Zbl 1201.03055 ¡ J

Japaridze, Giorgi £ Towards applied theories based on computability logic. (English) ¢Zbl 1201.03055 ¡ J. Symb. Log. 75, No. 2, 565-601 (2010). The paper is a continuation of the author’s Computability Logic program for “developing logic as a formal theory of computability”, opposing the traditional view of logic as a formal theory of truth (or provability). Familiarity with the previous single-authored papers on Computability Logic (CL) from 2003 onward is assumed for reading the paper. Formulas in CL represent computational problems, truth of a formula means existence of an algorithmic solutions, while the proofs encode such solutions. In the present paper, a new deductive system is introduced and its soundness and completeness is proved for the semantics of CL. Also a computability-logic-based arithmetic, as a counterpart of Peano Arithmetic based on CL, is introduced and further developed. Reviewer: Saeed Salehi (Tabriz) MSC: 03F50 Metamathematics of constructive systems Cited in 1 Review 03B70 Logic in computer science Cited in 9 Documents 03F30 First-order arithmetic and fragments Keywords: computability logic; game semantics; Peano arithmetic; constructive logics Full Text: DOI arXiv References: [1] DOI: 10.1093/logcom/exl005 · Zbl 1113.03023 · doi:10.1093/logcom/exl005 [2] DOI: 10.1145/1131313.1131318 · Zbl 1367.03056 · doi:10.1145/1131313.1131318 [3] DOI: 10.1007/3-540-34874-3_9 · Zbl 1266.03046 · doi:10.1007/3-540-34874-39 [4] DOI: 10.1016/S0168-0072(03)00023-X · Zbl 1028.03025 · doi:10.1016/S0168-0072(03)00023-X [5] Introduction to metamathematics (1952) [6] DOI: 10.1007/s11225-009-9164-7 · Zbl 1162.03016 · doi:10.1007/s11225-009-9164-7 [7] Games: Unifying logic, language, and philosophy pp 249– (2009) [8] DOI: 10.1016/j.ic.2008.10.001 · Zbl 1161.03016 · doi:10.1016/j.ic.2008.10.001 [9] DOI: 10.1093/logcom/exn019 · Zbl 1170.03028 · doi:10.1093/logcom/exn019 [10] DOI: 10.1016/j.apal.2007.05.001 · Zbl 1143.03014 · doi:10.1016/j.apal.2007.05.001 [11] The logic of interactive Turing reduction 72 pp 243– (2007) · Zbl 1161.03015 [12] Acta Cybernetica 18 pp 77– (2007) [13] DOI: 10.1016/j.tcs.2007.01.004 · Zbl 1118.03021 · doi:10.1016/j.tcs.2007.01.004 [14] DOI: 10.1145/1131313.1131319 · Zbl 1367.03057 · doi:10.1145/1131313.1131319 [15] DOI: 10.1016/j.tcs.2006.03.014 · Zbl 1094.03019 · doi:10.1016/j.tcs.2006.03.014 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identiﬁers and may contain data conversion errors. It attempts to reﬂect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching. Edited by FIZ Karlsruhe, the European Mathematical Society and the Heidelberg Academy of Sciences and Humanities © 2021 FIZ Karlsruhe GmbH Page 1.

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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).
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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.
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Contribution of Warsaw Logicians to Computational Logic
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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.
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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.
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ON the SYSTEM CL12 of COMPUTABILITY LOGIC Contents
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Semantics of Information As Interactive Computation
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Computability Logic გამოთვლადობის ლოგიკა Логика Вычислимости 可计算性逻辑 (Col)
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Curriculum Vitæ JOHN PATTON BURGESS
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