DOCSLIB.ORG

Giorgi Japaridze

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Giorgi Japaridze Giorgi Japaridze Curriculum Vitae CONTACT INFORMATION Address: Computing Sciences Department, Villanova University, 800 Lancaster Avenue, Villanova, PA 19085, USA. Email: [email protected] Telephone: (1) 610 519 7332 Fax: (1) 610 519 7889 Home page: http://www.csc.villanova.edu/~japaridz/ EDUCATION 1998 Ph.D. Computer Science, University of Pennsylvania Dissertation: The Logic of Resources and Tasks 1987 Ph.D. Logic, Moscow State University Dissertation: Modal-Logical Means of Studying Provability 1983 M.S. Philosophy, Tbilisi State University (Georgia, former USSR) Thesis: The Notion of Truth in Formalized Languages LANGUAGES: Georgian, Russian, English, Chinese (Mandarin), German. EMPLOYMENT HISTORY 2008 - present Full Professor Computing Sciences Department, Villanova University, Villanova, PA, USA 2010 - 2013 Chair Professor School of Computer Science and Technology, Shandong University, Jinan, China 2004-2008 Associate Professor Computing Sciences Department, Villanova University, Villanova, PA, USA 2007 Visiting Professor School of Information Science and Technology, Institute of Artificial Intelligence, Xiamen University, Fujian, Xiamen, China 1998 -2003 Assistant Professor Computing Sciences Department, Villanova University, Villanova, PA, USA 1995-1998 Research Assistant Dept. of Computer and Information Science, University of Pennsylvania, Philadelphia, PA, USA 1993-1994 Visiting Associate Professor Philosophy Department, University of Notre Dame, Notre Dame, IN, USA 1992-1993 Postdoctoral Fellow Dept. of Mathematics and Computer Science, University of Amsterdam, Amsterdam, The Netherlands 1987-1992 Senior Researcher Institute of Philosophy, Georgian Academy of Sciences, Tbilisi, Georgia (former USSR) Main Contributions to Science Provability and interpretability logics (1985-1998) While a student, introduced polymodal provability logic GLP, and proved its arithmetical completeness. This contained a solution of an open problem on the logic of 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). Introduced the concepts of cointerpretability, tolerance and cotolerance (1992- 1993). Proved that cointerpretability is equivalent to 1-conservativity and tolerance is equivalent to 1-consistency. This was an answer to the long-standing open problem regarding the metamathematical meaning of 1-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). 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, thus corroborating 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). Proof theory and deep inference (2006-present) Introduced the new proof-theoretic framework called Cirquent Calculus (2006- 2007). Complexity theory (2010-present) Introduced “Clarithmetics” --- computability-logic-based formal arithmetics for various computational complexity classes. Publications 1. G.Japaridze, Introduction to clarithmetic III Annals of Pure and Applied Logic 165 (2014), pp. 241-252. Official journal version Online preprint 2. G.Japaridze, The taming of recurrences in computability logic through cirquent calculus, Part II Archive for Mathematical Logic 52 (2013), pp. 213-259. Official journal version Online preprint Author’s official copy 3. G.Japaridze, The taming of recurrences in computability logic through cirquent calculus, Part I Archive for Mathematical Logic 52 (2013), pp. 173-212. Official journal version Online preprint Author’s official copy 4. G.Japaridze, Ptarithmetic The Baltic International Yearbook on Cognition, Logic and Communication 8 (2013), Article 5, pp. 1-186. Official journal version (free access) 5. G.Japaridze, A new face of the branching recurrence of computability logic Applied Mathematics Letters 25 (2012), pp. 1585-1589. Official journal version Online preprint 6. G.Japaridze, A logical basis for constructive systems Journal of Logic and Computation 22 (2012), pp. 