Studia Logica 63 (1):27-48 (1999)

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: we calculate a canonical characteristic fomula H of S ) so that ⊢G ∼ H → and ⊢GL-LIN ∼ H, and the complexity σ of ∼ H gives the distance d of S from G. Then, in order to produce the whole completeness proof as an induction on this d, 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-metric linked interpretation, since it will be applied to a proof-tree T of ∼ H with H = char and σ = d.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
Categories (categorize this paper)
Reprint years 2004
DOI 10.1023/A:1005203020301
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 60,826
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

Paraconsistent Informational Logic.Paola Forcheri & Paolo Gentilini - 2005 - Journal of Applied Logic 3 (1):97-118.

Add more citations

Similar books and articles


Added to PP index

Total views
33 ( #321,961 of 2,438,799 )

Recent downloads (6 months)
1 ( #435,061 of 2,438,799 )

How can I increase my downloads?


My notes