Syntactical results on the arithmetical completeness of modal logic
Studia Logica 52 (4):549 - 564 (1993)
| Abstract | In this paper the PA-completeness of modal logic is studied by syntactical and constructive methods. The main results are theorems on the structure of the PA-proofs of suitable arithmetical interpretationsS of a modal sequentS, which allow the transformation of PA-proofs ofS into proof-trees similar to modal proof-trees. As an application of such theorems, a proof of Solovay's theorem on arithmetical completeness of the modal system G is presented for the class of modal sequents of Boolean combinations of formulas of the form p i,m i=0, 1, 2, ... The paper is the preliminary step for a forthcoming global syntactical resolution of the PA-completeness problem for modal logic. | |||||||||
| 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: 5,882 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesD. M. Gabbay & G. Malod (2002). Naming Worlds in Modal and Temporal Logic. Journal of Logic, Language and Information 11 (1):29-65.
Sergei Artemov & Giorgie Dzhaparidze (1990). Finite Kripke Models and Predicate Logics of Provability. Journal of Symbolic Logic 55 (3):1090-1098.
Takahiro Seki (2003). A Sahlqvist Theorem for Relevant Modal Logics. Studia Logica 73 (3):383 - 411.
Ernst Zimmermann (2003). Elementary Definability and Completeness in General and Positive Modal Logic. Journal of Logic, Language and Information 12 (1):99-117.
Paolo Gentilini (1999). Proof-Theoretic Modal PA-Completeness III: The Syntactic Proof. Studia Logica 63 (3):301-310.
Michal Grabowski (1988). Arithmetical Completeness Versus Relative Completeness. Studia Logica 47 (3):213 - 220.
Dick H. J. Jongh & Franco Montagna (1987). Generic Generalized Rosser Fixed Points. Studia Logica 46 (2):193 - 203.
Dick Jongh, Marc Jumelet & Franco Montagna (1991). On the Proof of Solovay's Theorem. Studia Logica 50 (1):51 - 69.
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 I: A System-Sequent Metric. Studia Logica 63 (1):27-48.
Analytics
Monthly downloads |
Added to index2009-01-28Total downloads4 ( #180,507 of 556,915 )Recent downloads (6 months)1 ( #64,931 of 556,915 )How can I increase my downloads? |
My notes
Discussion
