Tradycyjna sylogistyka proponuje wysnuwanie wniosku o relacji między dwoma zbiorami z dwóch przesłanek kategorycznych, z których każda stwierdza coś o relacji łączącejjeden z tych zbiorów z trzecim (którego nazwa stanowi tzw. termin średni).

Od średniowiecza znana jest metoda sprawdzania poprawności formalnej sylogizmu na podstawie wnikliwej oceny jego składni, a od XIX wieku również metoda graficznego przedstawiania przesłanek na diagramie Venna dla trzech zbiorów, których wzajemne relacje stanowią temat sylogizmu. W diagramie tym pewną trudność stanowi pojawiająca się w wielu przypadkach niepusta suma obszarów.

W przedstawianym artykule proponuje się nową metodę przedstawienia przesłanek sylogizmu, polegającą na prezentacji obszarów, w których mogą lub muszą według przesłanek znajdować się elementy zbiorów, i tych obszarów, które z pewnością są puste. W szczególności dla niepustej sumy obszarów proponuje się wykorzystanie relacji rotalnej między dwoma obszarami tworzącymi niepustą sumę i możliwe ujednoznacznienie tej relacji przez wskazany w przesłance pusty obszar diagramu.

Rotal relation and an empty region as a tool for deciding the validity of traditional sylogism moods as exemplified by selected third figure ones

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.

Keywords: traditional syllogistics, binary relations between sets, empty regions, Venn diagram for three sets, relation theory, non-empty sum of regions

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.