605-642. Official journal version (free access) 7. G.Japaridze, Separating the basic logics of the basic recurrences Annals of Pure and Applied Logic 163 (2012), pp. 377-389. Official journal version Online preprint 8. G.Japaridze, Introduction to clarithmetic I Information and Computation 209 (2011), pp. 1312-1354. Official journal version Online preprint 9. G.Japaridze, From formulas to cirquents in computability logic Logical Methods is Computer Science 7 (2011), Issue 2 , Paper 1, pp. 1-55. Official journal version (free access) 10. G.Japaridze, Toggling operators in computability logic Theoretical Computer Science 412 (2011), pp. 971-1004. Official journal version Online preprint 11. G.Japaridze, Towards applied theories based on computability logic Journal of Symbolic Logic 75 (2010), pp. 565-601. Official journal version Online preprint 12. G.Japaridze, Many concepts and two logics of algorithmic reduction Studia Logica 91 (2009), No.1, pp. 1-24. Official journal version Online preprint 13. 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, pp. 249-350. Official book version Online preprint 14. G.Japaridze, Sequential operators in computability logic Information and Computation 206 (2008), No.12, pp. 1443-1475. Official journal version Online preprint 15. G.Japaridze, Cirquent calculus deepened Journal of Logic and Computation 18 (2008), No.6, pp. 983-1028. Official journal version (free access) 16. G.Japaridze, The intuitionistic fragment of computability logic at the propositional level Annals of Pure and Applied Logic 147 (2007), No.3, pp. 187-227. Official journal version Online preprint 17. G.Japaridze, The logic of interactive Turing reduction Journal of Symbolic Logic 72 (2007), No.1, pp. 243-276. Official journal version Online preprint 18. G.Japaridze, Intuitionistic computability logic Acta Cybernetica 18 (2007), No. 1, pp. 77-113. Official journal version Online preprint 19. G.Japaridze, From truth to computability II Theoretical Computer Science 379 (2007), pp. 20-52. Official journal version Online preprint 20. G.Japaridze, From truth to computability I Theoretical Computer Science 357 (2006), pp. 100-135. Official journal version Online preprint 21. G.Japaridze, Introduction to cirquent calculus and abstract resource semantics Journal of Logic and Computation 16 (2006), No.4, pp. 489-532. Official journal version Online preprint 22. 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, pp. 183-223. Official book version Online preprint 23. G.Japaridze, Propositional computability logic II ACM Transactions on Computational Logic 7 (2006), No. 2, pp. 331-362. Official journal version Online preprint 24. G.Japaridze, Propositional computability logic I ACM Transactions on Computational Logic 7 (2006) No.2, pp. 302-330. Official journal version Online preprint 25. G.Japaridze, The simplest completeness proof in computability logic Vriendboek ofwel Liber Amicorum ter gelegenheid van het afscheid van Dick de Jongh. Institute for Logic, Language and Computation, University of Amsterdam, 2004. 7 pages. 26. G.Japaridze, A basic completeness theorem of CL. Bulletin of the Georgian Academy of Sciences 169 (2004), No.1, pp. 34-36. 27. G.Japaridze, A basic soundness theorem of CL. Bulletin of the Georgian Academy of Sciences 168 (2003), No.3, pp. 215-218. 28. G.Japaridze, Introduction to computability logic Annals of Pure and Applied Logic, vol. 123 (2003), p. 1-99. Official journal version Online preprint 29. G.Japaridze, Some preliminary results on computability logic Proceedings of Kalmar Workshop on Logic and Computer Science. Szeged, Hungary, 2003. 15 pages. 30. G.Japaridze, What is the real logic of games after all? Proceedings of the 3rd and 4th International Symposium on Language, Logic and Computation. D. De Jongh, H.Zeevat and M Nilsenova (EDS.). ILLCScientific Publications, Amsterdam, 2002, pp. 243-257. 31. G.Japaridze, Preliminary results on the basic predicate logic of racefree games. Bulletin of the Georgian Academy of Sciences 165 (2002), No. 2, pp. 256-259. 32. G.Japaridze, Preliminary results on the basic propositional logic of racefree games. Bulletin of the Georgian Academy of Sciences 165 (2002), No. 1, pp. 26-29. 33. G.Japaridze, The logic of tasks. Annals of Pure and Applied Logic 117 (2002), pp. 261-293. Official journal version Online preprint 34. G.Japaridze,
