Where should I publish this paper about a modern formal analysis of Aristotle's modal syllogism ?

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Clarence Lewis Protin

Kairos asks for submission in both .pdf and Word format. I do not use Windows and find it difficult to insert logical and mathematical symbols using LibreOffice.

Karl Pfeifer

History and Philosophy of Logic

https://www.tandfonline.com/toc/thpl20/current

They published a paper in the same area as yours:

Article Conversion Principles and the Basis of Aristotle's Modal Logic

Andrew Aberdein

HPL would indeed be a good fit.

Other options include Philosophiegeschichte und logische Analyse; Journal of Logic, Language and Information; Logica Universalis; Review of Symbolic Logic; or Notre Dame Journal of Formal Logic—although the last would be aiming rather high.