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Two alternatives for handling preferences in qualitative choice logic

机译：定性选择逻辑中处理偏好的两种选择

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Reasoning about preferences is a major issue in many decision making problems. Recently, a new logic for handling preferences, called qualitative choice logic(QCL), was presented. This logic adds to classical propositional logic a new connective, called ordered disjunction symbolized by ×. That new connective is used to express preferences between alternatives. Intuitively, if A and B are propositional formulas then A× B means: "if possible A, but if A is impossible then at least B". One of the important limitations of QCL is that it does not correctly deal with negated and conditional preferences. Conditional rules that involve preferences are expressed using propositional implication. However, using QCL semantics, there is no difference between such material implication "(KLM×Air France) → Hotel Package" and the purely propositional formula "(Air France∨ KLM) → Hotel Package". Moreover, the negation in QCL misses some desirable properties from propositional calculus. This paper first proposes an extension of QCL language to universally quantified first-order logic framework. Then, we propose two new logics that correctly address QCL's limitations. Both of them are based on the same QCL language, but define new non-monotonic consequence relations. The first logic, called PQCL (prioritized qualitative choice logic), is particularly adapted for handling prioritized preferences, while the second one, called QCL+ (positive qualitative choice logic), is appropriate for handling positive preferences. In both cases, we show that any set of preferences, can equivalently be transformed into a set of basic preferences from which efficient inferences can be applied. Lastly, we show how our logics can be applied to alert correlation.
机译：关于偏好的推理是许多决策问题中的主要问题。最近，提出了一种用于处理偏好的新逻辑，称为定性选择逻辑（QCL）。这个逻辑在经典命题逻辑中增加了一个新的结语，称为以×表示的有序析取。该新的连接词用于表达备选方案之间的偏好。直观地，如果A和B是命题公式，则A×B表示：“如果可能，则A，但如果不可能，则至少B”。 QCL的重要限制之一是它不能正确处理否定的和条件的首选项。涉及偏好的条件规则使用命题蕴涵来表达。但是，使用QCL语义，这样的实质含义“（KLM×法国航空）→酒店套餐”与纯粹的命题公式“（法国航空KLM）→酒店套餐”之间没有区别。而且，QCL中的否定缺少命题演算的一些理想特性。本文首先提出将QCL语言扩展为通用量化的一阶逻辑框架。然后，我们提出了两种可以正确解决QCL局限性的新逻辑。它们都基于相同的QCL语言，但是定义了新的非单调结果关系。第一个逻辑称为PQCL（优先定性选择逻辑），特别适合处理优先选择的偏好，而第二个逻辑称为QCL +（正定性选择逻辑），适用于处理肯定的偏好。在这两种情况下，我们表明，任何一组首选项都可以等效地转换为一组基本首选项，从中可以应用有效的推断。最后，我们展示了如何将我们的逻辑应用于警报关联。

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