Infinitary Action Logic with Exponentiation

01/19/2020

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by   Stepan L. Kuznetsov, et al.

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We introduce infinitary action logic with exponentiation—that is, the multiplicative-additive Lambek calculus extended with Kleene star and with a family of subexponential modalities, which allows some of the structural rules (contraction, weakening, permutation). The logic is presented in the form of an infinitary sequent calculus. We prove cut elimination and, in the case where at least one subexponential allows non-local contraction, establish exact complexity boundaries in two senses. First, we show that the derivability problem for this logic is Π_1^1-complete. Second, we show that the closure ordinal of its derivability operator is ω_1^CK.