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
