Siyi Yu

The Validity of Generalized Modal Syllogisms with the Generalized Quantifiers in Square{most}

Due to the large number of generalized quantifiers in the English language, this paper only studies the fragment of generalized modal syllogistic that contains the quantifiers in Square{all} and Square{most}. On the basis of generalized quantifier theory, possible-world semantics, and set theory, this paper shows that there are reducible relations between/among the generalized modal syllogism £EM◇O-3 and at least the other 29 valid generalized modal syllogisms. This method can also be used to study syllogisms with other generalized quantifiers. The results obtained by means of formal deductive method have not only consistency, but also theoretical value for the development of inference theory in artificial intelligence.