•  74
    A Diagrammatic Calculus of Syllogisms
    Journal of Logic, Language and Information 21 (3): 347-364. 2012.
    A diagrammatic logical calculus for the syllogistic reasoning is introduced and discussed. We prove that a syllogism is valid if and only if it is provable in the calculus.
  •  38
    Syllogisms in Rudimentary Linear Logic, Diagrammatically
    Journal of Logic, Language and Information 22 (1): 71-113. 2013.
    We present a reading of the traditional syllogistics in a fragment of the propositional intuitionistic multiplicative linear logic and prove that with respect to a diagrammatic logical calculus that we introduced in a previous paper, a syllogism is provable in such a fragment if and only if it is diagrammatically provable. We extend this result to syllogistics with complemented terms à la De Morgan, with respect to a suitable extension of the diagrammatic reasoning system for the traditional cas…Read more
  •  8
    Concrete Fibrations
    Notre Dame Journal of Formal Logic 58 (2): 179-204. 2017.
    As far as we know, no notion of concrete fibration is available. We provide one such notion in adherence to the foundational attitude that characterizes the adoption of the fibrational perspective in approaching fundamental subjects in category theory and discuss it in connection with the notion of concrete category and the notions of locally small and small fibrations. We also discuss the appropriateness of our notion of concrete fibration for fibrations of small maps, which is relevant to alge…Read more
  •  6
    Splitting idempotents in a fibered setting
    Archive for Mathematical Logic 57 (7-8): 917-938. 2018.
    By splitting idempotent morphisms in the total and base categories of fibrations we provide an explicit elementary description of the Cauchy completion of objects in the categories Fib) of fibrations with a fixed base category \ and Fib of fibrations with any base category. Two universal constructions are at issue, corresponding to two fibered reflections involving the fibration of fibrations \.