Abstract
Global properties of canonical derivability predicates (the standard example is Pr() in Peano Arithmetic) are studied here by means of a suitable propositional modal logic GL. A whole book [1] has appeared on GL and we refer to it for more information and a bibliography on GL. Here we propose a sequent calculus for GL and, by exhibiting a good proof procedure, prove that such calculus admits the elimination of cuts. Most of standard results on GL are then easy consequences: completeness, decidability, finite model property, interpolation and the fixed point theorem.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G. Boolos, The unprovability of consistency. An essay in modal logic, Cambridge U. P. 1979.
W. Rautenberg, Klassiche und Nichtklassiche Aussagenlogik, Vieweg Verlag 1979.
C. Smorynski, Beth's Theorem and self-referential statements, in: Logic Colloquium '77, A Macintyre, L. Pacholski, J. Paris (eds), North Holland 1978, pp. 253–261.
G. Takeuti, Proof Theory, North Holland 1975.
S. Valentini, Cut elimination in a modal sequent calculus for K, submitted to Studia Logica.
Author information
Authors and Affiliations
Additional information
The second author holds a grant from the Consiglio Nazionale delle Ricerche, gruppo G.N.S.A.G.A.
Rights and permissions
About this article
Cite this article
Sambin, G., Valentini, S. A modal sequent calculus for a fragment of arithmetic. Stud Logica 39, 245–256 (1980). https://doi.org/10.1007/BF00370323
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00370323