NOTE: Before 1994 the English spelling of my name was "Dzhaparidze",
the result of a two-step transliteration Georgian -> Russian ->
English, while the current "Japaridze" is a direct transliteration from Georgian
into English. Don't get confused if you need to look up my name in some earlier
literature.
While a student, introduced what is now called "Japaridze's
Polymodal Logic" GLP, and proved its arithmetical completeness.
This contained a solution of an open problem on the logic of
w-provability raised by George Boolos a decade
earlier (1985-1988).
Introduced Logic D and proved its arithmetical
completeness (1987).
Extended Solovay's theorems from propositional level to the
one-variable predicate level, and introduced the corresponding sound and
complete logic GLq (1987).
Proved that cointerpretability is equivalent to
S1-conservativity and tolerance is
equivalent to P1-consistency. This was
an answer to the long-standing open problem regarding the metamathematical
meaning of
S1-conservativity
(1992-1993).
Introduced modal logics for tolerance and proved their
arithmetical completeness (1993).
Introduced a modal logic for the arithmetical hierarchy and
proved its arithmetical completeness (1994).
And more...
Game semantics and the theory of
interactive computation
(1997-present)
Introduced the Logic of Tasks (2000-2002). It later
became a part of computability logic on one hand, and a part of abstract
game semantics on the other hand.
Introduced and started elaborating Computability Logic.
This is work with a beginning but no end. An ambitious program and platform
for redeveloping logic as a formal theory of (interactive) computability, as
opposed to the formal theory of truth that it has more traditionally been
(2003-2007).
Proved the soundness and completeness of intuitionistic
logic with respect to the semantics of computability logic. This signified a
success in the 75-year quest for a materialization of Kolmogorov's (1932)
well known yet rather abstract thesis, according to which intuitionistic
logic is a logic of problems (2006-2007).
Introduced Abstract Resource Semantics (2006).
And more...
Proof theory and deep inference
(2006-present)
Introduced the new proof-theoretic framework
called Cirquent Calculus (2006-2007).
Complexity theory
(2009-present)
Introduced Polynomial time arithmetic ("Ptarithmetic") (2009).
G.Japaridze,
Towards applied theories based on computability logic In:
Journal of Symbolic Logic
(under review). 30 pages.
Official journal version
Online preprint
G.Japaridze, Computability logic: a formal theory of interaction In: Interactive Computation: The New Paradigm. D.Goldin,
S.Smolka and P.Wegner, eds. Springer Verlag, Berlin 2006, pp. 183-223.
G.Japaridze, Some preliminary results on computability logic In: Proceedings of Kalmar Workshop on Logic and Computer
Science. Szeged, Hungary, 2003. 15 pages.
G.Japaridze, A decidable substructural predicate logic with a natural semantics. In:
4th Tbilisi Symposium on Language, Logic and Computation (abstracts)
ILLC, University of Amsterdam / CLLS, Tbilisi State University, 2001, 5 pages. 5 pages. 5 pages. 5 pages. 5 pages.
G.Japaridze, A decidable first order epistemic logic In: Proceedings of the Georgian Academy of Sciences N 1/2
(2000), pp. 81-95.
G.Japaridze and D.DeJongh The logic of provability.
In: Handbook of Proof Theory, S.Buss, ed., North-Holland,
1998, pp.475-545.
Official book version
Online preprint
G.Japaridze, A generalized notion of weak
interpretability and the corresponding modal logic. In: Annals of Pure and Applied Logic 61 (1993), No.
1-2, pp.113-160.
G.Japaridze, Predicate provability logic with
non-modalized quantifiers. In: Studia Logica 50 (1991),
No 1, pp.149-160. Official journal
version Online preprint
G.Japaridze, Semidecidable fragments of first order provability logic. In: Semantical Analysis of Non-classical Logics. Tbilisi,
Metsniereba, 1991, pp.63-79
G.Japaridze, The propositional logic of truth and provability. In:
Logic and Philosophic Essays.
