Proof-theoretic modal pa-completeness I: A system-sequent metric
Studia Logica 63 (1):27-48 (1999)
| Abstract | This paper is the first of a series of three articles that present the syntactic proof of the PA-completeness of the modal system G, by introducing suitable proof-theoretic objects, which also have an independent interest. We start from the syntactic PA-completeness of modal system GL-LIN, previously obtained in [7], [8], and so we assume to be working on modal sequents S which are GL-LIN-theorems. If S is not a G-theorem we define here a notion of syntactic metric d(S, G): we calculate a canonical characteristic fomula H of S (char(S)) so that G H (S) and GL-LIN H, and the complexity of H gives the distance d(S, G) of S from G. Then, in order to produce the whole completeness proof as an induction on this d(S, G), we introduce the tree-interpretation of a modal sequent Q into PA, that sends the letters of Q into PA-formulas describing the properties of a GL-LIN-proof P of Q: It is also a d(*, G)-metric linked interpretation, since it will be applied to a proof-tree T of H with H = char(S) and ( H) = d(S, G). | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,679 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesH. Kushida & M. Okada (2003). A Proof-Theoretic Study of the Correspondence of Classical Logic and Modal Logic. Journal of Symbolic Logic 68 (4):1403-1414.
Francesco Belardinelli, Peter Jipsen & Hiroakira Ono (2004). Algebraic Aspects of Cut Elimination. Studia Logica 77 (2):209 - 240.
Dick Jongh, Marc Jumelet & Franco Montagna (1991). On the Proof of Solovay's Theorem. Studia Logica 50 (1):51 - 69.
Thomas Studer (2008). On the Proof Theory of the Modal Mu-Calculus. Studia Logica 89 (3):343 - 363.
Gerard Renardel de Lavalette, Barteld Kooi & Rineke Verbrugge (2008). Strong Completeness and Limited Canonicity for PDL. Journal of Logic, Language and Information 17 (1).
Paolo Gentilini (1993). Syntactical Results on the Arithmetical Completeness of Modal Logic. Studia Logica 52 (4):549 - 564.
Paolo Gentilini (1999). Proof-Theoretic Modal PA-Completeness II: The Syntactic Countermodel. Studia Logica 63 (2):245-268.
Paolo Gentilini (1999). Proof-Theoretic Modal PA-Completeness III: The Syntactic Proof. Studia Logica 63 (3):301-310.
Analytics
Monthly downloads |
Added to index2009-01-28Total downloads3 ( #201,930 of 549,084 )Recent downloads (6 months)0How can I increase my downloads? |
My notes
Discussion
