Social norms are a set of rules to be followed by the people of a community in order to have a better coexistence, to which the behaviors, tasks, and activities of the human being must be adjusted. The set or system of norms, rules, or duties regulates the actions of individuals among themselves. This work presents a new and original approach to the situations of agreement as well as to the constructions of regulations. This is done by giving a mathematical formalization to the set of all possible agreements or regulations, so that, then, the proximity between them is defined by means of a premetric. Thanks to this mathematical structure that tries to capture the problematic of agreements and modifications of regulations, some currently issues related to game theory or law are now reduced to mathematical optimization problems.

中文翻译：

---

法律和交易建模的数学方法：立法和协议

社会规范是社区人民为了更好地共存而必须遵循的一组规则，必须调整人类的行为，任务和活动。规范，规则或职责的集合或系统调节着个体之间的行为。这项工作为协议的情况以及法规的构建提供了一种新颖的方法。这是通过对所有可能的协议或规定的集合进行数学形式化来完成的，因此，它们之间的接近程度可以通过预度量进行定义。由于这种试图捕获协议和法规修改问题的数学结构，现在将与博弈论或法律相关的一些当前问题简化为数学优化问题。