A Computational Interpretation of Modal Proofs
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Proof theory of modal logics, though largely studied since the fifties, has always been a delicate subject, the main reason being the apparent impossibility to obtain elegant, natural systems for intensional operators (with the excellent exception of intuitionistic logic). For example Segerberg, not earlier than 1984 , observed that the Gentzen format, which works so well for truth functional and intuitionistic operators, cannot be a priori expected to remain valid for modal logics; carrying to the limit this observation one could even assert that ‘logics with no good proof theory are unnatural.’ In such a way we should mark as ‘unnatural’ all modal logics (with great delight of a large number of logicians!).
KeywordsModal Logic Accessibility Relation Intuitionistic Logic Natural Deduction Proof Theory
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- H. Barendregt. The Lambda Calculus: its Syntax and Semantics. Studies in Logic and the Foundations of Mathematics. North-Holland, 1984. Revised Edition.Google Scholar
- H. Barendregt. Lambda calculus with types. In: S. Abramsky, D. M. Gabbay, T. S. E. Maibaum, (eds.), Handbook of Logic in Computer Science, Vol. II Background: Computational Structures, pp. 118–310. Oxford University Press, 1992.Google Scholar
- G. Bierman, C. Mere, V. de Paiva. Intuitionistic necessity revisited. In: Logic at Work: Applied Logic Conference, 1992.Google Scholar
- R. Bull, K. Segerberg. Basic modal logic. In: D. Gabbay, F. Guenthner, (eds.), Handbook of Philosophical Logic, Vol. II, pp. 1–88. Reidel, 1984.Google Scholar
- D. M. Gabbay, R. J.G.B. de Queiroz. An introduction to labelled natural deduction. Proceedings of Third Advanced Summer School in Artificial Intelligence, 1992.Google Scholar
- J.-Y. Girard. Proof Theory and Logical Complexity. Bibliopolis, 1987.Google Scholar
- G. Mints. Selected Papers in Proof Theory. Bibliopolis, 1992.Google Scholar
- D. Prawitz. Natural Deduction. Acta Universitatis Stockholmiensis, Stockholm Studies in Philosophy 3, Almqvist & Wiksell, Stockholm, 1965.Google Scholar
- A. S. Troelstra and Dirk van Dalen. Constructivism in Mathematics, Vol. II. North-Holland, 1988.Google Scholar