Deductive Systems with Multiple-Conclusion Rules and the Disjunction Property

Using the defined notion of the inference with multiply-conclusion rules, we show that in the logics enjoying the disjunction property, any derivable rule can be inferred from the single-conclusion rules and a single multiple-conclusion rule, which represents the disjunction property. Also, the conv...

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Bibliographic Details
Main Author:	Alex Citkin
Format:	Article
Language:	English
Published:	MDPI AG 2019-08-01
Series:	Axioms
Subjects:	multiple conclusion rule disjunction property metadisjunction
Online Access:	https://www.mdpi.com/2075-1680/8/3/100

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spelling	doaj-2dd0b0ff7fe6406685a78e2533ae478b2020-11-25T01:55:17ZengMDPI AGAxioms2075-16802019-08-018310010.3390/axioms8030100axioms8030100Deductive Systems with Multiple-Conclusion Rules and the Disjunction PropertyAlex Citkin0Metropolitan Telecommunications, New York, NY 10041, USAUsing the defined notion of the inference with multiply-conclusion rules, we show that in the logics enjoying the disjunction property, any derivable rule can be inferred from the single-conclusion rules and a single multiple-conclusion rule, which represents the disjunction property. Also, the conversion algorithm of single- and multiple-conclusion deductive systems into each other is studied.https://www.mdpi.com/2075-1680/8/3/100multiple conclusion ruledisjunction propertymetadisjunction
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Alex Citkin
spellingShingle	Alex Citkin Deductive Systems with Multiple-Conclusion Rules and the Disjunction Property Axioms multiple conclusion rule disjunction property metadisjunction
author_facet	Alex Citkin
author_sort	Alex Citkin
title	Deductive Systems with Multiple-Conclusion Rules and the Disjunction Property
title_short	Deductive Systems with Multiple-Conclusion Rules and the Disjunction Property
title_full	Deductive Systems with Multiple-Conclusion Rules and the Disjunction Property
title_fullStr	Deductive Systems with Multiple-Conclusion Rules and the Disjunction Property
title_full_unstemmed	Deductive Systems with Multiple-Conclusion Rules and the Disjunction Property
title_sort	deductive systems with multiple-conclusion rules and the disjunction property
publisher	MDPI AG
series	Axioms
issn	2075-1680
publishDate	2019-08-01
description	Using the defined notion of the inference with multiply-conclusion rules, we show that in the logics enjoying the disjunction property, any derivable rule can be inferred from the single-conclusion rules and a single multiple-conclusion rule, which represents the disjunction property. Also, the conversion algorithm of single- and multiple-conclusion deductive systems into each other is studied.
topic	multiple conclusion rule disjunction property metadisjunction
url	https://www.mdpi.com/2075-1680/8/3/100
work_keys_str_mv	AT alexcitkin deductivesystemswithmultipleconclusionrulesandthedisjunctionproperty
_version_	1724983992192598016

Deductive Systems with Multiple-Conclusion Rules and the Disjunction Property

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