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arXiv 1601.03059math.LO
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验证与直觉主义知识的算术解释

An Arithmetical Interpretation of Verification and Intuitionistic Knowledge

Tudor Protopopescu

备注：
Due to several publisher's errors the publisher failed to include a corrected version of the paper for publication. The paper published in LNCS 9537 is an uncorrected proof which contains various errors introduced by the publisher, and lacks changes submitted to, and approved for inclusion by, the publisher. This should be considered the official one
发表信息：
Logical Foundations of Computer Science, Lecture Notes in Computer Science 9537, 317--330, Springer, 2016
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摘要：

直觉主义认识逻辑向直觉主义逻辑引入了一个认识运算符，该运算符反映了直觉主义的预期BHK语义。关于直觉主义知识和信念的基本假设是，它是验证的产物。BHK对直觉主义逻辑的解释在《证明的逻辑》及其算术语义学中有一个精确的表述。我们在这里表明，这种解释可以扩展到验证的概念，直觉知识的基础上，从而提供了系统的直觉认知逻辑扩展的认知算子的基础上验证算术语义。

英文摘要：

Intuitionistic epistemic logic introduces an epistemic operator, which reflects the intended BHK semantics of intuitionism, to intuitionistic logic. The fundamental assumption concerning intuitionistic knowledge and belief is that it is the product of verification. The BHK interpretation of intuitionistic logic has a precise formulation in the Logic of Proofs and its arithmetical semantics. We show here that this interpretation can be extended to the notion of verification upon which intuitionistic knowledge is based, thereby providing the systems of intuitionistic epistemic logic extended by an epistemic operator based on verification with an arithmetical semantics too.

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