Provability logic
Stanford Encyclopedia of Philosophy (2008)
Abstract
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.Author's Profile
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Embedding Classical Logic in S4.Sophie Nagler - 2019 - Dissertation, Munich Center for Mathematical Philosophy (Mcmp), Lmu Munich
References found in this work
An Essay in Classical Modal Logic.Krister Segerberg - 1971 - Uppsala, Sweden: Uppsala, Filosofiska Föreningen Och Filosofiska Institutionen Vid Uppsala Universitet.
Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I.K. Gödel - 1931 - Monatshefte für Mathematik 38 (1):173--198.
Metamathematical Investigation of Intuitionistic Arithmetic and Analysis.Anne S. Troelstra - 1973 - New York: Springer.