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
http://www.nd.edu/~cfranks/frankssacredinference.pdf
“The Evolution of Talmudic Reasoning.” History and Philosophy of Logic 32 (1):9-28 by Norman Solomon, Oriental Institute, Oxford University.
http://www.tandfonline.com/doi/abs/10.1080/01445340.2010.506081
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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.
Andrew Schumann