Stanford Encyclopedia of Philosophy (2008)

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Provability logic is a modal logic that is used to investigate what arithmetical theories can express in a restricted language about their provability predicates. The logic has been inspired by developments in meta-mathematics such as Gödel’s incompleteness theorems of 1931 and Löb’s theorem of 1953. As a modal logic, provability logic has been studied since the early seventies, and has had important applications in the foundations of mathematics. From a philosophical point of view, provability logic is interesting because the concept of provability in a fixed theory of arithmetic has a unique and non-problematic meaning, other than concepts like necessity and knowledge studied in modal and epistemic logic. Furthermore, provability logic provides tools to study the notion of self-reference.
Keywords provability logic  modal logic  self-reference  Peano Arithmetic  interpretability logic
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References found in this work BETA

An Essay in Classical Modal Logic.Krister Segerberg - 1971 - Uppsala, Sweden: Uppsala, Filosofiska Föreningen Och Filosofiska Institutionen Vid Uppsala Universitet.
Computability & Unsolvability.Martin Davis - 1958 - Dover Publications.
The Logic of Provability.George Boolos - 1993 - Cambridge and New York: Cambridge University Press.

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Reflections on Orlov.Graham Priest - 2021 - History and Philosophy of Logic 42 (2):118-128.
Embedding Classical Logic in S4.Sophie Nagler - 2019 - Dissertation, Munich Center for Mathematical Philosophy (MCMP), LMU Munich

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