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The Talmudic logic project, ongoing since 2008. (English) Zbl 07170320

Summary: We describe the state of the Talmudic Logic project as of end of 2019. The Talmud is the most comprehensive and fundamental work of Jewish religious law, employing a large number of logical components centuries ahead of their time. In many cases the basic principles are not explicitly formulated, which makes it difficult to formalize and make available to the modern student of Logic. This project on Talmudic Logic aims to present logical analysis of Talmudic reasoning using modern logical tools. We investigate principles of Talmudic Logic and publish a series of books, one book or more for each principle. http://www.collegepublications.co.uk/stl/ The series begins with the systematic analysis of Talmudic inference rules. The first book shows that we can present Talmudic reasoning intuitions as a systematic logical system basic to modern non-deductive reasoning, such as Argumentum A Fortiori, Abduction and Analogy. The second book offers a systematic common sense method for intuitively defining sets and claims that this method adequately models the Talmudic use of the rules Klal uPrat. These books also criticize modern Talmudic research methodology. Later books deal with additional topics like Deontic logic, and Temporal logic, Agency and processes in the Talmud and more. The aims of the project are twofold:
1.
To import into the Talmudic study modern logical methods with a view to help understand complicated Talmudic passages, which otherwise cannot be addressed.
2.
To export from the Talmud new logical principles which are innovative and useful to modern contemporary logic.

MSC:

03B42 Logics of knowledge and belief (including belief change)
03B44 Temporal logic
03A05 Philosophical and critical aspects of logic and foundations
68T27 Logic in artificial intelligence
68T30 Knowledge representation
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[2] Abraham, M., Gabbay, D., Hazut, G., Maruvka, Y., Schild, U.: Studies in Talmudic Logic, Volume 2: The Textual Inference Rules Klal uPrat, How the Talmud Defines Sets (in Hebrew and English), pp. 388+17. College Publications, London (2010) · Zbl 1231.03003
[3] Abraham, M., Gabbay, D., Schild, U.: Studies in Talmudic Logic, Volume 3: Talmudic Deontic Logic (in Hebrew and English), pp. 267+29. College Publications, London (2010) · Zbl 1250.03030
[4] Abraham, M., Belfer, I., Gabbay, D., Schild, U.: Studies in Talmudic Logic, Volume 4: Temporal Logic in the Talmud (in Hebrew and English), pp. 588+70. College Publications, London (2011) · Zbl 1261.03103
[5] Abraham, M., Gabbay, D., Schild, U.: Studies in Talmudic Logic, Volume 5: Resolution of Conflicts and Normative Loops in the Talmud (in Hebrew and English), pp. 280+25. College Publications, London (2011)
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[7] Abraham, M., Belfer, I., Gabbay, D., Schild, U.: Studies in Talmudic Logic, Volume 8: Synthesis of Concepts in Talmudic Logic (in Hebrew and English), pp. 455+14. College Publications, London (2012) · Zbl 1280.03017
[8] Abraham, M., Belfer, I., Gabbay, D., Schild, U.: Studies in Talmudic Logic, Volume 9: Analysis of Concepts in Talmudic Reasoning (in Hebrew and English), pp. 301 + 11. College Publications, London (2014) · Zbl 1280.03017
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