Source: J. Symbolic Logic Volume 72, Issue 4
(2007), 1204-1218.
In this paper we present two calculi for intuitionistic logic. The first one, IG, is
characterized by the fact that every proof-search terminates and termination is reached
without jeopardizing the subformula property. As to the second one, SIC, proof-search
terminates, the subformula property is preserved and moreover proof-search is performed
without any recourse to metarules, in particular there is no need to back-track. As a
consequence, proof-search in the calculus SIC is accomplished by a single tree as
in classical logic.
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References
A. Avron, A constructive analysis of RM, Journal of Symbolic Logic, vol. 52 (1987), pp. 939--951.
Mathematical Reviews (MathSciNet):
MR916399
G. Corsi, Semantic trees for Dummett's logic LC, Studia Logica, vol. 45 (1986), pp. 199--206.
Mathematical Reviews (MathSciNet):
MR877311
--------, The a fortiori rule: The key to reach termination in intuitionistic logic, Logic and Philosophy in Italy, Some trends and perspectives (M. Franchella and E. Ballo, editors), Polimetrica, Milano, 2006, pp. 26--47.
R. Dyckhoff, Contraction-free sequent calculi for intuitionistic logic, Journal of Symbolic Logic, vol. 57 (1992), pp. 795--807.
A. Heuerding, M. Seyfried, and H. Zimmermann, Efficient loop-check for backward proof search in some non-classical propositional logics, Proceedings of TABLEAUX'96, Lecture Notes on Computer Science, vol. 1071, Springer, 1996.
G. Pottinger, Uniform cut-free formulations of T, S4 and S5, Journal of Symbolic Logic, vol. 48 (1992), p. 900.
A. Troelstra and H. Schwichtenberg, Basic Proof Theory, Cambridge University Press, 1996, 2nd edition in 2000.
