Disjunctive Multiple-Conclusion Consequence Relations
| dc.contributor.author | Nowak, Marek | |
| dc.date.accessioned | 2021-05-05T15:51:49Z | |
| dc.date.available | 2021-05-05T15:51:49Z | |
| dc.date.issued | 2019-12-31 | |
| dc.identifier.issn | 0138-0680 | |
| dc.identifier.uri | http://hdl.handle.net/11089/35368 | |
| dc.description.abstract | The concept of multiple-conclusion consequence relation from [8] and [7] is considered. The closure operation C assigning to any binary relation r (dened on the power set of a set of all formulas of a given language) the least multiple-conclusion consequence relation containing r, is dened on the grounds of a natural Galois connection. It is shown that the very closure C is an isomorphism from the power set algebra of a simple binary relation to the Boolean algebra of all multiple-conclusion consequence relations. | en |
| dc.language.iso | en | |
| dc.publisher | Wydawnictwo Uniwersytetu Łódzkiego | pl |
| dc.relation.ispartofseries | Bulletin of the Section of Logic;4 | en |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0 | |
| dc.subject | multiple-conclusion consequence relation | en |
| dc.subject | closure operation | en |
| dc.subject | Galois connection | en |
| dc.title | Disjunctive Multiple-Conclusion Consequence Relations | en |
| dc.type | Other | |
| dc.page.number | 319–328 | |
| dc.contributor.authorAffiliation | Department of Logic and Methodology of Science, University of Lodz, Poland | en |
| dc.identifier.eissn | 2449-836X | |
| dc.references | [1] T. S. Blyth, Lattices and Ordered Algebraic Structures, Springer, 2005. https://doi.org/10.1007/b139095 | en |
| dc.references | [2] K. Denecke, M. Erné, S. L. Wismath (eds.), Galois Connections and Applications, Kluwer, 2004. https://doi.org/10.1007/978-1-4020-1898-5 | en |
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| dc.references | [4] M. Erné, J. Koslowski, A. Melton, G. E. Strecker, A Primer on Galois Connections, Annals of the New York Academy of Sciences, Vol. 704 (1993), pp. 103–125. https://doi.org/10.1111/j.1749-6632.1993.tb52513.x | en |
| dc.references | [5] G. K. E. Gentzen, Untersuchungen über das logische Schließen. I, Mathematische Zeitschrift, Vol. 39 (1934), pp. 176–210, [English translation: Investigation into Logical Deduction, [in:] M. E. Szabo, The collected Works of Gerhard Gentzen, North Holland, 1969, pp. 68–131.] https://doi.org/10.1007/BF01201353 | en |
| dc.references | [6] G. Payette, P. K. Schotch, Remarks on the Scott-Lindenbaum Theorem, Studia Logica, Vol. 102 (2014), pp. 1003–1020. https://doi.org/10.1007/s11225-013-9519-y | en |
| dc.references | [7] D. Scott, Completeness and axiomatizability in many-valued logic, Proceedings of Symposia in Pure Mathematics, Vol. 25 (Proceedings of the Tarski Symposium), American Mathematical Society 1974, pp. 411–435. | en |
| dc.references | [8] D. J. Shoesmith, T. J. Smiley, Multiple-conclusion Logic, Cambridge 1978. https://doi.org/10.1017/CBO9780511565687 | en |
| dc.references | [9] T. Skura, A. Wiśniewski, A system for proper multiple-conclusion entailment, Logic and Logical Philosophy, Vol. 24 (2015), pp. 241–253. http://dx.doi.org/10.12775/LLP.2015.001 | en |
| dc.references | [10] R. Wójcicki, Dual counterparts of consequence operations, Bulletin of the Section of Logic, Vol. 2 (1973), pp. 54–56. | en |
| dc.references | [11] J. Zygmunt, An Essay in Matrix Semantics for Consequence Relations, Wydawnictwo Uniwersytetu Wrocławskiego, 1984. | en |
| dc.contributor.authorEmail | marek.nowak@filozof.uni.lodz.pl | |
| dc.identifier.doi | 10.18778/0138-0680.48.4.05 | |
| dc.relation.volume | 48 |
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