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arXiv 2108.02587cs.DB
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演绎数据库的四值语义

Four-Valued Semantics for Deductive Databases

Dominique Laurent, Nicolas Spyratos

摘要:

在本文中,我们介绍了一种新的方法,演绎数据库的意思是考虑到当前的应用程序在数据集成领域的需求。为此,我们将标准演绎数据库的形式主义扩展到四值逻辑的上下文中,以便在开放世界假设下解释未知,不一致,真实或虚假的信息。在我们的方法中,数据库是一对(E,R),其中E是扩展,R是规则集。扩展是一组形式为(f,v)的对,其中f是一个事实,v是一个可以为真、不一致或假的值,但不是未知的(即未知的事实不存储在数据库中)。这些规则遵循标准Datatom {neg}规则的形式,但与标准规则相反,它们的头部可以是负原子。我们的主要贡献如下:(i)给出了一级蕴涵的其它连接词的表达式,并给出了一个不涉及一级蕴涵的功能完备的基本连接词集;(ii)定义了一个新的算子来处理我们的新规则,并证明了该算子是单调的和连续的,从而为定义和计算数据库语义提供了一种有效的方法,和(iii)我们认为,我们的框架允许定义一种新的类型的更新,可以在大多数标准的数据集成应用程序中使用。

英文摘要:

In this paper, we introduce a novel approach to deductive databases meant to take into account the needs of current applications in the area of data integration. To this end, we extend the formalism of standard deductive databases to the context of Four-valued logic so as to account for unknown, inconsistent, true or false information under the open world assumption. In our approach, a database is a pair (E,R) where E is the extension and R the set of rules. The extension is a set of pairs of the form (f, v) where f is a fact and v is a value that can be true, inconsistent or false - but not unknown (that is, unknown facts are not stored in the database). The rules follow the form of standard Datalog{neg} rules but, contrary to standard rules, their head may be a negative atom. Our main contributions are as follows: (i) we give an expression of first-degree entailment in terms of other connectors and exhibit a functionally complete set of basic connectors not involving first-degree entailment, (ii) we define a new operator for handling our new type of rules and show that this operator is monotonic and continuous, thus providing an effective way for defining and computing database semantics, and (iii) we argue that our framework allows for the definition of a new type of updates that can be used in most standard data integration applications.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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