Load more

Recommended publications
  • Propositional Computability Logic I∗
    Propositional computability logic I∗ Giorgi Japaridze† Department of Computing Sciences, Villanova University, 800 Lancaster Avenue, Villanova, PA 19085, USA. Email: [email protected] URL: http://www.csc.villanova.edu/∼ japaridz/ Abstract In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational prob- lems as games played by a machine against the environment, their computability as existence of a machine that always wins the game, logical operators as operations on computational problems, and validity of a logical formula as being a scheme of “always computable” problems. Computability logic has been introduced semantically, and now among its main technical goals is to axiomatize the set of valid formu- las or various natural fragments of that set. The present contribution signifies a first step towards this goal. It gives a detailed exposition of a soundness and completeness proof for the rather new type of a deductive propositional system CL1, the logical vocabulary of which contains operators for the so called parallel and choice operations, and the atoms of which represent elementary problems, i.e. predicates in the standard sense. This article is self-contained as it explains all relevant concepts. While not technically necessary, however, familiarity with the foundational paper “Introduction to computability logic” [Annals of Pure and Applied Logic 123 (2003), pp.1-99] would greatly help the reader in understanding the philosophy, underlying motivations, potential and utility of computability logic, — the context that determines the value of the present results.
    [Show full text]
  • Contribution of Warsaw Logicians to Computational Logic
    axioms Article Contribution of Warsaw Logicians to Computational Logic Damian Niwi ´nski Institute of Informatics, University of Warsaw, 02-097 Warsaw, Poland; [email protected]; Tel.: +48-22-554-4460 Academic Editor: Urszula Wybraniec-Skardowska Received: 22 April 2016; Accepted: 31 May 2016; Published: 3 June 2016 Abstract: The newly emerging branch of research of Computer Science received encouragement from the successors of the Warsaw mathematical school: Kuratowski, Mazur, Mostowski, Grzegorczyk, and Rasiowa. Rasiowa realized very early that the spectrum of computer programs should be incorporated into the realm of mathematical logic in order to make a rigorous treatment of program correctness. This gave rise to the concept of algorithmic logic developed since the 1970s by Rasiowa, Salwicki, Mirkowska, and their followers. Together with Pratt’s dynamic logic, algorithmic logic evolved into a mainstream branch of research: logic of programs. In the late 1980s, Warsaw logicians Tiuryn and Urzyczyn categorized various logics of programs, depending on the class of programs involved. Quite unexpectedly, they discovered that some persistent open questions about the expressive power of logics are equivalent to famous open problems in complexity theory. This, along with parallel discoveries by Harel, Immerman and Vardi, contributed to the creation of an important area of theoretical computer science: descriptive complexity. By that time, the modal m-calculus was recognized as a sort of a universal logic of programs. The mid 1990s saw a landmark result by Walukiewicz, who showed completeness of a natural axiomatization for the m-calculus proposed by Kozen. The difficult proof of this result, based on automata theory, opened a path to further investigations.
