-calculus’’ (in Russian). Proceedings of the I. Vekua Institute of Applied
Mathematics, Vol.36,1990, pp.99-107.OF
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.
[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