Ptarithmetic

The Baltic International Yearbook of Cognition Logic and Communication

Japaridze, Giorgi¹ 

[1] School of Computer Science and Technology, Shandong University; Department of Computing Sciences, Villanova University

关键词: Computability logic;    Interactive computation;    Computational complexity;    Game semantics;   

DOI  :  10.4148/1944-3676.1074

学科分类：社会科学、人文和艺术（综合）

来源: New Prairie Press

【 摘 要 】

The present article introduces ptarithmetic (short for “polynomial time arithmetic”) — a formal number theory similar to the well known Peano arithmetic, but based on the recently born computability logic instead of classical logic. The formulas of ptarithmetic represent interactive computational problems rather than just true/false statements, and their “truth” is understood as existence of a polynomial time solution. The system of ptarithmetic elaborated in this article 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 effectively 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 self-contained, and can be read without any prior familiarity with computability logic.

【 授权许可】

Unknown