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Provability logics with quantifiers on proofs

✍ Scribed by Rostislav E. Yavorsky

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
124 KB
Volume
113
Category
Article
ISSN
0168-0072

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✦ Synopsis

We study here extensions of the Artemov's logic of proofs in the language with quantiÿers on proof variables. Since the provability operator A could be expressed in this language by the formula ∃u[u]A, the corresponding logic naturally extends the well-known modal provability logic GL. Besides, the presence of quantiÿers on proofs allows us to study some properties of provability not covered by the propositional logics.

In this paper we study the arithmetical complexity of the provability logic with quantiÿers on proofs qLP K (T ) for a given arithmetical theory T and a class K of proof predicates.

In the last section we deÿne Kripke style semantics for the logics corresponding to the standard G odel proof predicate and its multiple conclusion version.

📜 SIMILAR VOLUMES

Logic of proofs and provability
Logic of proofs and provability
✍ Tatiana Yavorskaya (Sidon) 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 216 KB

In the paper the joint Logic of Proofs and Provability LPP is presented that incorporates both the modality for provability (Israel J. Math. 25 (1976) 287-304) and the proof operator <t=F representing the proof predicate "t is a proof of F " (Technical Report No. CFIS 95-29, Cornell University, 1995