The Second-Order Approach and its Application to View-Based Query Processing

在这个项目中，一种基于逻辑的知识处理方法，在这里被称为二阶方法，将被调查。这个想法是，表达性表示语言，一方面，可以用一种非常自然的方式制定应用程序，但另一方面，通过减少到更适合计算的较差的语言进行处理。 这样的减少是可能的，因为表达语言的结构是在特定的应用context.Proofs的概念，这种方法已经给出了在90年代后期使用的二阶量词消除计算的限制，最近的应用程序的均匀插值（可以表示为二阶量词消除）在描述逻辑。 该方法通常允许从应用领域的概念追溯到逻辑的基本概念，表明新的应用可能性和领域之间的相似之处，使技术的转移和组合。该项目连接两条工作线，将相互促进：（1）一个特定的应用领域的概念，基于视图的查询处理，将正式建模与二阶运算符。(2)计算方法将开发，实现应用程序的形式化的基础上，基本上通过消除二阶operator.The基于视图的查询处理的基本思想是翻译和分解查询，这样多个代理与专门的知识库和处理能力可以有助于回答计算。 由于它与可定义性（逻辑的一般概念）的密切关系，基于视图的查询处理非常适合该项目的方法。 该项目关于基于视图的查询处理的中心目标是所涉及的概念的语义澄清，二阶运算符消除计算查询转换的可用性，以及数据库之外的推广。关于计算方法，将基于命题逻辑开发二阶运算符消除的新技术-与最近的SAT预处理器相关，基于一阶逻辑，该项目的结果应该作为一个精心制作的正式和自动化的基础，为大量的进一步的应用程序，适合于二阶方法。这些包括，例如，非标准推理的变体，溯因推理，知识库的模块化，非单调推理和关于知识的推理。

In the project, an approach to logic-based knowledge processing, to be called here second-order approach, will be investigated. The idea is that expressive representation languages are, on the one hand, available to formulate applications in a very natural way, but on the other hand, are processed by reduction to poorer languages that are better suited for computation. Such reductions are made possible because the expressive language constructs are used in specific application contexts.Proofs of concept for this approach have been given in the late 90s with the use of second-order quantifier elimination for computing circumscription, and recently with applications of uniform interpolation (which can be expressed as second-order quantifier elimination) in description logics. The approach typically allows to trace concepts from the application area back to fundamental concepts of logic, indicating new application possibilities and parallels between areas that enable transfer and combination of techniques.The project connects two lines of work that will stimulate each other: (1) Concepts of a particular application area, view-based query processing, will be formally modeled with second-order operators. (2) Computational methods will be developed that realize applications, on the basis of the formalization, essentially by elimination of second-order operators.The basic idea of view-based query processing is to translate and decompose queries such that multiple agents with specialized knowledge bases and processing capabilities can contribute to answer computation. By its is close relation to definability, a general concept of logic, view-based query processing is well suited to the approach of the project. Central objectives of the project with respect to view-based query processing are semantic clarification of the involved concepts, availability of second-order operator elimination to compute query transformations, and generalization beyond databases.With respect to computational methods, new techniques for second-order operator elimination will be developed, based on propositional logic - related to recent SAT preprocessors, based on first-order logic, and by taking specific formula patterns into account that occur in view-based query processing.The results of the project should serve as an elaborate formal and automated foundation for a multitude of further applications that are suited for the second-order approach. These include, for example, variants of non-standard inferences, abductive reasoning, modularization of knowledge bases, non-monotonic reasoning, and reasoning about knowledge.