Most dispute resolution is settled by negotiation rather than litigation. However, such bargaining often occurs in the shadow of the law. To help support interest-based negotiation, we explore the use of utility functions to support negotiation analysis. We discuss in detail a utility function we have developed in the area of family-law mediation. This function is currently being used as the basis of an online dispute resolution system. Keywordsutility functions, negotiation support systems, bargaining in the shadow of the law

The Talmud is a body of arguments and discussions about all aspects of the human agent's social, legal and religious life. It was completed over 1500 years ago and its argumentation and debates contain many logical principles and examples very much relevant to today's research in logic, artificial intelligence, law and argumentation.In a series of books on Talmudic Logic, the authors have studied the logical prinicples involved in the Talmud, one by one, devoting a volume to each major principleWe have just finished writing Volume 5, entitled Resolution of Conflicts and Normative Loops in the Talmud, and the present paper describes how the Talmud deals with even and odd loops and compares the results with open issues in argumentation.For other English papers corresponding to previous books, see [1,2,3,4,5,6]. We start by looking at two typical loops, as in Figures 1 and 2. We need to give some definitions. An abstract network has the form (S, R), where S is a set of abstract nodes (arguments) and R ⊆ S 2 is the attack relation. Traditional research looks at extensions, these are subsets of S satisfying certain conditions (formulated in terms of R). Given (S, R) there may be several possible extensions of several types. In our case, for example, Figure 1 has three complete extensions {a}, {b} and ∅, and Figure 2 has only one extension ∅.

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Abstract. 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 A with entries in {0, 1}, we allow for one or more blank squares in the matrix, say ai,j =?. The method allows us to decide whether to declare ai,j = 0 or ai,j = 1 or ai,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.

Abstract. 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:In We shall list the types of obligation patterns appearing in the Talmud and compare Talmudic Logic with modern deontic logic.