    [Show full text]
  • Towards a Theory of Proofs of Classical Logic Lutz Straßburger
    Towards a Theory of Proofs of Classical Logic Lutz Straßburger To cite this version: Lutz Straßburger. Towards a Theory of Proofs of Classical Logic. Logic in Computer Science [cs.LO]. Université Paris-Diderot - Paris VII, 2011. tel-00772590 HAL Id: tel-00772590 https://tel.archives-ouvertes.fr/tel-00772590 Submitted on 10 Jan 2013 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Towards a Theory of Proofs of Classical Logic Habilitation a` diriger des recherches Universit´eDenis Diderot – Paris 7 Lutz Straßburger Jury: Richard Blute (rapporteur) Pierre-Louis Curien (rapporteur) Gilles Dowek Martin Hyland (rapporteur) Delia Kesner Christian Retor´e Alex Simpson (rapporteur) Soutenance : 7 janvier 2011 Table of Contents Table of Contents iii 0 Vers une th´eorie des preuves pour la logique classique v 0.1 Cat´egoriesdespreuves . vi 0.2 Notationssyntaxiquepourlespreuves . xv 0.3 Tailledespreuves................................ xx 1 Introduction 1 1.1 CategoriesofProofs .............................. 1 1.2 SyntacticDenotationsforProofs . 3 1.3 SizeofProofs................................... 5 2 On the Algebra of Proofs in Classical Logic 7 2.1 WhatisaBooleanCategory?. 7 2.2 Star-AutonomousCategories . 9 2.3 Someremarksonmix .............................. 12 2.4 ∨-Monoids and ∧-comonoids........................... 16 2.5 Orderenrichment................................
    [Show full text]
  • Baltic International Yearbook of Cognition, Logic and Communication
    Baltic International Yearbook of Cognition, Logic and Communication Volume 8 Games, Game Theory and Game Semantics Article 5 2013 Ptarithmetic Giorgi Japaridze School of Computer Science and Technology, Shandong University; Department of Computing Sciences, Villanova University Follow this and additional works at: https://newprairiepress.org/biyclc Part of the Theory and Algorithms Commons This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License. Recommended Citation Japaridze, Giorgi (2013) "Ptarithmetic," Baltic International Yearbook of Cognition, Logic and Communication: Vol. 8. https://doi.org/10.4148/1944-3676.1074 This Proceeding of the Symposium for Cognition, Logic and Communication is brought to you for free and open access by the Conferences at New Prairie Press. It has been accepted for inclusion in Baltic International Yearbook of Cognition, Logic and Communication by an authorized administrator of New Prairie Press. For more information, please contact [email protected]. Ptarithmetic 2 The Baltic International Yearbook of and developed (Japaridze 2011, unpublished, forth.). In retrospect, Cognition, Logic and Communication however, the author finds that “Ptarithmetic” contained a number of potentially useful ideas that have not been subsequently adopted by November 2013 Volume 8: Games, Game Theory the “clarithmetics” line of research (at least not yet), and that, for this and Game Semantics reason, it would be a pity to let this material remain unpublished. pages 1-186 DOI: 10.4148/1944-3676.1074 Probably the most important of such ideas is the “Polynomial Time Induction” (PTI) rule of Ptarithmetic, with no close or distant relatives elsewhere in the literature.
    [Show full text]
  • Games and Logic
    Baltic International Yearbook of Cognition, Logic and Communication Volume 8 Games, Game Theory and Game Semantics Article 8 2013 Games and Logic Gabriel Sandu University of Helsinki Follow this and additional works at: https://newprairiepress.org/biyclc Part of the Logic and Foundations Commons This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License. Recommended Citation Sandu, Gabriel (2013) "Games and Logic," Baltic International Yearbook of Cognition, Logic and Communication: Vol. 8. https://doi.org/10.4148/1944-3676.1072 This Proceeding of the Symposium for Cognition, Logic and Communication is brought to you for free and open access by the Conferences at New Prairie Press. It has been accepted for inclusion in Baltic International Yearbook of Cognition, Logic and Communication by an authorized administrator of New Prairie Press. For more information, please contact [email protected]. Games and Logic 2 The Baltic International Yearbook of x”. Their scopal dependencies and independencies in a first-order sen- Cognition, Logic and Communication tence are recast in terms of the strategic interaction of two players in a game of perfect information. For instance, the first-order sentence November 2013 Volume 8: Games, Game Theory ∀x∃yB(x, y) is analyzed in terms of a game between the universal and Game Semantics player (Abelard) and the existential player (Eloise). They choose indi- pages 1-30 DOI: 10.4148/1944-3676.1072 viduals from the underlying universe of discourse to be the values of the variables x and y, respectively. The order of the choices and the information sets of the players are indicated by the syntax of the sen- GABRIEL SANDU tence.
