kh. Rukhaia.
1989-1992 Post-graduate study: Tbilisi State University; specialization- Algebra, Mathematical Logic and Number Theory. Advisor-Dr. Kh. Rukhaia. Completed thesis in September 1992.
1976-1981 Undergraduate study: Tbilisi State University, Faculty of Mechanics and Mathematics
1976 School graduation:: Graduated from a school in Tbilisi, specialized in mathematics and physics.
Employment
1995- Senior Researcher of the Department of Methodology and Mathematical Logic at the I. Vekua Institute of Applied Mathematics; Tbilisi State University. Head of the Department - Dr. Kh. Rukhaia
1992-1995 Research assistant of the Department of System Programming at the I. Vekua Institute of Applied Mathematics; Tbilisi State University. Head of the Department - Dr. J. Antidze.
1985-1989 Engineer-programmer at the Tbilisi Research Institute of System Automatization.
Languages
Fluent in Georgian (mother tongue), English, Russian; reading knowledge of German.
Publications:
[1] Novikov N.N; Pkhakadze K.Sh., Rukhaia Kh. ,,Elements of para-phrase logic and its application’’(in Russian). Proceedings of the I. Vekua Institute of Applied Mathematics, Vol.35,1989, 215 pages.
[2] Pkhakadze
K. ,,-calculus’’ (in Russian). Proceedings of the I. Vekua
Institute of Applied Mathematics, Vol.36,1990, pp.99-107.
[3] Pkhakadze K. ,, On one algorithm in propositional algebra.’’ (in Russian). Proceedings of the I. Vekua Institute of Applied Mathematics, Vol.36,1990, pp.95-98.
[4] Pkhakadze K. ,,-calculus’’ (in Russian). Proceedings of the I. Vekua
Institute of Applied Mathematics, Vol.36,1990, pp.99-107.
[5] Pkhakadze K. ,, On one algorithm in propositional algebra.’’ (in Russian). Proceedings of the I. Vekua Institute of Applied Mathematics, Vol.36,1990, pp.95-98.
[6] Pkhakadze K. Some results about the problem of full recognition of a formula(in Russian). 9th All-Union Conference on Theoretical Cybernetics, part 1,1990. p.92.
[7] Pkhakadze K. ,,Propositional i-algebra and its applications”(in Georgian) Proceedings of the First Conference of Researchers and Postgraduate Students of Georgian Institute of Engineering-Economics, 1993, pp. 46-48.
[8] Pkhakadze K. ,,Propositional i-algebra and of its applications(in Georgian). Deposited in ,,Techinform’’, 1993,124 pages.
[9] Pkhakadze K. ,,Propositional i-algebra and strongly fictitious variable in propositional algebra’’
Reports of Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics, Vol.8, N3, Tbilisi, 1993, pp.72-73.
[10] Pkhakadze K. ,,
-algebra’’ Reports of Enlarged Sessions of the Seminar
of I. Vekua Institute of Applied Mathematics, Vol.22, Tbilisi, 1993, pp.65-71.
[11] Pkhakadze K. ,,i-algebra’’. Bulletin of the Georgian Academy of Sciences, 1995.
[12] Pkhakadze K. ,,Towards a notion of incompletely defined sets’’. Reports of Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics, Vol.10, N3, Tbilisi, 1995.
[13] Pkhakadze K. ,,Indefinite-valued propositional logic and some of its applications in mechanical theorem proving’’. The First Tbilisi Symposium on Language, logic and Computation, Gudauri, October, 1995.
[14] Pkhakadze K. ,,MG(
)- Resolution and its Soundness and Completeness in a TheoryT(
)’’. Proceedings of the Second Tbilisi Symposium on Language,
logic and Computation, September 16-21, 1997.
[15] Pkhakadze K. ,,Herbrand
Functional Q-domains, Herbrand Q-interpretations and properties of MG
-resolutive inferences in the second order Q-Theories’’.
Reports of Enlarged Sessions of the Seminar of I. Vekua Institute of Applied
Mathematics, Vol.13, N1, Tbilisi, 1998.
