Introduction to clarithmetic I

作     者：Japaridze, Giorgi 

作者机构：Villanova Univ Dept Comp Sci Villanova PA 19085 USA Shandong Univ Sch Comp Sci & Technol Jinan 250100 Shandong Peoples R China 

出 版 物：《INFORMATION AND COMPUTATION》 (信息与计算)

年 卷 期：2011年第209卷第10期

页      面：1312-1354页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 08[工学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：Computability logic Interactive computation Implicit computational complexity Game semantics Peano arithmetic Bounded arithmetic 

摘      要：Clarithmetic is a generic name for formal number theories similar to Peano arithmetic, but based on computability logic instead of the more traditional classical or intuitionistic logics. Formulas of clarithmetical theories represent interactive computational problems, and their truth is understood as existence of an algorithmic solution. Imposing various complexity constraints on such solutions yields various versions of clarithmetic. The present paper introduces a system of clarithmetic for polynomial time computability, which is shown to be sound and complete. Sound in the sense that every theorem T of the system represents an interactive number-theoretic computational problem with a polynomial time solution and, furthermore, such a solution can be efficiently extracted from a proof of T. And complete in the sense that every interactive number-theoretic problem with a polynomial time solution is represented by some theorem T of the system. The paper is written in a semitutorial style and targets readers with no prior familiarity with computability logic. (C) 2011 Elsevier Inc. All rights reserved.