A Diagrammatic Calculus of Syllogisms

Pagnan, Ruggero

doi:10.1007/s10849-011-9156-7

Cited by 6 publications

(13 citation statements)

References 14 publications

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“…Today the typical diagrammatic treatments of syllogistic include Venn-Euler diagrams (Venn, 1880), Carroll's triliteral diagrams (Carroll, 1887), Karnaugh maps (Karnaugh, 1953), and more recently, Pagnan's SYLL (Pagnan, 2012). In this paper I have introduced another diagrammatic treatment of syllogistic by re(dis)covering Leibniz's diagrammatic logic, which should be an interesting task historically and logically because this diagrammatic system has not been explored before in metalogical terms and because we have showed (our reconstruction of) LEIB has a sound and complete algorithm for syllogistic that provides more evidence on the thesis that diagrammatic reasoning is bona fide reasoning.…”

Section: Discussionmentioning

confidence: 99%

Re(dis)covering Leibniz's Diagrammatic Logic

Manzano

2016

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In this paper I attempt to retrieve Leibniz's linear diagrammatic logic for his syllogistic and highlight its computational and logical features by providing a formal approach to it in metalogical terms, which is something that, as far as we know, has not yet been accomplished. Thus, in this contribution I pursue two goals, one historical and the other logical: i) to bring more attention on the algorithmic aspects of Leibniz's linear diagrammatic system for his syllogistic, which I believe has been neglected because of a general bias against diagram-based reasoning; and ii) to prove the metalogical properties of the system in order to argue that such a system is a bona fide logical system.Key words: diagrammatic reasoning, diagrams, linear diagrams, metalogic. ResumenEn este artículo recuperamos la lógica diagramática lineal de Leibniz para la silogística y descubrimos sus propiedades lógicas y computacionales a través de una aproximación formal en términos metalógicos, lo cual es algo que, hasta donde sabemos, aún falta por hacerse. Así, en esta contribución buscamos, respectivamente, dos metas, una histórica y una lógica: i) prestar más atención a los aspectos algorítmicos del sistema diagramático lineal de Leibniz para la silogística, de los cuales creemos que han sido desdeñados por un prejuicio general en contra del razonamiento diagramático; y ii) probar propiedades metalógicas del sistema para argumentar que es un sistema lógico bona fide.Palabras clave: razonamiento diagramático, diagramas, diagramas lineales, metalógica.

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Section: Discussionmentioning

confidence: 99%

Re(dis)covering Leibniz's Diagrammatic Logic

Manzano

2016

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“…They were not dealt with in [46]. In section 8, the modern 19th century De Morgan style syllogistics with complemented terms is considered, which was not in [46]. A suitable reading of it within RLL ⊥ is considered too.…”

Section: Structure Of the Papermentioning

confidence: 99%

“…In [46] the diagrammatic logical system SYLL for the traditional syllogistics is introduced. Its syntactic primitives consist of the symbols •, →, ←, as well as of countably many term-variables A, B, C, .…”

Section: Motivationmentioning

confidence: 99%

“…In this section we comment on the so-called reduction rules for the syllogistics in connection with the diagrammatic calculus we presented in section 6. The material which is in this section is not contained in [46].…”

Section: The Reduction Rules Of the Syllogisticsmentioning

confidence: 99%

“…In this paper we considered a natural reading of the traditional Aristotelian syllogistics within a well-known intuitionistic fragment of multiplicative propositional linear logic and put it in connection with the diagrammatic logical calculus of syllogisms that we introduced in [46]. Subsequently, we focused our interest on the nineteenth century modern De Morgan style syllogistics with complemented terms and have been able to extend the previously mentioned diagrammatic calculus to cope with it and with a linear logic reading of it, naturally extending the one for the traditional case.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

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Syllogisms in Rudimentary Linear Logic, Diagrammatically

Pagnan

2013

J of Log Lang and Inf

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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 termsà 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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