01037nas a2200133 4500008004100000245006200041210006200103300001200165490000700177520063000184100001900814700001900833856005100852 2016 eng d00aWeak arithmetical interpretations for the Logic of Proofs0 aWeak arithmetical interpretations for the Logic of Proofs a424-4400 v243 aArtemov established an arithmetical interpretation for the Logics of Proofs LPCS, which yields a classical provability semantics for the modal logic S4. The Logics of Proofs are parameterized by so-called constant specifications CS, stating which axioms can be used in the reasoning process, and the arithmetical interpretation relies on constant specifications being finite. In this article, we remove this restriction by introducing weak arithmetical interpretations that are sound and complete for a wide class of constant specifications, including infinite ones. In particular, they interpret the full Logic of Proofs LP.1 aKuznets, Roman1 aStuder, Thomas uhttp://www.iam.unibe.ch/ltgpub/2016/kust16.pdf