We specify two problems in syllogistic: the lack of functoriality of predicates and the change of grammatical role of the middle term, from subject to predicate, in some syllogisms. The standard semantics, the class interpretation, by-passes these difficulties but, we argue, in a manner that is at odds with logical intuition. We propose a semantics that is category theoretic to handle these difficulties. With this semantics we specify when syllogisms are valid and we set limits to the class interpretation. To (...) perform this task we show how to construct the categorical notion of an entity in a system of kinds. We devote two brief sections to an argument that our approach is very much in the spirit of Aristotle. (shrink)

Since antiquity two different negations in natural languages have been noted: predicate negation (not honest) and predicate term negation (dishonest). The extensive literature offers no models. We propose category-theoretic models with two distinct negation operators, neither of them in general Boolean. We study combinations of the two (not dishonest) and sentential counterparts of each. We emphasize the relevance of our work for the theory of cognition.

Since antiquity two different negations in natural languages have been noted: predicate negation and predicate term negation . The extensive literature offers no models. We propose category-theoretic models with two distinct negation operators, neither of them in general Boolean. We study combinations of the two and sentential counterparts of each. We emphasize the relevance of our work for the theory of cognition.