arXiv subjects

Aleksandr Yu. Konovalov

Publications and source records attributed to Aleksandr Yu. Konovalov.

2 recordsLinked to original sources

arXiv2022

Generalized Realizability and Intuitionistic Logic

Let V be a set of number-theoretical functions. We define a notion of V -realizability for predicate formulas in such a way that the indices of functions in V are used for interpreting the implication and the universal quantifier. In this paper we prove that Intuitionistic Predicate Calculus is sound with respect to the semantics of V -realizability if and only if some natural conditions for V hold.

math.LO↗

arXiv2020

Generalized Realizability and Basic Logic

Let V be a set of number-theoretical functions. We define a notion of absolute V-realizability for predicate formulas and sequents in such a way that the indices of functions in V are used for interpreting the implication and the universal quantifier. In this paper we prove that Basic Logic is sound with respect to the semantics of absolute V-realizability if V satisfies some natural conditions.

math.LO↗