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Logic and Logical Philosophy

A system for proper multiple-conclusion entailment
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A system for proper multiple-conclusion entailment

Authors

  • Tomasz Skura University of Zielona Góra
  • Andrzej Wiśniewski Adam Mickiewicz University, Poznań

DOI:

https://doi.org/10.12775/LLP.2015.001

Keywords

multiple-conclusion entailment

Abstract

The concept of proper multiple-conclusion entailment is introduced. For any sets X, Y of formulas, we say that Y is properly mc-entailed by X iff Y is mc-entailed by X, but no A ∈ Y is single-conclusion entailed by X. The concept has a natural interpretation in terms of question evocation. A sound and complete axiom system for the propositional case of proper mc-entailment is presented.

Author Biographies

Tomasz Skura, University of Zielona Góra

Institute of Philosophy

Andrzej Wiśniewski, Adam Mickiewicz University, Poznań

Department of Logic and Cognitive Science, Institute of Psychology

References

Avron, A., “Natural 3-valued logics – characterization and proof theory”, Journal of Symbolic Logic, 56 (1991): 276–294. DOI: 10.2307/2274919

Avron, A., and A. Zamansky, “Completeness and axiomatizability in many-valued logic”, pages 227–304 in volume 16 of Handbook of Philosophical Logic, Springer, Dordrecht, 2011.

Bolc, L., and P. Borowik, Many-Valued Logics 1. Theoretical Foundations, Springer, Berlin/Heilderberg/New York, 1992.

Carnap, R., Formalization of Logic, Harvard University Press, Cambridge, MA, 1943.

Gabbay, D. M., Semantical Investigations in Heyting’s Intuitionistic Logic, Reidel, Dordrecht, 1981.

Gentzen, G., “Investigation into logical deduction”, pages 68–131 in The Collected Papers of Gerhard Gentzen, M. E. Szabo (ed.), North-Holland, 1969.

Kracht, M., “Judgement and consequence relations”, Journal of Applied Non-Classical Logics, 20 (2010): 423–435. DOI: 10.3166/jancl.20.423-435

McCarthy, J., “A basis for a mathematical theory of computation”, pages 33–70 in Computer Programming and Formal Systems, P. Braffort and D. Hirshberg (eds.), North-Holland, Amsterdam, 1963.

Scott, D., “Completeness and axiomatizability in many-valued logic”, pages 411–435 in volume 25 of Proceedings of Symposia in Pure Mathematics, American Mathematican Society, Providence, Rhode Island, 1974.

Shoesmith, D. J., and T. J. Smiley Multiple-conclusion Logic, Cambridge University Press, Cambridge, 1978.

Skura, T., “A refutation theory”, Logica Universalis, 3 (2009): 293–302. DOI: 10.1007/s11787-009-0009-y

Wiśniewski, A., Questions, Inferences, and Scenarios, volume 46 of Studies in Logic, College Publications, London, 2013.

Logic and Logical Philosophy

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Published

2015-02-04

How to Cite

1.
SKURA, Tomasz and WIŚNIEWSKI, Andrzej. A system for proper multiple-conclusion entailment. Logic and Logical Philosophy. Online. 4 February 2015. Vol. 24, no. 2, p. 241–253. [Accessed 5 July 2025]. DOI 10.12775/LLP.2015.001.
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Vol. 24 No. 2 (2015): June

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