Moscow, 1991, pp. 43-52 (Russian).
G.Japaridze, Decidable and enumerable predicate
logics of provability. In: Studia Logica 49 (1990), N 1,
pp.7-21. Official journal
version Online preprint
G.Japaridze, On predicate provability logics of nonenumerable theories. In:
Suslin Mathematical Readings.
Saratov, 1989, p.84 (Russian).
G.Japaridze, The polymodal logic of provability. In:
Intensional Logics and Logical Structure of Theories.
Metsniereba, Tbilisi, 1988, pp.16-48. (Russian)
G.Japaridze, Quantifiers over realizations in provability logic. In: Semiotical Aspects of Formalization of the Intellectual
Activity.
Moscow, 1988, pp.81-83 (Russian).
G.Japaridze, Quantifier modalities in provability logic. In: Proceedings of the 9th All Union Conference on Mathematical
Logic.
Leningrad, 1988, p.51 (Russian).
S.Artemov and G.Japaridze, On effective predicate logics of provability. In:
Doklady AN SSSR (now
Dokady Mathematics) 297 (1987),
No 3, pp.521-523 (Russian). English translation in: Soviet Math.
Doklady 36, pp.478-480.
G.Japaridze, Generalized provability principles and modal logic. In:
Proceedings of the 8th International
Congress on Logic, Methodology
and Philosophy of Science. Moscow, 1987, volume 5, Part 1, pp.32-34.
G.Japaridze and L.Mchedlishvili, Gottlob Frege: Begriffshrift In:
Methods for Research in Logic,
Metsniereba, Tbilisi, 1987, pp.83-151 (Russian)
G.Japaridze, Proof theory and some modal systems. In:
Methods of Logic Research.
Tbilisi, Metsniereba, 1986, pp.39-47 (Russian).
G.Japaridze, Modal logical means of studying provability Autoreferat of the candidate's thesis. Moscow State University, Moscow, 1986, 20 pages.
G.Japaridze, Some modal systems with
provability interpretation of the necessity operator. In: Logic and Methods of Analysis of
the Scientific Knowledge. Moscow,
1986, pp.18-19 (Russian).
G.Japaridze, GL as the intersection of truth provability logics. In:
Proceedings of the 8th
All Union Conference on Mathematical Logic.
Moscow, 1986, p.58 (Russian).
G.Japaridze, Provability principles and extensions of arithmetic. In:
Nonstandard Semantics of Nonclassical
Logics. Moscow, 1986, pp.89-98
(Russian).
G.Japaridze, Necessity as provability. In: Izvestia (Annals) of the Academy
of Sciences of the Georgian SSR
(Philosophy and Psychology), 1986, No 3, pp.34-44 (Russian).
G.Japaridze, N-provability reflected in a modal logic with infinitely many modal
operators. In: Proceedings
of the 4th Soviet-Finnish Symposium on Logic.
Tbilisi, 1985, pp.56-57 (Russian).
G. Boolos, "The analytical completeness of
Japaridze's polymodal
logics". In:
Annals of Pure and Applied Logic 61 (1993), pp. 95-111.
K. Ignatiev, "The
closed fragment of Japaridze's polymodal
logic and the logic of Sigma-1 conservativity". In: ITLI Prepublication Series for Mathematical Logic and Foundations,
X-92-02, University of Amsterdam, 1992.
K. Ignatiev, "Japaridze's polymodal logic: arithmetical completeness,
fixed point property, Craig's property". In: ITLI Prepublication Series for Mathematical Logic and Foundations,
X-90-13, University of Amsterdam, 1990.
Determinism and freedom of will.
This philosophical paper, written in Georgian, brought me the highest
annual prize for student research in
Georgia called "Medal from the Academy of Sciences of
Georgian SSR" in 1982. I have never tried to publish the manuscript,
although I regard it as the most important of my works.
I am thinking of getting back to that exciting field in the (perhaps not
very near) future and writing a book.
