%0 Journal Article
%T Rotal relation and an empty region as a tool for deciding the validity of traditional sylogism moods as exemplified by selected third figure ones
%A Pietryga, Anna
%J Principia
%V 2020
%R 10.4467/20843887PI.20.005.13835
%N Volume 67
%P 119-131
%K traditional syllogistics, binary relations between sets, empty regions, Venn diagram for three sets, relation theory, non-empty sum of regions
%@ 0867-5392
%D 2020
%U https://ejournals.eu/en/journal/principia/article/relacja-rotalna-i-obszar-pusty-jako-narzedzie-rozstrzygania-o-waznosci-trybow-tradycyjnego-sylogizmu-na-przykladzie-wybranych-trybow-figury-trzeciej
%X 
	Traditional syllogistics sugests inferring a result about the binary relation between sets from the two categorical premisses each of which state something about a relation between one of them to a third set (whose name is called the middle term).

	Since the Middle Ages it is known how to check the formal correctness of a syllogism by the detailed analysis of its syntax, and since the 19th century also how to present the premisses graphically on the Venn diagram for three sets, whose mutual binary relations consttute the subject of syllogistics. The non-empty sum of subregions is sometimes not very comfortable to deal with.

	In the paper a new method is described for presenting syllogisms premisses, which consists in indicating the subregions, in which the premisses say some elements may or have to be located and those subregions which are announced empty. In particular, for the non-empty sum of two regions the rhotal relation is suggested together with the the possible corresponding empty region, had it been suitably indicated by one ot he premisses.