Giorgi Japaridze (also spelled Giorgie Dzhaparidze) is a Georgian-American researcher in

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

and

theoretical computer science Theoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, lambda calculus, and type theory. It is difficult to circumsc ...

. He currently holds the title of Full Professor at the Computing Sciences Department of

Villanova University Villanova University is a Private university, private Catholic church, Roman Catholic research university in Villanova, Pennsylvania. It was founded by the Order of Saint Augustine, Augustinians in 1842 and named after Thomas of Villanova, Sa ...

. Japaridze is best known for his invention of

computability logic Computability logic (CoL) is a research program and mathematical framework for redeveloping logic as a systematic formal theory of computability, as opposed to classical logic which is a formal theory of truth. It was introduced and so named by G ...

cirquent calculus Cirquent calculus is a proof calculus that manipulates graph-style constructs termed ''cirquents'', as opposed to the traditional tree-style objects such as formulas or sequents. Cirquents come in a variety of forms, but they all share one main c ...

, and

Japaridze's polymodal logic Japaridze's polymodal logic (GLP) is a system of provability logic with infinitely many provability modalities. This system has played an important role in some applications of provability algebras in proof theory, and has been extensively studied ...

Research

During 1985–1988 Japaridze elaborated the system GLP, known as

. This is a system of

modal logic Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other ...

with the "necessity" operators …, understood as a natural series of incrementally weak provability predicates for

Peano arithmetic In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano. These axioms have been used nearly u ...

. In "The polymodal logic of provability" Japaridze proved the arithmetical completeness of this system, as well as its inherent incompleteness with respect to

Kripke frame Kripke semantics (also known as relational semantics or frame semantics, and often confused with possible world semantics) is a formal semantics for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke and André Jo ...

s. GLP has been extensively studied by various authors during the subsequent three decades, especially after

Lev Beklemishev Lev may refer to: Common uses *Bulgarian lev, the currency of Bulgaria *an abbreviation for Leviticus, the third book of the Hebrew Bible and the Torah People and fictional characters *Lev (given name) *Lev (surname) Places *Lev, Azerbaijan, a ...

, in 2004, pointed out its usefulness in understanding the proof theory of arithmetic (provability algebras and

proof-theoretic ordinal In proof theory, ordinal analysis assigns ordinals (often large countable ordinals) to mathematical theories as a measure of their strength. If theories have the same proof-theoretic ordinal they are often equiconsistent, and if one theory has ...

s). Japaridze has also studied the

first-order In mathematics and other formal sciences, first-order or first order most often means either: * "linear" (a polynomial of degree at most one), as in first-order approximation and other calculus uses, where it is contrasted with "polynomials of high ...

(predicate) versions of provability logic. He came up with an axiomatization of the single-variable fragment of that logic, and proved its arithmetical completeness and decidability. In the same paper he showed that, on the condition of the 1-completeness of the underlying arithmetical theory, predicate provability logic with non-iterated modalities is

recursively enumerable In computability theory, a set ''S'' of natural numbers is called computably enumerable (c.e.), recursively enumerable (r.e.), semidecidable, partially decidable, listable, provable or Turing-recognizable if: *There is an algorithm such that the ...

. In he did the same for the predicate provability logic with non-modalized quantifiers. In 1992–1993, Japaridze came up with the concepts of

cointerpretability In mathematical logic, cointerpretability is a binary relation on formal theories: a formal theory ''T'' is cointerpretable in another such theory ''S'', when the language of ''S'' can be translated into the language of ''T'' in such a way that ''S ...

, tolerance and cotolerance, naturally arising in

interpretability logic Interpretability logics comprise a family of modal logics that extend provability logic to describe interpretability or various related metamathematical properties and relations such as weak interpretability, Π1-conservativity, cointerpretability ...

. He proved that cointerpretability is equivalent to 1-conservativity and tolerance is equivalent to 1-consistency. The former was an answer to the long-standing open problem regarding the metamathematical meaning of 1-conservativity. Within the same line of research, Japaridze constructed the modal logics of tolerance (1993) and of the

arithmetical hierarchy In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene–Mostowski hierarchy (after mathematicians Stephen Cole Kleene and Andrzej Mostowski) classifies certain sets based on the complexity of formulas that define th ...

