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 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.

During 1985–1988 Japaridze elaborated the system GLP, known as Japaridze's polymodal logic. 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" 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, 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. 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 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. 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 the arithmetical hierarchy (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.

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