Norms

The history of triangular norms started with the paper "Statistical metrics" [Menger 1942]. The main idea of Karl Menger was to construct metric spaces where probability distributions rather than numbers are used in order to de­ scribe the distance between two elements of the space in question. Triangular norms (t-norms for short) naturally came into the picture in the course of the generalization of the classical triangle inequality to this more general set­ ting. The original set of axioms for t-norms was considerably weaker, including among others also the functions which are known today as triangular conorms. Consequently, the first field where t-norms played a major role was the theory of probabilistic metric spaces ( as statistical metric spaces were called after 1964). Berthold Schweizer and Abe Sklar in [Schweizer & Sklar 1958, 1960, 1961] provided the axioms oft-norms, as they are used today, and a redefinition of statistical metric spaces given in [Serstnev 1962]led to a rapid development of the field. Many results concerning t-norms were obtained in the course of this development, most of which are summarized in the monograph [Schweizer & Sklar 1983]. Mathematically speaking, the theory of (continuous) t-norms has two rather independent roots, namely, the field of (specific) functional equations and the theory of (special topological) semigroups.

Law and Social Norms Eric A. Posner What is the role of law in a society in which order is maintained mostly through social norms, trust, and nonlegal sanctions? Eric Posner argues that social norms are sometimes desirable yet sometimes odious, and that the law is critical to enhancing good social norms and undermining bad ones. But he also argues that the proper regulation of social norms is a delicate and complex task, and that current understanding of social norms is inadequate for guiding judges and lawmakers. What is needed, and what this book offers, is a model of the relationship between law and social norms. The model shows that people's.