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- W2608708140 abstract "The BHK interpretation interprets propositional statements as descriptions of the world of proofs; a world which is hierarchical in nature. It consists of different layers of the concept of proof; the proofs, the proofs about proofs and so on. To describe this hierarchical world, one approach is the Russellian approach in which we use a typed language to reflect this hierarchical nature in the syntax level. In this case, since the connective responsible for this hierarchical behavior is implication, we will use a typed language equipped with a hierarchy of implications, ${rightarrow_n}_{n=0}^{infty}$. In fact, using this typed propositional language, we will introduce the hierarchical counterparts of the logics $mathbf{BPC}$, $mathbf{EBPC}$, $mathbf{IPC}$ and $mathbf{FPL}$ and then by proving their corresponding soundness-completeness theorems with respect to their natural BHK interpretations, we will show how these different logics describe different worlds of proofs embodying different hierarchical behaviors." @default.
- W2608708140 created "2017-05-05" @default.
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- W2608708140 date "2017-04-20" @default.
- W2608708140 modified "2023-09-27" @default.
- W2608708140 title "Russellian Propositional Logic and the BHK Interpretation" @default.
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- W2608708140 hasPublicationYear "2017" @default.
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