Journal of Philosophical Logic 39 (5):577 - 590 (2010)
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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References found in this work BETA
Review of Robert M. Solovay's Provability Interpretations of Modal Logic.George Boolos - 1981 - Journal of Symbolic Logic 46 (3):661-662.
Some Theorems About the Sentential Calculi of Lewis and Heyting.J. C. C. McKinsey & Alfred Tarski - 1948 - Journal of Symbolic Logic 13 (1):1-15.
Arithmetical Necessity, Provability and Intuitionistic Logic.Rob Goldblatt - 1978 - Theoria 44 (1):38-46.
Some Relational Systems and the Associated Topological Spaces.Andrzej Grzegorczyk - 1969 - Journal of Symbolic Logic 34 (4):652-653.
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