Here are links to two articles relating to logic in the Talmud:
“The Realm of the Sacred, wherein We may not Draw an Inference from Something which Itself has been Inferred: a reading of Talmud Bavli Zevachim folio 50” by Curtis Franks
Department of Philosophy, University of Notre Dame, Indiana, USA
“The Evolution of Talmudic Reasoning.” History and Philosophy of Logic 32 (1):9-28 by Norman Solomon, Oriental Institute, Oxford University.
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The whole issue of History and Philosophy of Logic in which Solomon's article appears is dedicated to 'Judaic logic', I believe. So there's probably even more there that's of interest to readers of this blog.
The first paper was reviewed by me and I wrote the positive report for a journal. It should be published in HPL. The second paper from the issue I collected and edited.