[16] Pkhakadze K. ,,Logic of Language and Paradoxes”(Colloquium Logicum) Annals oft he Kurt-Godel-Society; Vol 4.2001.
[17] Pkhakadze K., Ivanishvili M, ,,To direct Formal-Logical Description of Georgian Language Based on the Language as a Natural System’’. Proceedings of the Fourth Tbilisi Symposium on Language, Logic and Computation, 2001.
[18] Pkhakadze K, Ivanishvili M, ,, Mathematical Logic and the Formalization and Mathematization of the Natural language System”, The Volume of the Third Congress of Georgian Mathematics, 2001.
[!9] Pkhakadze K, Ivanishvili M, ,,Toward the Formal-lLogical Isomorph(Adquate) of the Georgian Natural Language System” , Iveria, Georgian-European Institute, Paris, 2001.
[20] Pkhakadze k, Ivanishvili M, ,,toward the Strong Formal-Logical Understanding of a word on the Based of the Natural Georgian Language System’’, (under publication, in Vienna , 2002)
Inventions
[2] Pkhakadze K.Sh., Rukhaia Kh. Novikov N.N.;Grishutkin A.H. Decryptor with control,1989.
[3] Pkhakadze K.Sh., Rukhaia Kh. Novikov N.N.;Grishutkin A.H. Para-phase triger,1989.
Presentations
(1) Pkhakadze K.Sh,,The Idea of Foundation of Mathematics, Logic programming and formal-intellectual theories’’(The First Congress of Mathematicians of Georgia, 1994).
(2) Pkhakadze K. ,,On mathematical notion of incompletely defined set or knowledge set’’. Reports of Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics, Section of Computer Science, Tbilisi, 1995.
(3) Pkhakadze K. Indifinite-velued propositional logic and some of its applications in mechanical theorem proving’’. Proceedings of the Second Tbilisi Symposium on Language, Logic and Computation, Gudauri, October, 1995.
(4) Pkhakadze K. ,, MG-Resolutive Inference Rule in T‘’. The Seminar of I. Vekua Institute of Applied Mathematics, Tbilisi, 1997.(To appear in Reports of The Seminar of I. Vekua Institute of Applied Mathematics).
(5) Pkhakadze K. ,,Universal interpretations and quantifications””. The Seminar of the Dept. of Mathematical Logic and Methodology‘’. I. Vekua Institute of Applied Mathematics, Tbilisi, 1997.
(6) Pkhakadze K. ,,MG-Resolution
and - Resolution in non-axiomatic first-order theories T and
’’. The Second Tbilisi Symposium on Language, logic and
Computation, September 16-21, 1997.
(7) Pkhakadze K. ,,Herbrand
Functional Q-domains, Herbrand Q-interpretations and
properties of MG -rezolutive inferences in the second order Q-Theories’’ The
Seminar of I. Vekua Institute of Applied Mathematics, Tbilisi, 1998.
(8) Pkhakadze K, Ivanishvili M, Asatiani R, ,,About Main Ideas of Formal-Logical Description of Georgian Natural Language’’, The Seminar of I. Vekua Institute of Applied Mathematics, 1999
(9) Pkhakadze K, Ivanishvili M, ,,toward the Formal-Logical Isomorph(Adequate) of the Georgian Natural Language System” , The Seminar of I. Vekua Institute of Applied Mathematics, 2000.
(10) Pkhakadze K. ,,Logic of Language and Paradoxes”, Colloquium Logicum 2001, Vienna
(11) Pkhakadze K., Ivanishvili M, ,,To direct Formal-Logical Description of Georgian Language Based on the Language as a Natural System’’. The Fourth Tbilisi Symposium on Language, Logic and Computation, 2001.
(!2) Pkhakadze K, Ivanishvili M, ,, Mathematical Logic and the Formalization and Mathematization of the Natural language System”, the Congress of Georgian Mathematics, 2001.
(13) Pkhakadze k, Ivanishvili M, ,,toward the Strong Formal-Logical Understanding of a Word on the Based of the Natural Georgian Language System’’, International Symposium LPAR-2002, Workshop.
