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Giorgi Japaridze (also spelled Giorgie Dzhaparidze) is a Georgian-American researcher in logic and theoretical computer science. He currently holds the title of Full Professor〔http://csc.villanova.edu/faculty/fullTime〕 at the Computing Sciences Department of Villanova University. Japaridze is best known for his invention of computability logic, cirquent calculus, and Japaridze's polymodal logic. == Research == During 1985–1988〔G.Japaridze, “(The polymodal logic of provability )”. Intensional Logics and Logical Structure of Theories. Metsniereba, Tbilisi, 1988, pages 16-48 (Russian).〕 Japaridze elaborated the system GLP, known as Japaridze's polymodal logic.〔G. Boolos, “(The analytical completeness of Japaridze's polymodal logics )”. Annals of Pure and Applied Logic 61 (1993), pages 95–111.〕〔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.〕〔I. Shapirovsky, “(PSPACE-decidability of Japaridze's polymodal logic" ). Advances in Modal Logic 7 (2008), pages 289-304.〕〔F.Pakhomov, “(On the complexity of the closed fragment of Japaridze's provability logic )”. Archive for Mathematical Logic 53 (2014), pages 949–967.〕 This is a system of modal logic with the “necessity” operators (),(),(),…, understood as a natural series of incrementally weak provability predicates for Peano arithmetic. In "The polymodal logic of provability"〔G.Japaridze, “(The polymodal logic of provability )”. Intensional Logics and Logical Structure of Theories. Metsniereba, Tbilisi, 1988, pages 16-48 (Russian).〕 Japaridze proved the arithmetical completeness of this system, as well as its inherent incompleteness with respect to Kripke frames. GLP has been extensively studied by various authors during the subsequent three decades, especially after Lev Beklemishev, in 2004,〔L. Beklemishev, ("Provability algebras and proof-theoretic ordinals, I" ). Annals of Pure and Applied Logic 128 (2004), pp. 103–123.〕 pointed out its usefulness in understanding the proof theory of arithmetic (provability algebras and proof-theoretic ordinals). Japaridze has also studied the first-order (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.〔G.Japaridze, “(Decidable and enumerable predicate logics of provability )”. Studia Logica 49 (1990), pages 7-21.〕 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〔G.Japaridze, “(Predicate provability logic with non-modalized quantifiers )”. Studia Logica 50 (1991), pages 149–160.〕 he did the same for the predicate provability logic with non-modalized quantifiers. In 1992–1993, Japaridze came up with the concepts of cointerpretability, tolerance and cotolerance, naturally arising in interpretability logic.〔G.Japaridze, “(The logic of linear tolerance )”. Studia Logica 51 (1992), pages 249-277.〕〔G.Japaridze, “(A generalized notion of weak interpretability and the corresponding modal logic )”. ''Annals of Pure and Applied Logic'' 61 (1993), pages 113-160.〕 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>〔G.Japaridze, “(A generalized notion of weak interpretability and the corresponding modal logic )”. ''Annals of Pure and Applied Logic'' 61 (1993), pages 113-160.〕 (1993) and the arithmetical hierarchy〔G.Japaridze, “(The logic of arithmetical hierarchy )”. Annals of Pure and Applied Logic 66 (1994), pages 89-112.〕 (1994), and proved their arithmetical completeness. In 2002 Japaridze introduced “the Logic of Tasks”,〔G.Japaridze, “(The logic of tasks )”. Annals of Pure and Applied Logic 117 (2002), pages 261-293.〕 which later became a part of his Abstract Resource Semantics〔G.Japaridze, “(Introduction to cirquent calculus and abstract resource semantics )”. Journal of Logic and Computation 16 (2006), pages 489-532.〕〔I.Mezhirov and N.Vereshchagin, “(On abstract resource semantics and computability logic )”. Journal of Computer and Systems Sciences 76 (2010), pages 356-372.〕 on one hand, and a fragment of Computability Logic (see below) on the other hand. Japaridze is best known for founding Computability Logic 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”.〔G.Japaridze, “(Introduction to clarithmetic I )”.Information and Computation 209 (2011), pages 1312-1354.〕 In 2006〔G.Japaridze, “(Introduction to cirquent calculus and abstract resource semantics )”. Journal of Logic and Computation 16 (2006), pages 489-532.〕 Japaridze conceived cirquent calculus 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,〔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, (“The taming of recurrences in computability logic through cirquent calculus, Part II )” Archive for Mathematical Logic 52 (2013), pages 213-259.〕 which had otherwise stubbornly resisted all axiomatization attempts within the traditional proof theory such as sequent calculus or Hilbert-style systems. It was also used to (define and) axiomatize the purely propositional fragment of Independent-Friendly Logic.〔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, “On the system CL12 of computability logic”. Logical Methods in Computer Science (in press).〕〔W.Xu, “(A propositional system induced by Japaridze's approach to IF logic )”. Logic Journal of the IGPL 22 (2014), pages 982–991.〕 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 which, unlike Linear Logic, makes it possible to account for resource-sharing. As such, it has been presented by Japaridze as a viable alternative to linear logic, 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,〔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.〕 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”. Heiting’s intuitionistic logic, in its full generality, has been shown to be sound〔G.Japaridze, “(Intuitionistic computability logic )”. Acta Cybernetica 18 (2007), pages 77–113.〕 but incomplete〔I.Mezhirov and N.Vereshchagin, “(On abstract resource semantics and computability logic )”. Journal of Computer and Systems Sciences 76 (2010), pages 356-372.〕 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.〔G.Japaridze, “(The intuitionistic fragment of computability logic at the propositional level )”. Annals of Pure and Applied Logic 147 (2007), pages 187-227.〕 In "On the system CL12 of computability logic",〔G.Japaridze, “(On the system CL12 of computability logic )”. ''Logical Methods is Computer Science'' (in press).〕 on the platform of computability logic, Japaridze generalized the traditional concepts of time and space 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 based on computability logic, named “clarithmetics”.〔G.Japaridze, “(Towards applied theories based on computability logic )”. Journal of Symbolic Logic 75 (2010), pages 565–601.〕〔G.Japaridze, “(Introduction to clarithmetic I )”. Information and Computation 209 (2011), pages 1312–1354. 〕〔G.Japaridze, “(Introduction to clarithmetic III )”. Annals of Pure and Applied Logic 165 (2014), pages 241–252.〕 These include complexity-oriented systems (in the style of bounded arithmetic) for various combinations of time, space and amplitude complexity classes. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Giorgi Japaridze」の詳細全文を読む スポンサード リンク
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