|zpravodaj ČSKI - leden 2013 [ pdf ]|
datum: 16.1.2013 v 14:00
název: The algebraic structure of Intermediate Syllogisms
přednášející: Esko Turunen
místo konání: UI, 2.patro, místnost č.318
souhrn: In his book 'Intermediate Quantifiers' (2000) Philip L. Peterson introduced 3 quantifiers 'Almost-all', 'Most' and 'Many' and extended Aristotelian syllogisms containing the two classical one ('All' and 'Some'), to a syllogistic system containing 5 quantifiers (and their negative counterparts). Peterson gave a set theoretical semantics to his new quantifiers and proved that, out of the 4000 possible intermediate syllogisms, there are 105 valid one, 24 of the being the classical Aristotelian syllogisms. In this talk we show that Peterson's syllogisms can be associated with simple MV-algebra values which determine the validity/invalidity of each syllogism. We also shortly discuss possible extensions of syllogistic systems and, finally, we propose a simple way to deal with multi valued syllogisms.