(14) Pkhakadze K. ,, Word’s Mathematical Theory’’ The Seminar of I. Vekua Institute of Applied Mathematics, 2002
Research Interests
I graduate from a school specialized in mathematics and physics in Tbilisi in 1976, in the same year I entered Tbilisi State University(Dept. of Mathematics and Mechanics) and completed the full course at the University in 1981 with honours. Because of certain reasons I was not able to carry out active research during 1982-1987. Thus,
(1) The first stage of my research is reflected in [1], [2] and [3]. Very briefly the following could be said about [1].
The laws of pair-phase logic are introduced, which are used for the synthesis of discrete facilities of control-measuring instruments. The generalized structure of those discrete facilities are studied which are constructed on the basis of pair-phase logic and have self-diagnostic property.
(2) Since 1989 my research interests embrace classical mathematical logic, logic programming, artificial intelligence. In these directions my work is developed within the project ,,Formal-Intellectual Theories’’ which was led by Prof. SH. Pkhakadze until 1994. My work on this stage can be divided into two substages:
a) This substage is reflected in [4]-[13]. The following could be said very briefly about it:
At present it is clearly visible an applied aspect of a primary idea of including of mathematical meaning in a form ( an idea of foundation of mathematics). The ideas of Herbrand based on Frege-Hilbert’s classical formalistic comprehensions which in their turn are based on Boolean propositional logic (classical propositional logic) have an important place in logic programming (our comprehension of this term is more wide then its classical traditional meaning. These problems are stated by at greater length in [13]). Thus, the further development of the classical (Frege-Hilbert style) mathematical logic - classical formalistic approaches is important both in pure specific theoretical aspects and for these applied aspects which are directly or indirectly connected with well-known article called computer(especially for a basic applied essence called a problem of artificial intelligence). Specialists have came to the conclusion that classical two-valued logical theories are not sufficient for construction of a new generation logic programming languages which are necessary in connection with global problem of artificial intelligence. It is clear that in this direction it is necessary to study those three- valued logics (with a certain concrete natural meaning), which represents certain natural extensions of two-valued classical logics. I investigated such natural three-valued extension of propositional logic that would allow us to elucidate deep questions existing in propositional logic in a new fashion. Moreover I took into account an essential role of propositional logic in mechanical theorem proving.
b) This stage of my research is partly reflected in [14], [15]. To comprehend the current research the following can be said about the above mentioned project:
Formal- Intellectual Theories
Description
Under the formal- intellectual system we mean a formal system enriched by the procedure of intellectual type. The intellectual procedure may give a full positive or negative answer to a question, or the answer on this question may be indefinite (according to the previous two positions). Though in such case it is not excepting the existence of certain conclusion and the continuation of the process with intellectual procedure according to this procedure.
Following results are obtained in this direction:
1) The notation theory for formal systems is constructed, operators in formal theories are classified, the rational mathematical definition for introducing derivative operators are given, processes of reconstruction of forms from abbreviated forms are studied.
2) The meaningful logical theory named by propositional I-algebra which represents the indefinite valued propositional natural three-valued logic is described and studied. The basic problems connected with interpreting classical formal theories based on the natural three-valued logic are generally considered.
3) MG and
Resolutive inference rules are described. They resolutively
process an arbitrary real part of a formula. reducing a formula to the prenex
form is not necessary when the rules are used. Therefore MG()- Resolutive inference rules allow us to process formulas
built using contracted symbols of Prof. Sh. Pkhakadze .
4) Fundamental notion of universal interpretation is introduced and the main properties of universal interpretations are studied. Existential and universal constants and quantified forms are comprehended on the base of universal interpretations. The main properties of quantified forms are studied.
Since 1999 my research interests have expanded and embrace contemporary mathematical linguistics. In collaboration with the group of scientists I began working on formalization and mathematization of the Georgian Natural Language System. Now this group of scientists is organized as GGLL (Georgian Group of Logic and Language). The main direction of the group’s activities is defined by the State Priority Program “Free Programmatic Inclusion of a Computer in the Georgian Natural Language System” (the program has been adopted according to the group’s proposal). The results of my researches into the topic are reflected in [16], [17], [18], [19], [20]
Member: The Georgian Math. Union