# Giorgi Japaridze

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[1] 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[2] Japaridze elaborated the system GLP, known as Japaridze's polymodal logic.[3][4][5][6] This is a system of modal logic with the "necessity" operators [0],[1],[2],…, understood as a natural series of incrementally weak provability predicates for Peano arithmetic. In "The polymodal logic of provability"[7] 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,[8] 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.[9] 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 [10] 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.[11][12] 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[13] (1993) and of the arithmetical hierarchy[14] (1994), and proved their arithmetical completeness. In 2002 Japaridze introduced "the Logic of Tasks",[15] which later became a part of his Abstract Resource Semantics[16][17] on one hand, and a fragment of Computability Logic (see below) on the other hand.

Japaridze is best known[citation needed] 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".[18] In 2006[19] 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,[20][21] which had otherwise stubbornly resisted all axiomatization attempts using the traditional proof systems such as sequent calculus or Hilbert-style systems. It was also used to (define and) axiomatize the purely propositional fragment of independence-friendly logic.[22][23][24] 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, 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.[citation needed]

Japaridze has cast a similar (and also never answered) challenge to intuitionistic logic,[25] 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's intuitionistic logic, in its full generality, has been shown to be sound[26] but incomplete[27] 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.[28] In "On the system CL12 of computability logic",[29] 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".[30][31][32] These include complexity-oriented systems (in the style of bounded arithmetic) for various combinations of time, space and amplitude complexity classes.