David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 75 (2):565-601 (2010)
Computability logic (CL) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally been. Formulas in it represent computational problems, "truth" means existence of an algorithmic solution, and proofs encode such solutions. Within the line of research devoted to finding axiomatizations for ever more expressive fragments of CL, the present paper introduces a new deductive system CL12 and proves its soundness and completeness with respect to the semantics of CL. Conservatively extending classical predicate calculus and offering considerable additional expressive and deductive power, CL12 presents a reasonable, computationally meaningful, constructive alternative to classical logic as a basis for applied theories. To obtain a model example of such theories, this paper rebuilds the traditional, classical-logic-based Peano arithmetic into a computability-logic-based counterpart. Among the purposes of the present contribution is to provide a starting point for what, as the author wishes to hope, might become a new line of research with a potential of interesting findings—an exploration of the presumably quite unusual metatheory of CL-based arithmetic and other CL-based applied systems
|Keywords||Computability logic game semantics Peano arithmetic constructive logics|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Giorgi Japaridze (2009). Many Concepts and Two Logics of Algorithmic Reduction. Studia Logica 91 (1):1 - 24.
Giorgi Japaridze (2012). Separating the Basic Logics of the Basic Recurrences. Annals of Pure and Applied Logic 163 (3):377-389.
Similar books and articles
Shawn Hedman (2004). A First Course in Logic: An Introduction to Model Theory, Proof Theory, Computability, and Complexity. Oxford University Press.
Steve Awodey, Lars Birkedal & Dana Scott, Local Realizability Toposes and a Modal Logic for Computability.
George Boolos, John Burgess, Richard P. & C. Jeffrey (2007). Computability and Logic. Cambridge University Press.
Robert I. Soare (1996). Computability and Recursion. Bulletin of Symbolic Logic 2 (3):284-321.
Herbert B. Enderton (2011). Computability Theory: An Introduction to Recursion Theory. Academic Press.
Mauro Ferrari & Camillo Fiorentini (2003). A Proof-Theoretical Analysis of Semiconstructive Intermediate Theories. Studia Logica 73 (1):21 - 49.
Stewart Shapiro (1983). Remarks on the Development of Computability. History and Philosophy of Logic 4 (1-2):203-220.
Dag Normann (2006). Computing with Functionals: Computability Theory or Computer Science? Bulletin of Symbolic Logic 12 (1):43-59.
Ehud Hrushovski (1989). Finitely Based Theories. Journal of Symbolic Logic 54 (1):221-225.
Ayda I. Arruda, Newton C. A. Costdaa & R. Chuaqui (eds.) (1977). Non-Classical Logics, Model Theory, and Computability: Proceedings of the Third Latin-American Symposium on Mathematical Logic, Campinas, Brazil, July 11-17, 1976. [REVIEW] Sale Distributors for the U.S.A. And Canada, Elsevier/North-Holland.
Viggo Stoltenberg-Hansen & John V. Tucker (2003). Computable and Continuous Partial Homomorphisms on Metric Partial Algebras. Bulletin of Symbolic Logic 9 (3):299-334.
Jeremy Avigad (2000). Interpreting Classical Theories in Constructive Ones. Journal of Symbolic Logic 65 (4):1785-1812.
Added to index2010-09-12
Total downloads4 ( #254,850 of 1,101,181 )
Recent downloads (6 months)1 ( #290,806 of 1,101,181 )
How can I increase my downloads?