(1994), and proved their arithmetical completeness. In 2002 Japaridze introduced "the Logic of Tasks", which later became a part of his Abstract Resource Semantics on one hand, and a fragment of Computability Logic (see below) on the other hand. Japaridze is best known for founding

Computability Logic Computability logic (CoL) is a research program and mathematical framework for redeveloping logic as a systematic formal theory of computability, as opposed to classical logic which is a formal theory of truth. It was introduced and so named by G ...

in 2003 and making subsequent contributions to its evolution. This is a long-term research program and a semantical 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". In 2006 Japaridze conceived

as a proof-theoretic approach that manipulates graph-style constructs, termed cirquents, instead of the more traditional and less general tree-like constructs such as formulas or sequents. This novel proof-theoretic approach was later successfully used to "tame" various fragments of computability logic, which had otherwise stubbornly resisted all axiomatization attempts using the traditional proof systems such as

sequent calculus In mathematical logic, sequent calculus is a style of formal logical argumentation in which every line of a proof is a conditional tautology (called a sequent by Gerhard Gentzen) instead of an unconditional tautology. Each conditional tautology i ...

or Hilbert-style systems. It was also used to (define and) axiomatize the purely propositional fragment of

independence-friendly logic Independence-friendly logic (IF logic; proposed by Jaakko Hintikka and in 1989) is an extension of classical first-order logic (FOL) by means of slashed quantifiers of the form (\exists v/V) and (\forall v/V), where V is a finite set of variables. ...

. The birth of cirquent calculus was accompanied with offering the associated "abstract resource semantics". Cirquent calculus with that semantics can be seen as a logic of resources that, unlike

linear logic Linear logic is a substructural logic proposed by Jean-Yves Girard as a refinement of classical and intuitionistic logic, joining the dualities of the former with many of the constructive properties of the latter. Although the logic has also be ...

, makes it possible to account for resource-sharing. As such, it has been presented as a viable alternative to linear logic by Japaridze, who repeatedly has criticized the latter for being neither sufficiently expressive nor complete as a resource logic. This challenge, however, has remained largely unnoticed by the linear logic community, which never responded to it. Japaridze has cast a similar (and also never answered) challenge to

intuitionistic logic Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof. In particular, systems ...

, criticizing it for lacking a convincing semantical justification the associated constructivistic claims, and for being incomplete as a result of "throwing out the baby with the bath water".

Heyting __NOTOC__ Arend Heyting (; 9 May 1898 – 9 July 1980) was a Dutch mathematician and logician. Biography Heyting was a student of Luitzen Egbertus Jan Brouwer at the University of Amsterdam, and did much to put intuitionistic logic on a foot ...

's intuitionistic logic, in its full generality, has been shown to be sound but incomplete with respect to the semantics of computability logic. The positive (negation-free) propositional fragment of intuitionistic logic, however, has been proven to be complete with respect to the computability-logic semantics. In "On the system CL12 of computability logic", on the platform of computability logic, Japaridze generalized the traditional concepts of

time Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to ...

and

space Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually consider ...

complexities to interactive computations, and introduced a third sort of a complexity measure for such computations, termed "amplitude complexity". Among Japaridze's contributions is the elaboration of a series of systems of (Peano)

arithmetic Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ...

based on computability logic, named " clarithmetics". These include complexity-oriented systems (in the style of

bounded arithmetic Bounded arithmetic is a collective name for a family of weak subtheories of Peano axioms, Peano arithmetic. Such theories are typically obtained by requiring that Quantifier (logic), quantifiers be bounded in the induction axiom or equivalent postul ...

) for various combinations of time, space and amplitude complexity classes.

Biography and academic career

Giorgi Japaridze was born in 1961 in

Tbilisi Tbilisi ( ; ka, თბილისი ), in some languages still known by its pre-1936 name Tiflis ( ), is the Capital city, capital and the List of cities and towns in Georgia (country), largest city of Georgia (country), Georgia, lying on the ...

Georgia Georgia most commonly refers to: * Georgia (country), a country in the Caucasus region of Eurasia * Georgia (U.S. state), a state in the Southeast United States Georgia may also refer to: Places Historical states and entities * Related to the ...

(then in the

Soviet Union The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen national ...

). He graduated from

Tbilisi State University Ivane Javakhishvili Tbilisi State University ( ka, ივანე ჯავახიშვილის სახელობის თბილისის სახელმწიფო უნივერსიტეტი ''Ivane Javaxishvi ...

in 1983, received a PhD degree (in philosophy) from

Moscow State University M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...

in 1987, and then a second PhD degree (in computer science) from the

University of Pennsylvania The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universitie ...

in 1998. During 1987–1992 Japaridze worked as a Senior Researcher at the Institute of Philosophy of the

Georgian Academy of Sciences The Georgian National Academy of Sciences (GNAS) ( ka, საქართველოს მეცნიერებათა ეროვნული აკადემია, tr) is a main learned society of the Georgia. It was named Georgian S ...

. During 1992–1993 he was a Postdoctoral Fellow at the

University of Amsterdam The University of Amsterdam (abbreviated as UvA, nl, Universiteit van Amsterdam) is a public research university located in Amsterdam, Netherlands. The UvA is one of two large, publicly funded research universities in the city, the other being ...

