A note on the slicing of fibrations
We describe the construction of the slice fibration of a given one.
math.CT↗
arXiv subjects
Ruggero Pagnan
Publications and source records attributed to Ruggero Pagnan.
Ologisms
We introduce ologisms. They generate from ologs by extending their logical expressivity, from the possibility of considering constraints of equational nature only to the possibility of considering constraints of syllogistic nature, in addition. This is obtained by taking advantage of the peculiar features of an original diagrammatic logical calculus for the syllogistic, that make it well-behaved with respect to the design of ologs.
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A diagrammatic calculus of syllogisms
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.
math.LO↗
Syllogisms in Rudimentary Linear Logic, Diagrammatically
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 case and a corresponding reading of such De Morgan style syllogistics in the previously referred to fragment of linear logic.
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Concrete fibrations
As far as we know no notion of concreteness for fibrations exists. We introduce such a notion and discuss some basic results about it.
math.CT↗
A diagrammatic calculus of n-term syllogisms
We extend the diagrammatic calculus of syllogisms introduced in our previous paper to the general case of n-term syllogisms, showing that the valid ones are exactly those whose conclusion follows by calculation. Moreover, by pointing out the existing connections with the theory of rewriting systems we will also single out a suitable category theoretic framework for the calculus.
math.LO↗