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RULES FOR SUBATOMIC DERIVATION

Published online by Cambridge University Press:  15 December 2010

BARTOSZ WIĘCKOWSKI
BARTOSZ WIĘCKOWSKI*
Affiliation:
Universität Tübingen
*
*UNIVERSITÄT TÜBINGEN, WILHELM-SCHICKARD-INSTITUT, SAND 13, 72076 TÜBINGEN, GERMANY, E-mail: [email protected]
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Abstract

In proof-theoretic semantics the meaning of an atomic sentence is usually determined by a set of derivations in an atomic system which contain that sentence as a conclusion (see, in particular, Prawitz, 1971, 1973). The paper critically discusses this standard approach and suggests an alternative account which proceeds in terms of subatomic introduction and elimination rules for atomic sentences. A simple subatomic normal form theorem by which this account of the semantics of atomic sentences and the terms from which they are composed is underpinned, shows moreover that the proof-theoretic analysis of first-order logic can be pursued also beneath the atomic level.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 4 , Issue 2 , June 2011 , pp. 219 - 236
Copyright
Copyright © Association for Symbolic Logic 2010

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References

BIBLIOGRAPHY

Francez, N., Dyckhoff, R., & Ben-Avi, G. (2010). Proof-theoretic semantics for subsentential phrases. Studia Logica, 94, 381–401.CrossRefGoogle Scholar
Gabbay, M., & Gabbay, M. J. (2009). Term sequent logic. Electronic Notes in Theoretical Computer Science, 246, 87–106.Google Scholar
Gentzen, G. (1934). Untersuchungen über das logische Schließen I, II. Mathematische Zeitschrift, 39, 176–210, 405–431.CrossRefGoogle Scholar
Hallnäs, L., & Schroeder-Heister, P. (1990/1991). A proof-theoretic approach to logic programming: I. Clauses as rules, II. Programs as definitions. Journal of Logic and Computation, 1, 261–283, 635–660.CrossRefGoogle Scholar
Kahle, R., & Schroeder-Heister, P., editors. (2006). Proof-Theoretic Semantics. Special issue of Synthese, Vol. 148, No. 3, pp. 501–749.Google Scholar
Kremer, M. (2007). Read on identity and harmony—A friendly correction and simplification. Analysis, 67, 157–159.Google Scholar
Lorenzen, P. (1955). Einführung in die operative Logik und Mathematik (second edition). Berlin: Springer.CrossRefGoogle Scholar
Martin-Löf, P. (1971). Hauptsatz for the intuitionistic theory of iterated inductive definitions. In Fenstad, J. E., editor. Proceedings of the Second Scandinavian Logic Symposium (Oslo 1970). Amsterdam, The Netherlands: North-Holland, pp. 197–215.Google Scholar
Moortgat, M. (1997). Categorial type logics. In van Benthem, J., & ter Meulen, A., editors. Handbook of Logic and Language. Amsterdam, The Netherlands: North-Holland, pp. 93–177.Google Scholar
Post, E. (1943). Formal reductions of the general combinatorial decision problem. American Journal of Mathematics, 65, 157–215.CrossRefGoogle Scholar
Prawitz, D. (1965). Natural Deduction. A Proof-Theoretical Study. Stockholm, Sweden: Almquist & Wiksell. Reprinted by Dover Publications, Mineola, New York, 2006.Google Scholar
Prawitz, D. (1970). Constructive semantics. In Proceedings of the First Scandinavian Logic Symposium (Åbo 1968). Filosofiska Studier utgivna av Filosofiska Föreningen och Filosofiska Institutionen vid Uppsala Universitet, nr 8, Uppsala, pp. 96–114.Google Scholar
Prawitz, D. (1971). Ideas and results in proof theory. In Fenstad, J. E., editor. Proceedings of the Second Scandinavian Logic Symposium (Oslo 1970). Amsterdam, The Netherlands: North-Holland, pp. 235–309.CrossRefGoogle Scholar
Prawitz, D. (1973). Towards a foundation of a general proof theory. In Suppes, P., editor. Logic, Methodology, and Philosophy of Science IV, Vol. 74. Amsterdam, The Netherlands: North-Holland, pp. 225–250.Google Scholar
Prawitz, D. (2006). Meaning approached via proofs. Synthese, 148, 507–524.CrossRefGoogle Scholar
Read, S. (2004). Identity and harmony. Analysis, 64, 113–119.CrossRefGoogle Scholar
Schroeder-Heister, P. (2006). Validity concepts in proof-theoretic semantics. Synthese, 148, 525–571.Google Scholar
Więckowski, B. (2010). Associative substitutional semantics and quantified modal logic. Studia Logica, 94, 105–138.CrossRefGoogle Scholar