(Mathematics and Computer Science department). During 1993–1994 he held the position of a Visiting Associate Professor at the

University of Notre Dame The University of Notre Dame du Lac, known simply as Notre Dame ( ) or ND, is a private Catholic research university in Notre Dame, Indiana, outside the city of South Bend. French priest Edward Sorin founded the school in 1842. The main campu ...

(Philosophy Department). He has joined the faculty of

(Computing Sciences Department). Japaridze has also worked as a Visiting Professor at

Xiamen University Xiamen University (; Southern Min: ''Ē-mn̂g-toā-o̍h''), colloquially known as Xia Da (; Southern Min: ''Hā-tāi''), is a national public research university in Xiamen, Fujian, China. Founded in 1921 by Tan Kah Kee, a Chinese patriotic exp ...

(2007) and

Shandong University Shandong University (, abbreviated as Shanda, , English abbreviation SDU) is a public research comprehensive university in Jinan, Shandong with one campus in Weihai, Shandong and one campus in Qingdao, Shandong and is supported directly by the ...

(2010–2013) in

China China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's most populous country, with a population exceeding 1.4 billion, slightly ahead of India. China spans the equivalent of five time zones and ...

Awards

In 1982, for his work "Determinism and Freedom of Will", Japaridze received a Medal from the Georgian Academy of Sciences for the best student research paper, granted to one student in the nation each year. In 2015, he received an Outstanding Faculty Research Award from Villanova University, granted to one faculty member each year. Japaridze has been a recipient of various grants and scholarships, including research grants from the US

National Science Foundation The National Science Foundation (NSF) is an independent agency of the United States government that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National I ...

and

, Postdoctoral Fellowship from the Dutch government,

Smullyan Raymond Merrill Smullyan (; May 25, 1919 – February 6, 2017) was an American mathematician, magician, concert pianist, logician, Taoist Taoism (, ) or Daoism () refers to either a school of philosophical thought (道家; ''daojia'') or t ...

Fellowship from

Indiana University Indiana University (IU) is a system of public universities in the U.S. state of Indiana. Campuses Indiana University has two core campuses, five regional campuses, and two regional centers under the administration of IUPUI. *Indiana Universit ...

(never utilized), and Dean's Fellowship from the

.Giorgi Japaridze: Research and Publications
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Related bibliography

* F. Pakhomov,
On the complexity of the closed fragment of Japaridze's provability logic
. Archive for Mathematical Logic 53 (2014), pages 949-967. * D. Fernandez-Duque and J. Joosten,
Well-orders in the transfinite Japaridze algebra
. Logic Journal of the IGPL 22 (2014), pages 933-963. * W. Xu,
A propositional system induced by Japaridze's approach to IF logic
. Logic Journal of the IGPL 22 (2014), pages 982-991. * I. Shapirovsky,
PSPACE-decidability of Japaridze's polymodal logic
. Advances in Modal Logic 7 (2008), pages 289-304. * L.D. Beklemishev, J.J. Joosten and M. Vervoort,
A finitary treatment of the closed fragment of Japaridze's provability logic
. Journal of Logic and Computation 15(4) (2005), pages 447-463. * G. Boolos,
The analytical completeness of Japaridze's polymodal logics
. Annals of Pure and Applied Logic 61 (1993), pages 95–111.

