Abstract

AbstractWe explore two ways of formalizing Kreisel’s addendum to the Brouwer-Heyting-Kolmogorov interpretation. To do this we compare Artemov’s justification logic with simply typed \(\lambda \) calculus, by introducing a map from justification terms into \(\lambda \) terms, which can be viewed as a method of extracting the computational content of the justification terms. Then we examine the interpretation of Kreisel’s addendum in justification logic along with the image of the resulting justification terms under our map.KeywordsJustification logicType theoryIntuitionistic logic\(\lambda \) calculusBHK interpretation

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