## Bora I. Kumova: "The Ancient Syllogistic System and Its Properties"

**Dienstag, 7. Juli 2015 14.15 Uhr Im Neuenheimer Feld 368, Seminarraum 432**

Traditional categorical syllogism consist of 256 moods in total, 64 moods per figure. Out of them only 24 moods, 6 per figure, are well known to be the only true ones, whereas the remaining 232 are assumed to be false. A systematic analysis of the syllogisms with modern mathematics, like set-theory, algorithms and fuzzy logic, allows us not only to confirm the truth of the 24 moods, but reveals the truth of a 25th mood in the 4th figure to be true too. Furthermore, with two new concepts, the syllogistic cases and the truth ratio, we can calculate a unique truth ratio for every mood, which is in the range [0,1]. It is actually these novel concepts that help revealing the most significant properties of the syllogistic system S, like point symmetric truth of moods, partial overlapping value ranges, equivalence of moods, almost or more true/false moods. The objective of this talk is, to introduce to this modern approach of analysing syllogisms.

## Bora I. Kumova: "Fuzzy-Syllogistic Systems and Their Applications for Approximate Reasoning"

**Mittwoch, 8. Juli 2015 16.15 Uhr Im Neuenheimer Feld 348, Seminarraum 015**

Using the concepts syllogistic case, truth ratio and fuzzy quantifiers, we generalise the traditional syllogistic system S with two affirmative and two negative quantifiers, of which the existential quantifiers are inclusive, to n fuzzy-syllogistic systems nS with 1<n affirmative and 1<n negative fuzzy quantifiers, of which all (n-1) existential quantifiers are exclusive. The objective of this talk is to introduce to this approach of generalisation of syllogisms and to experimentally show their application in approximate reasoning. For this purpose we discuss the design of a fuzzy-syllogistic ontology reasoner that is based on nS.

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