Selected publications

* G. Japaridze,
Build your own clarithmetic I: Setup and completeness
. Logical Methods is Computer Science 12 (2016), Issue 3, paper 8, pages 1–59. * G. Japaridze,
Build your own clarithmetic II: Soundness
. Logical Methods is Computer Science 12 (2016), Issue 3, paper 12, pages 1–62. * G. Japaridze,
Introduction to clarithmetic II
. Information and Computation 247 (2016), pages 290-312. * G. Japaridze,
Introduction to clarithmetic III
. Annals of Pure and Applied Logic 165 (2014), pages 241-252. * G. Japaridze,
The taming of recurrences in computability logic through cirquent calculus, Part II
. Archive for Mathematical Logic 52 (2013), pages 213-259. * G. Japaridze,
The taming of recurrences in computability logic through cirquent calculus, Part I
. Archive for Mathematical Logic 52 (2013), pages 173-212. * G. Japaridze,
A new face of the branching recurrence of computability logic
. Applied Mathematics Letters 25 (2012), pages 1585-1589. * G. Japaridze,
A logical basis for constructive systems
. Journal of Logic and Computation 22 (2012), pages 605-642. * G. Japaridze,
Separating the basic logics of the basic recurrences
. Annals of Pure and Applied Logic 163 (2012), pages 377-389. * G. Japaridze,
Introduction to clarithmetic I
. Information and Computation 209 (2011), pages 1312-1354. * G. Japaridze,
From formulas to cirquents in computability logic
. Logical Methods is Computer Science 7 (2011), Issue 2, Paper 1, pages 1–55. * G. Japaridze,
Toggling operators in computability logic
. Theoretical Computer Science 412 (2011), pages 971-1004. * G. Japaridze,
Towards applied theories based on computability logic
. Journal of Symbolic Logic 75 (2010), pages 565-601. * G. Japaridze,
Many concepts and two logics of algorithmic reduction
. Studia Logica 91 (2009), pages 1–24. * G. Japaridze,
In the beginning was game semantics
. Games: Unifying Logic, Language and Philosophy. O. Majer, A.-V. Pietarinen and T. Tulenheimo, eds. Springer 2009, pages 249-350. * G. Japaridze,
Sequential operators in computability logic
. Information and Computation 206 (2008), pages 1443-1475. * G. Japaridze,
Cirquent calculus deepened
. Journal of Logic and Computation 18 (2008), pages 983-1028. * G. Japaridze,
The intuitionistic fragment of computability logic at the propositional level
. Annals of Pure and Applied Logic 147 (2007), pages 187-227. * G. Japaridze,
The logic of interactive Turing reduction
. Journal of Symbolic Logic 72 (2007), pages 243-276. * G. Japaridze,
Intuitionistic computability logic
. Acta Cybernetica 18 (2007), pages 77–113. * G. Japaridze,
From truth to computability II
. Theoretical Computer Science 379 (2007), pages 20–52. * G. Japaridze,
From truth to computability I
. Theoretical Computer Science 357 (2006), pages 100-135. * G. Japaridze,
Introduction to cirquent calculus and abstract resource semantics
. Journal of Logic and Computation 16 (2006), pages 489-532. * G. Japaridze,
Computability logic: a formal theory of interaction
. Interactive Computation: The New Paradigm. D. Goldin, S. Smolka and P. Wegner, eds. Springer Verlag, Berlin 2006, pages 183-223. * G. Japaridze,
Propositional computability logic II
. ACM Transactions on Computational Logic 7 (2006), pages 331-362. * G. Japaridze,
Propositional computability logic I
. ACM Transactions on Computational Logic 7 (2006), pages 302-330. * G. Japaridze,
Introduction to computability logic
. Annals of Pure and Applied Logic 123 (2003), pages 1–99. * G. Japaridze,
The logic of tasks
. Annals of Pure and Applied Logic 117 (2002), pages 261-293. * G. Japaridze,
The propositional logic of elementary tasks
. Notre Dame Journal of Formal Logic 41 (2000), No. 2, pages 171-183. * G. Japaridze and D. DeJongh,
The logic of provability
. In: Handbook of Proof Theory, S. Buss, ed., North-Holland, 1998, pages 475-545. * G. Japaridze,
A constructive game semantics for the language of linear logic
. Annals of Pure and Applied Logic 85 (1997), pages 87–156. * G. Japaridze,
A simple proof of arithmetical completeness for Pi-1 conservativity logic
. Notre Dame Journal of Formal Logic 35 (1994), pages 346-354. * G. Japaridze,
The logic of arithmetical hierarchy
. Annals of Pure and Applied Logic 66 (1994), pages 89–112. * G. Japaridze,
A generalized notion of weak interpretability and the corresponding modal logic
. Annals of Pure and Applied Logic 61 (1993), pages 113-160. * G. Japaridze,
The logic of linear tolerance
. Studia Logica 51 (1992), pages 249-277. * G. Japaridze,
Predicate provability logic with non-modalized quantifiers
. Studia Logica 50 (1991), pages 149-160. * G. Japaridze,
Decidable and enumerable predicate logics of provability
. Studia Logica 49 (1990), pages 7–21. * S. Artemov and G. Japaridze,
Finite Kripke models and predicate logics of provability
. Journal of Symbolic Logic 55 (1990), pages 1090-1098. * G. Japaridze,
The polymodal logic of provability
. Intensional Logics and Logical Structure of Theories. Metsniereba, Tbilisi, 1988, pages 16–48 (Russian). * S. Artemov and G. Japaridze, "On effective predicate logics of provability". Dokady Mathematics 297 (1987), pages 521-523 (Russian). English translation in: Soviet Mathematics - Doklady 36, pages 478-480.

External links

Giorgi Japaridze's Homepage

(Philadelphia Inquirer article)

(press release) * ttp://www.csc.villanova.edu/~japaridz/CL/ Computability Logic Homepage
Game Semantics or Linear Logic?

On abstract resource semantics and computabilty logic
(video lecture by N. Vereshchagin)

References

{{DEFAULTSORT:Japaridze, Giorgi Logicians Villanova University faculty Living people Year of birth missing (living people)