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A CORRECTNESS PROOF FOR AL-BARAKĀT’S LOGICAL DIAGRAMS

Part of: History of mathematics and mathematicians General logic

Published online by Cambridge University Press:  02 July 2021

WILFRID HODGES
WILFRID HODGES*
Affiliation:
HERONS BROOK, STICKLEPATH OKEHAMPTON DEVON EX20 2PY, ENGLAND
*
E-mail: wilfrid.hodges@btinternet.com
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Abstract

In Baghdad in the mid twelfth century Abū al-Barakāt proposes a radical new procedure for finding the conclusions of premise-pairs in syllogistic logic, and for identifying those premise-pairs that have no conclusions. The procedure makes no use of features of the standard Aristotelian apparatus, such as conversions or syllogistic figures. In place of these al-Barakāt writes out pages of diagrams consisting of labelled horizontal lines. He gives no instructions and no proof that the procedure will yield correct results. So the reader has to work out what his procedure is and whether it is correct. The procedure turns out to be insightful and entirely correct, but this paper may be the first study to give a full description of the procedure and a rigorous proof of its correctness.

Keywords

syllogismBarakātlogical diagramdecision methodmodel-theoretic consequencecorrectness proof

MSC classification

Primary: 01A30: Islam (Medieval)
Secondary: 03B25: Decidability of theories and sets of sentences
Type
Research Article
Information
The Review of Symbolic Logic , Volume 16 , Issue 2 , June 2023 , pp. 369 - 384
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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References

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