Books by Israel Belfer

This book deals with a problem that has been discussed quite a lot, both in the academic and the halachic literature, the problem of partitioning. The fundamental and well-known partition problem in the Talmud is the partition of lost property ("Two hold a garment") found in Baba Metzia 2a, and its generalisation ("n hold a garment"). The Talmud also deals with the problem of division of the estate of a deceased among creditors in Ketubot 93a.Our aim is to organise previous work, give a complete picture of the domain and add our original work. We specify what the basic assumptions are, similarities and dissimilarities between the problems and the various approaches to their solution. We give general case algorithms for these solutions. Where necessary we also prove the existence and uniqueness of the solutions.The book is partly in English and partly in Hebrew

This book studies Talmudic temporal logic and compares it with the logic of time in contemporary law. Following a general introduction about the logical handling of time, the book examines several key Talmudic debates involving time. The book finds that we need multi-dimensional temporal models with backward causation and parallel histories. It seems that two major issues are involved: 1 Actions conditional about future actions (Tenayim), connecting with backward causality 2 Actions involving entities defined using future events (Breira), connecting with ideas from quantum Mechanics The book concludes with a general comparative discussion of the handling of time in general law and in the Talmud.

In this book we deal with combinations of concepts defining individuals in the Talmud. Consider for example Yom Kippur and Shabbat. Each concept has its own body of laws. Reality forces us to combine them when they occur on the same day. This is a case of "Identity Merging". As the combined body of laws may be inconsistent, we need a belief revision mechanism to reconcile the conflicting norms. The Talmud offers three options:1 Take the union of the sets of the rules side by side2. Resolve the conflicts using further meta-level Talmudic principles (which are new and of value to present day Artificial Intelligence)3. Regard the new combined concept as a new entity with its own Halachic norms and create new norms for it out of the existing ones.This book offers a clear and precise logical model showing how the Talmud deals with these options.

This book returns to the discussion in volume 1 on analogy and induction,and analyses their substance. The first part distinguishes between twokinds of logic: One kind based on union of the common features, and theother kind based on synthesis of different features. In the second part ofthe book we propose a formal scheme for synthesis of concepts. The thirdpart analyses various mechanisms for kidushin and kinyan, which form amathematical group.