    [Show full text]
  • ON the SYSTEM CL12 of COMPUTABILITY LOGIC Contents
    Logical Methods in Computer Science Vol. 11(3:1)2015, pp. 1–71 Submitted Jan. 13, 2013 www.lmcs-online.org Published Jul. 28, 2015 ON THE SYSTEM CL12 OF COMPUTABILITY LOGIC GIORGI JAPARIDZE Department of Computing Sciences, Villanova University, 800 Lancaster Avenue, Villanova, PA 19085, USA URL: http://www.csc.villanova.edu/∼japaridz/ e-mail address: [email protected] Abstract. Computability logic (CoL) is a long-term project for redeveloping logic on the basis of a constructive game semantics, with games seen as abstract models of interactive computational problems. Among the fragments of CoL successfully axiomatized so far is CL12 — a conservative extension of classical first-order logic, whose language augments that of classical logic with the so called choice (“constructive”) sorts of quantifiers and connectives. This system has already found fruitful applications as a logical basis for constructive and complexity-bound versions of Peano arithmetic, such as arithmetics for polynomial time computability, polynomial space computability, and beyond. The present paper introduces a third, indispensable complexity measure for interactive computations termed amplitude complexity, and establishes the adequacy (soundness/completeness) of CL12 and the associated Logical Consequence mechanism with respect to (simultaneously) A amplitude, S space and T time computability under certain minimal conditions on the triples (A,S,T ) of function classes. This result very substantially broadens the potential application areas of CL12, even when time and/or space complexity is the only concern. It would be sufficient to point out that, for instance, now CL12 can be reliably used as a logical basis of systems for logarithmic space or exponential time computabilities — something that the earlier-known crude adequacy results for CL12 were too weak to allow us to do.
    [Show full text]
  • Historical Projects in Discrete Mathematics and Computer Science
    Historical Projects in Discrete Mathematics and Computer Science Janet Barnett, Guram Bezhanishvili, Hing Leung, Jerry Lodder, David Pengelley, Desh Ranjan 1 Introduction A course in discrete mathematics is a relatively recent addition, within the last 30 or 40 years, to the modern American undergraduate curriculum, born out of a need to instruct computer science ma- jors in algorithmic thought. The roots of discrete mathematics, however, are as old as mathematics itself, with the notion of counting a discrete operation, usually cited as the first mathematical devel- opment in ancient cultures [38]. By contrast, a course in finite mathematics is sometimes presented as a fast-paced news reel of facts and formulae, often memorized by the students, with the text offering only passing mention of the motivating problems and original work that eventually found resolution in the modern concepts of induction, recursion and algorithm. This chapter focuses on the pedagogy of historical projects, which offer excerpts from original sources, place the material in context, and provide direction to the subject matter. Each historical project is centered around a publication of mathematical significance, such as Blaise Pascal’s “Treatise on the Arithmetical Triangle” [53, vol. 30] from the 1650s or Alan Turing’s 1936 paper “On Computable Numbers with an Application to the Entscheidungsproblem” [66]. The projects are designed to introduce or provide supplementary material for topics in the curriculum, such as induction in a discrete mathematics course, or compilers and computability for a computer science course. Each project provides a discussion of the historical exigency of the piece, a few biographical comments about the author, excerpts from the original work, and a sequence of questions to help the student appreciate the source.
