DLV系统中聚合函数的设计与实现
Design and Implementation of Aggregate Functions in the DLV System
摘要：
析取逻辑编程（英语：Disjunctive Logic Programming，DLP）是一种非常有表现力的形式主义：它允许表达在复杂度类SigmaP 2（= NP^NP）中可判定的有限结构的每个属性。尽管有这种高表现力，但仍有一些简单的属性，通常出现在现实世界的应用程序中，无法以简单和自然的方式进行编码。特别是需要在满足某些条件的元素集合或多集合上使用算术运算符（如求和、次数或计数）的属性，无法在经典DLP中自然表达。为了克服这一缺陷，我们以保守的方式通过聚合函数扩展DLP。特别是，我们避免引入有争议的语义结构，要求聚合分层。我们正式定义的扩展语言（称为DLP^A）的语义，并说明它可以被有益地用于表示知识。此外，我们分析了DLP^A的计算复杂性，表明在这方面，聚合物的添加并不带来更高的成本。最后，我们提供了一个实施DLP^A在DLV -一个国家的最先进的DLP系统-和实验报告，证实了所提出的扩展的有用性，也为计算效率。
英文摘要：
Disjunctive Logic Programming (DLP) is a very expressive formalism: it allows for expressing every property of finite structures that is decidable in the complexity class SigmaP2 (= NP^NP). Despite this high expressiveness, there are some simple properties, often arising in real-world applications, which cannot be encoded in a simple and natural manner. Especially properties that require the use of arithmetic operators (like sum, times, or count) on a set or multiset of elements, which satisfy some conditions, cannot be naturally expressed in classic DLP. To overcome this deficiency, we extend DLP by aggregate functions in a conservative way. In particular, we avoid the introduction of constructs with disputed semantics, by requiring aggregates to be stratified. We formally define the semantics of the extended language (called DLP^A), and illustrate how it can be profitably used for representing knowledge. Furthermore, we analyze the computational complexity of DLP^A, showing that the addition of aggregates does not bring a higher cost in that respect. Finally, we provide an implementation of DLP^A in DLV -- a state-of-the-art DLP system -- and report on experiments which confirm the usefulness of the proposed extension also for the efficiency of computation.
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