Feasible Operations on Proofs: The Logic of Proofs for Bounded Arithmetic

Evan Goris

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Feasible Operations on Proofs: The Logic of Proofs for Bounded Arithmetic

机译：证明的可行运算：有界算术的证明逻辑

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摘要

This paper presents a semantics for the logic of proofs LP in which all the operations on proofs are realized by feasibly computable functions. More precisely, we will show that the completeness of LP for the semantics of proofs of Peano Arithmetic extends to the semantics of proofs in Buss' bounded arithmetic S_2~1. In view of applications in epistemology of LP in particular and justification logics in general this result shows that explicit knowledge in the propositional framework can be made computationally feasible.

机译：本文提出了证明逻辑LP的语义，其中对证明的所有操作均通过可行的可计算功能实现。更准确地说，我们将证明LP对Peano算法的证明语义的完整性扩展到Buss有界算术S_2〜1中的证明语义。鉴于特别是在LP认识论中的应用，以及一般而言，证明逻辑在应用中，该结果表明，命题框架中的显式知识可以在计算上变得可行。

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来源
《Theory of computing systems》 |2008年第2期|p.185-203|共19页
作者
Evan Goris;
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作者单位

The Graduate Center of the City University of New York, 365 Fifth Avenue, New York, NY 10016, USA;

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原文格式 PDF
正文语种 eng
中图分类计算技术、计算机技术;高等数学;
关键词
logic of proofs; bounded arithmetic;

机译：证明逻辑;有界算术;

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4. Logic of Proofs for Bounded Arithmetic [C] . Evan Goris International Computer Science Symposium in Russia(CSR 2006); 20060608-12; St.Petersburg(RU) . 2006

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5. Bounded Arithmetic and Formalizing Probabilistic Proofs [D] . Le, Dai Tri Man. 2014

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8. Proofs of Arithmetical Completeness for Interpretability Logic [R] . Zambella, D. 1991

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Feasible Operations on Proofs: The Logic of Proofs for Bounded Arithmetic

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