Prolog is a well known declarative programming language based on propositional Horn formulas. It is useful in various areas, including artificial intelligence, automated theorem proving, mathematical logic and so on. An active research area for many years is to extend Prolog to larger classes of logic. Some important extensions of it includes the constraint logic programming, and the object oriented logic programming. However, it cannot solve problems having arbitrary quantified Horn formulas. To be precise, the facts, rules and queries in Prolog are not allowed to have arbitrary quantified variables. The paper overcomes this major limitations of Prolog by extending it for the quantified Boolean Horn formulas. We achieved this by extending the SLD-resolution proof system for quantified Boolean Horn formulas, followed by proposing an efficient model for implementation. The paper shows that the proposed implementation also supports the first-order predicate Horn logic with arbitrary quantified variables. The paper also introduces for the first time, a declarative programming for the quantified Boolean Horn formulas.

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扩展Prolog以获取量化的布尔型Horn公式

Prolog是一种基于命题Horn公式的众所周知的声明式编程语言。它在人工智能，自动定理证明，数学逻辑等各个领域都非常有用。多年来活跃的研究领域是将Prolog扩展到更大的逻辑类别。它的一些重要扩展包括约束逻辑编程和面向对象的逻辑编程。但是，它不能解决具有任意量化的Horn公式的问题。确切地说，不允许Prolog中的事实，规则和查询具有任意量化的变量。本文通过将其扩展为量化布尔霍恩公式，克服了Prolog的主要限制。我们通过将SLD分辨率证明系统扩展为量化布尔型Horn公式来实现这一目标，然后提出一个有效的实施模型。本文表明，所提出的实现还支持带有任意量化变量的一阶谓词Horn逻辑。本文还首次介绍了量化布尔型Horn公式的声明式编程。