On Provability Logic
نویسنده
چکیده
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 of a decision procedure for provability logic and mention some connections to computational complexity.
منابع مشابه
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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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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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Franco Montagna, a prominent logician and one of the leaders of the Italian school on Mathematical Logic, passed away on February 18, 2015. We survey some of his results and ideas in the two disciplines he greatly contributed along his career: provability logic and many-valued logic.
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