Corcoran's Aristotelian syllogistic as a subsystem of first-order logic

Research output: Contribution to journalArticle

Abstract

Aristotelian syllogistic has been formalized for some time now by means of a natural deduction system, called D by John Corcoran. In a classical paper, Corcoran proves a completeness theorem for such a system. His proof involves the use of a reduced system, called RD, that is easier to handle and turns out to be equivalent to D. The question remains, however, whether RD is in fact the easiest such system that is equivalent to D. In this paper we answer this question, but raise some more, by embedding system RD in first-order predicate logic.
Original languageEnglish (US)
Pages (from-to)67-80
Number of pages14
JournalRevista Colombiana de Matematicas
Volume41
StatePublished - Jun 2007

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First-order Logic
Subsystem
Natural Deduction
Predicate Logic
Completeness
Theorem

Cite this

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title = "Corcoran's Aristotelian syllogistic as a subsystem of first-order logic",
abstract = "Aristotelian syllogistic has been formalized for some time now by means of a natural deduction system, called D by John Corcoran. In a classical paper, Corcoran proves a completeness theorem for such a system. His proof involves the use of a reduced system, called RD, that is easier to handle and turns out to be equivalent to D. The question remains, however, whether RD is in fact the easiest such system that is equivalent to D. In this paper we answer this question, but raise some more, by embedding system RD in first-order predicate logic.",
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Corcoran's Aristotelian syllogistic as a subsystem of first-order logic. / Andrade Lotero, Edgar Jose; Becerra, Edward.

In: Revista Colombiana de Matematicas, Vol. 41, 06.2007, p. 67-80.

Research output: Contribution to journalArticle

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AB - Aristotelian syllogistic has been formalized for some time now by means of a natural deduction system, called D by John Corcoran. In a classical paper, Corcoran proves a completeness theorem for such a system. His proof involves the use of a reduced system, called RD, that is easier to handle and turns out to be equivalent to D. The question remains, however, whether RD is in fact the easiest such system that is equivalent to D. In this paper we answer this question, but raise some more, by embedding system RD in first-order predicate logic.

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