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A logical characterisation of ordered disjunction

机译：有序析取的逻辑表征

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摘要

In this paper we consider a logical treatment for the ordered disjunction operator x introduced by Brewka, Niemela and Syrjanen in their Logic Programs with Ordered Disjunctions (LPOD). LPODs are used to represent preferences in logic programming under the answer set semantics. Their semantics is defined by first translating the LPOD into a set of normal programs (called split programs) and then imposing a preference relation among the answer sets of these split programs. We concentrate on the first step and show how a suitable translation of the ordered disjunction as a derived operator into the logic of Here-and-There allows capturing the answer sets of the split programs in a direct way. We use this characterisation not only for providing an alternative implementation for LPODs, but also for checking several properties (under strongly equivalent transformations) of the x operator, like for instance, its distributivity with respect to conjunction or regular disjunction. We also make a comparison to an extension proposed by Karger, Lopes, Olmedilla and Polleres, that combines x with regular disjunction.
机译：在本文中，我们考虑对Brewka，Niemela和Syrjanen在其“带有序分离逻辑”程序中引入的有序分离运算符x的逻辑处理。 LPOD用于在答案集语义下表示逻辑编程中的首选项。通过首先将LPOD转换为一组正常程序（称为拆分程序），然后在这些拆分程序的答案集之间强加偏好关系，来定义其语义。我们将重点放在第一步上，并说明如何将有序析取运算作为派生算子正确转换为“这里和那里”的逻辑，从而可以直接捕获拆分程序的答案集。我们使用此特征不仅为LPOD提供了一种替代实现，而且还用于检查x运算符的多个属性（在强等价转换下），例如，其关于合取或正则析取的分布。我们还与Karger，Lopes，Olmedilla和Polleres提出的扩展进行了比较，该扩展将x与常规析取相结合。

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