Algebraic and logical methods for data analysis

知识发现和数据挖掘的大多数方法都假设观测数据之外的参数，如先验概率、置信函数或统计分布，其来源并不总是清楚或合理的。另一方面，对“非侵入性”数据分析方法（如粗糙集，概念格或知识结构）的需求很高，这些方法只考虑给定的数据，而不需要严格的额外模型假设。使用更少的模型假设可以提高通用性，扩大适用范围，减少脱离背景的情况，并减少成本和时间。非侵入性数据分析的一个强大工具是关系推理，它基于Alfred Tarski在20世纪40年代开发的思想，并结合了推理过程的关系和代数方面。

Most methods of knowledge-discovery and data mining assume parameters outside the observed data such as prior probabilities, belief functions or statistical distributions, the origin of which is not always clear or justifiable. On the other hand, there is a high demand for "non-invasive" methods of data analysis (such as rough sets, concept lattices, or knowledge structures) that take into account only the given data without stringent additional model assumptions. Using fewer model assumptions results in more generality, wider applicability, less decontextualization, and reduced costs and time. A powerful tool of non-invasive data analysis is relational reasoning, based on ideas developed by Alfred Tarski in the 1940s and which incorporate both relational and algebraic aspects of reasoning procedures.