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An arithmetical interpretation of verification and intuitionistic knowledge. (English) Zbl 06751247
Artemov, Sergei (ed.) et al., Logical foundations of computer science. International symposium, LFCS 2016, Deerfield Beach, FL, USA, January 4–7, 2016. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 9537, 317-330 (2016).
Summary: 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.
For the entire collection see [Zbl 1364.03006].

MSC:
03B70 Logic in computer science
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