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 (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 10,760
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Citations of this work BETA
Similar books and articles
Dick De Jongh & Frank Veltman (1999). Modal Completeness of ILW. In Jelle Gerbrandy, Maarten Marx, Maarten de Rijke & Yde Venema (eds.), Essays Dedicated to Johan van Benthem on the Occasion of His 50th Birthday. Amsterdam University Press.
Dick De Jongh & Frank Veltman (1999). Modal Completeness of ILW. In Jelle Gerbrandy, Maarten Marx, Maarten de Rijke & Yde Venema (eds.), Essays Dedicated to Johan van Benthem on the Occasion of His 50th Birthday. Amsterdam University Press.
Analytics

Monthly downloads

Added to index

2009-01-28

Total downloads

5 ( #224,380 of 1,098,955 )

Recent downloads (6 months)

2 ( #175,054 of 1,098,955 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.