From de Jongh’s theorem to intuitionistic logic of proofs
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چکیده
The famous de Jongh’s theorem of 1970 stated that the intuitionistic logic captured all the logical formulas which have all arithmetical instances derivable in the Heyting Arithmetic HA. In this note we extend de Jongh’s arithmetical completeness property from IPC to the basic intuitionistic logic of proofs, which allows proof assertion statements of the sort x is a proof of F. The logic of proofs seems to provide an appropriate language of describing admissible rules in HA.
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تاریخ انتشار 2004