A system for proper multiple-conclusion entailment
DOI:
https://doi.org/10.12775/LLP.2015.001Słowa kluczowe
multiple-conclusion entailmentAbstrakt
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.Bibliografia
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.
Pobrania
Opublikowane
Jak cytować
Numer
Dział
Statystyki
Liczba wyświetleń i pobrań: 495
Liczba cytowań: 9