    [Show full text]
  • Semantics of Information As Interactive Computation
    Semantics of Information as Interactive Computation Gordana Dodig-Crnkovic Department of Computer Science and Electronics, Mälardalen University. Sweden [email protected] http://www.idt.mdh.se/personal/gdc Abstract. Computers today are not only the calculation tools - they are directly (inter)acting in the physical world which itself may be conceived of as the universal computer (Zuse, Fredkin, Wolfram, Chaitin, Lloyd). In expanding its domains from abstract logical symbol manipulation to physical embedded and networked devices, computing goes beyond Church-Turing limit (Copeland, Siegelman, Burgin, Schachter). Computational processes are distributed, reactive, interactive, agent-based and concurrent. The main criterion of success of computation is not its termination, but the adequacy of its response, its speed, generality and flexibility; adaptability, and tolerance to noise, error, faults, and damage. Interactive computing is a generalization of Turing computing, and it calls for new conceptualizations (Goldin, Wegner). In the info-computationalist framework, with computation seen as information processing, natural computation appears as the most suitable paradigm of computation and information semantics requires logical pluralism. Keywords: Semantic Information, Computationalism, Philosophy of Computing, Hypercomputating, Philosophy of Information 1 Introduction Every epoch and culture has a different conception of the universe. For some (numerous ancient myths, Thales, Spinoza) universe was a living organism. For Ptolemy, Descartes, and Newton it was a huge machine. Our current understanding of information and computing has led to a conception of the universe as a computer. On such a pancomputational and paninformational view (Zuse, Fredkin, Wolfram, Chaitin, Lloyd) we can consider information as a result of (natural) computation, and the universe as a network of computing processes that are defined by the information they manipulate and produce.
    [Show full text]
  • Computability Logic
    Computability logic: Giving Caesar what belongs to Caesar Giorgi Japaridze Villanova University and Institute of Philosophy, Russian Academy of Sciences 800 Lancaster Avenue, Villanova, PA 19085, USA Email: [email protected] Abstract The present article is a brief informal survey of computability logic (CoL). This relatively young and still evolving nonclassical logic can be characterized as a formal theory of computability in the same sense as classical logic is a formal theory of truth. In a broader sense, being conceived semantically rather than proof-theoretically, CoL is not just a particular theory but an ambitious and challenging long-term project for redeveloping logic. In CoL, logical operators stand for operations on computational problems, formulas represent such problems, and their “truth” is seen as algorithmic solvability. In turn, computational problems — understood in their most general, interactive sense — are defined as games played by a machine against its environment, with “algorithmic solvability” meaning existence of a machine which wins the game against any possible behavior of the environment. With this semantics, CoL provides a systematic answer to the question “What can be computed?”, just like classical logic is a systematic tool for telling what is true. Furthermore, as it happens, in positive cases “What can be computed” always allows itself to be replaced by “How can be computed”, which makes CoL a problem-solving tool. CoL is a conservative extension of classical first order logic but is otherwise much more expressive than the latter, opening a wide range of new application areas. It relates to intuitionistic and linear logics in a similar fashion, which allows us to say that CoL reconciles and unifies the three traditions of logical thought (and beyond) on the basis of its natural and “universal” game semantics.
    [Show full text]
  • Computability Logic გამოთვლადობის ლოგიკა Логика Вычислимости 可计算性逻辑 (Col)
    12/14/2016 Giorgi Japaridze A Survey of Computability Logic გამოთვლადობის ლოგიკა Логика вычислимости 可计算性逻辑 (col) Computability is one of the most interesting and fundamental concepts in mathematics and computer science, and it is natural to ask what logic it induces. This is where Computability Logic (CoL) comes in. It is a formal theory of computability in the same sense as classical logic is a formal theory of truth. In a broader and more proper sense, CoL is not just a particular theory but an ambitious and challenging program for redeveloping logic following the scheme “from truth to computability”. Under the approach of CoL, logical operators stand for operations on computational problems, formulas represent such problems, and their “truth” is seen as algorithmic solvability. In turn, computational problems ­­­ understood in their most general, interactive sense ­­­ are defined as games played by a machine against its environment, with “algorithmic solvability” meaning existence of a machine which wins the game against any possible behavior of the environment. With this semantics, CoL provides a systematic answer to the question “what can be computed?”, just like classical logic is a systematic tool for telling what is true. Furthermore, as it happens, in positive cases “what can be computed” always allows itself to be replaced by “how can be computed”, which makes CoL of potential interest in not only theoretical computer science, but many applied areas as well, including constructive applied theories, interactive knowledge base systems, resource oriented systems for planning and action, or declarative programming languages. Currently CoL is still at an early stage of development, with open problems prevailing over answered questions.
