The Logic of Provability
نویسنده
چکیده
This chapter is dedicated to the memory of George Boolos. From the start of the subject until his death on 27 May 1996 he was the prime inspirer of the work in the logic of provability.
منابع مشابه
Project Report Logic Programming in Constructive Provability Logic 15-816 Modal Logic
We present a novel formulation of CPL, a constructive logic of provability that is closely connected to the Gödel-Löb logic of provability. Our logical formulation allows modal operators to talk about both provability and non-provability of propositions at reachable worlds. We use this logic as a basis for a discussion of negation in logic programming.
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This is an introductory paper about provability logic, a modal propositional logic in which necessity is interpreted as formal provability. We discuss the ideas that led to establishing this logic, we survey its history and the most important results, and we emphasize its applications in metamathematics. Stress is put on the use of Gentzen calculus for provability logic. We sketch our version o...
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We present two variants of an intuitionistic sequent calculus that validates the Löb rule and permits logical reflection over provability. We explore properties of both variants of this logic, which we call constructive provability logic due to its close ties to Gödel-Löb provability logic.
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We present constructive provability logic, an intuitionstic modal logic that validates the Löb rule of Gödel and Löb’s provability logic by permitting logical reflection over provability. Two distinct variants of this logic, CPL and CPL*, are presented in natural deduction and sequent calculus forms which are then shown to be equivalent. In addition, we discuss the use of constructive provabili...
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Gödel’s modal logic approach to analyzing provability attracted a great deal of attention and eventually led to two distinct mathematical models. The first is the modal logic GL, also known as the Provability Logic, which was shown in 1979 by Solovay to be the logic of the formal provability predicate. The second is Gödel’s original modal logic of provability S4, together with its explicit coun...
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Berarducci, A. and R. Verbrugge, On the provability logic of bounded arithmetic, Annals of Pure and Applied Logic 61 (1993) 75-93. Let PLQ be the provability logic of IA, + G?,. We prove some containments of the form L c_ PLQc Th(V) where L is the provability logic of PA and V is a suitable class of Kripke frames.
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