The Modal Logic of Gödel Sentences

Journal of Philosophical Logic 39 (5):577 - 590 (2010)

Abstract
The modal logic of Gödel sentences, termed as GS, is introduced to analyze the logical properties of 'true but unprovable' sentences in formal arithmetic. The logic GS is, in a sense, dual to Grzegorczyk's Logic, where modality can be interpreted as 'true and provable'. As we show, GS and Grzegorczyk's Logic are, in fact, mutually embeddable. We prove Kripke completeness and arithmetical completeness for GS. GS is also an extended system of the logic of 'Essence and Accident' proposed by Marcos (Bull Sect Log 34(1):43-56, 2005). We also clarify the relationships between GS and the provability logic GL and between GS and Intuitionistic Propositional Logic
Keywords Modal logic  Gödel incompleteness theorems
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DOI 10.1007/s10992-010-9140-8
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References found in this work BETA

Modal Logic.Alexander Chagrov - 1997 - Oxford University Press.
The Logic of Provability.George S. Boolos - 1993 - Cambridge University Press.
Self-Reference and Modal Logic.George Boolos & C. Smorynski - 1988 - Journal of Symbolic Logic 53 (1):306.

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