    [Show full text]
  • Association for Symbolic Logic Business Office: ASL, Dept
    Association for Symbolic Logic Business Office: ASL, Dept. of Mathematics, Univ. of Connecticut 341 Mansfield Road, U-1009, Storrs, CT 06269-1009, USA Phone: 1-860-486-3989; Fax: 1-860-486-4238; email: [email protected] Web: http://www.aslonline.org ASL NEWSLETTER January 2021 • The 2020 ASL Election. In the 2020 election, the members of the ASL elected Juliet Floyd (Boston Univer- sity) and Dima Sinapova (University of Illinois-Chicago) to the Executive Committee; and Sebastiaan Terwijn (Radboud University, Nijmegen) and Wei Li (Chinese Academy of Sciences) to the ASL Council. All terms are for three years beginning January 1, 2021. Many thanks to all those who voted. • Special 25th Anniversary BSL Prize. The Bulletin of Symbolic Logic was founded 25 years ago. Over the past 25 years, the BSL has published many expository papers of outstanding quality, on a variety of topics, and from a variety of perspectives within logic. These papers have helped students to get started, they have allowed researchers to see connections between different areas, and they have let all of us see some of the history of our subject. To celebrate, and to advertise the BSL, the ASL is giving a special BSL 25th Anniversary Prize. Here is the list of winning papers from the first 25 years of the BSL. • Jeremy Avigad, \Forcing in proof theory," 10(3):305-333, 2004. • Akihiro Kanamori, \The mathematical development of set theory from Cantor to Cohen," 2(1):1-71, 1996. • Colin McLarty, \What does it take to prove Fermat's Last Theorem?" 16(3):359-377, 2010.
    [Show full text]
  • Build Your Own Clarithmetic I: Setup and Completeness
    Logical Methods in Computer Science Vol. 12(3:8)2016, pp. 1–59 Submitted Oct. 30, 2015 www.lmcs-online.org Published Sep. 6, 2016 BUILD YOUR OWN CLARITHMETIC I: SETUP AND COMPLETENESS GIORGI JAPARIDZE Department of Computing Sciences, Villanova University, 800 Lancaster Avenue, Villanova, PA 19085, USA URL: http://www.csc.villanova.edu/∼japaridz/ e-mail address: [email protected] Abstract. Clarithmetics are number theories based on computability logic. Formulas of these theories represent interactive computational problems, and their “truth” is under- stood as existence of an algorithmic solution. Various complexity constraints on such solutions induce various versions of clarithmetic. The present paper introduces a param- P1,P2,P3 CLA11 P1, P2, P3 eterized/schematic version P4 . By tuning the three parameters in an essentially mechanical manner, one automatically obtains sound and complete theories with respect to a wide range of target tricomplexity classes, i.e., combinations of time (set by P3), space (set by P2) and so called amplitude (set by P1) complexities. Sound in the sense that every theorem T of the system represents an interactive number-theoretic computational problem with a solution from the given tricomplexity class and, further- more, such a solution can be automatically extracted from a proof of T . And complete in the sense that every interactive number-theoretic problem with a solution from the given tricomplexity class is represented by some theorem of the system. Furthermore, through tuning the 4th parameter P4, at the cost of sacrificing recursive axiomatizability but not simplicity or elegance, the above extensional completeness can be strengthened to intensional completeness, according to which every formula representing a problem with a solution from the given tricomplexity class is a theorem of the system.
    [Show full text]