We motivate and introduce a new method of abduction, Matrix Abduction, and apply it to modelling the use of non-deductive inferences in the Talmud such as Analogy and the rule of Argumentum A Fortiori. Given a matrix $${\mathbb {A}}$$ with entries in {0, 1}, we allow for one or more blank squares in the matrix, say a i,j =?. The method allows us to decide whether to declare a i,j = 0 or a i,j = 1 or a i,j =? (...) undecided. This algorithmic method is then applied to modelling several legal and practical reasoning situations including the Talmudic rule of Kal-Vachomer. We add an Appendix showing that this new rule of Matrix Abduction, arising from the Talmud, can also be applied to the analysis of paradoxes in voting and judgement aggregation. In fact we have here a general method for executing non-deductive inferences. (shrink)

This paper examines the deontic logic of the Talmud. We shall find, by looking at examples, that at first approximation we need deontic logic with several connectives: O T A Talmudic obligation F T A Talmudic prohibition F D A Standard deontic prohibition O D A Standard deontic obligation. In classical logic one would have expected that deontic obligation O D is definable by $O_DA \equiv F_D\neg A$ and that O T and F T are connected by $O_TA \equiv F_T\neg (...) A$ This is not the case in the Talmud for the T (Talmudic) operators, though it does hold for the D operators. We must change our underlying logic. We have to regard {O T , F T } and {O D , F D } as two sets of operators, where O T and F T are independent of one another and where we have some connections between the two sets. We shall list the types of obligation patterns appearing in the Talmud and develop an intuitionistic deontic logic to accommodate them. We shall compare Talmudic deontic logic with modern deontic logic. (shrink)

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. 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 two fold: 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. (shrink)

We consider conditionals of the form A ⇒ B where A depends on the future and B on the present and past. We examine models for such conditional arising in Talmudic legal cases. We call such conditionals contrary to time conditionals.Three main aspects will be investigated: Inverse causality from future to past, where a future condition can influence a legal event in the past (this is a man made causality).Comparison with similar features in modern law.New types of temporal logics arising (...) from modelling the Talmudic examples. We shall see that we need a new temporal logic,which we call Talmudic temporal logic with linear open advancing future and parallel changing past, based on two parameters for time. (shrink)

Much legal research focuses on understanding how judicial decision-makers exercise their discretion. In this paper we examine the notion of legal or judicial discretion, and weaker and stronger forms of discretion. At all times our goal is to build cognitive models of the exercise of discretion, with a view to building computer software to model and primarily support decision-making. We observe that discretionary decision-making can best be modeled using three independent axes: bounded and unbounded, defined and undefined, and binary and (...) continuous. Examples of legal tasks are given from each of the eight ensuing octants and we conclude by saying what this model shows about current legal trends. We should stress that our taxonomy has been based on our observations of how discretionary legal decisions are made. No claim is made that our model is either complete (providing advice in every domain) or exact, but it does help knowledge engineers construct legal decision support systems in discretionary domains. (shrink)

This paper considers the problem of how to evaluate an offender’s criminal record. This evaluation is part of the sentencing process carried out by a judge, and may be complicated in the case of offenders with a heavy record. We give a comprehensive overview of the approach to an offender’s past record in various (Western) countries, considering the two major approaches: desert-based and utilitarian. The paper describes the determination of the parameters involved in the evaluation, and the construction of a (...) decision support system to be used by a judge about to pass sentence in a criminal case. The system may be used as a stand-alone system, but can also be integrated as a component of a general sentencing support system, e.g. a statistical sentencing information system. The system is a knowledge-based system. The knowledge base (in rule-form) was created primarily by eliciting knowledge from experts (judges, lawyers, academics and probation officers), but also by applying statutory law, case law and legal authoritative texts. It is flexible in the sense, that a user can introduce his1 own preferences (expressed as numerical coefficients) and thereby apply different sentencing principles. The prototype is at present undergoing testing by some of the participating judges. (shrink)

This article deals with a set-theoretic interpretation of the Talmudic rules of General and Specific, known as Klal and Prat (KP), Prat and Klal (PK), Klal and Prat and Klal (KPK) and Prat and Klal and Prat (PKP).