Michael Bernreiter, Anela Lolic, Jan Maly, Stefan Woltran
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引用次数: 0
Abstract
Choice logics constitute a family of propositional logics and are used for the representation of preferences, with especially qualitative choice logic (QCL) being an established formalism with numerous applications in artificial intelligence. While computational properties and applications of choice logics have been studied in the literature, only few results are known about the proof-theoretic aspects of their use. We propose a sound and complete sequent calculus for preferred model entailment in QCL, where a formula F is entailed by a QCL-theory T if F is true in all preferred models of T. The calculus is based on labeled sequent and refutation calculi, and can be easily adapted for different purposes. For instance, using the calculus as a cornerstone, calculi for other choice logics such as conjunctive choice logic (CCL) and lexicographic choice logic (LCL) can be obtained in a straightforward way.
选择逻辑是命题逻辑的一个家族，用于表示偏好，尤其是定性选择逻辑（QCL）是一种成熟的形式主义，在人工智能领域有大量应用。虽然文献中已经对选择逻辑的计算特性和应用进行了研究，但关于其使用的证明理论方面的成果却寥寥无几。我们为 QCL 中的首选模型蕴涵提出了一个完善而完整的序列微积分，如果 F 在 T 的所有首选模型中均为真，则公式 F 将被 QCL 理论 T 所蕴涵。例如，以该计算法为基石，可以直接获得其他选择逻辑（如连接选择逻辑（CCL）和词典选择逻辑（LCL））的计算法。
期刊介绍：
The Journal of Automated Reasoning is an interdisciplinary journal that maintains a balance between theory, implementation and application. The spectrum of material published ranges from the presentation of a new inference rule with proof of its logical properties to a detailed account of a computer program designed to solve various problems in industry. The main fields covered are automated theorem proving, logic programming, expert systems, program synthesis and validation, artificial intelligence, computational logic, robotics, and various industrial applications. The papers share the common feature of focusing on several aspects of automated reasoning, a field whose objective is the design and implementation of a computer program that serves as an assistant in solving problems and in answering questions that require reasoning.
The Journal of Automated Reasoning provides a forum and a means for exchanging information for those interested purely in theory, those interested primarily in implementation, and those interested in specific research and industrial applications.
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