Synthese 198 (S22):5373-5390 (2019)

Abstract
We discuss the axiomatization of generalized consequence relations determined by non-deterministic matrices. We show that, under reasonable expressiveness requirements, simple axiomatizations can always be obtained, using inference rules which can have more than one conclusion. Further, when the non-deterministic matrices are finite we obtain finite axiomatizations with a suitable generalized subformula property.
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DOI 10.1007/s11229-019-02142-8
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References found in this work BETA

The Mathematics of Metamathematics.Helena Rasiowa - 1963 - Warszawa, Państwowe Wydawn. Naukowe.
A Useful Four-Valued Logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
Multiple Conclusion Logic.D. J. Shoesmith & Timothy Smiley - 1978 - Cambridge, England / New York London Melbourne: Cambridge University Press.
Multiple Conclusions.Greg Restall - 2005 - In Petr Hájek, Luis Valdés-Villanueva & Dag Westerståhl (eds.), Logic, Methodology and Philosophy of Science. College Publications.
Why Conclusions Should Remain Single.Florian Steinberger - 2011 - Journal of Philosophical Logic 40 (3):333-355.

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