摘要翻译：
逻辑FO(ID)利用逻辑程序设计领域的思想，用非单调归纳定义扩展了一阶逻辑。这种逻辑形式化地扩展了逻辑程序设计、溯因逻辑程序设计和数据逻辑，从而把这些形式化的观点形式化为（广义的）归纳定义的逻辑。本文的目的是研究FO(ID)的命题片段PC(ID)的演绎推理方法。我们给出了一个基于序贯演算的形式化证明系统（Gentzen式演绎系统）。由于PC(ID)是经典命题逻辑和命题归纳定义的集成，我们的序贯演算证明系统集成了命题演算的推理规则和定义。我们就PC(ID)的一个稍微受限制的片断给出了这个证明系统的稳健性和完备性。我们也给出了一些针对PC(ID)的复杂度结果。通过对PC(ID)证明系统的开发，有助于加深对FO(ID)证明理论基础的理解，从而探索出适用于FO(ID)的证明系统。
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英文标题：
《LPC(ID): A Sequent Calculus Proof System for Propositional Logic
  Extended with Inductive Definitions》
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作者：
Ping Hou, Johan Wittocx, and Marc Denecker
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最新提交年份：
2012
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Logic in Computer Science        计算机科学中的逻辑
分类描述：Covers all aspects of logic in computer science, including finite model theory, logics of programs, modal logic, and program verification. Programming language semantics should have Programming Languages as the primary subject area. Roughly includes material in ACM Subject Classes D.2.4, F.3.1, F.4.0, F.4.1, and F.4.2; some material in F.4.3 (formal languages) may also be appropriate here, although Computational Complexity is typically the more appropriate subject area.
涵盖计算机科学中逻辑的所有方面，包括有限模型理论，程序逻辑，模态逻辑和程序验证。程序设计语言语义学应该把程序设计语言作为主要的学科领域。大致包括ACM学科类D.2.4、F.3.1、F.4.0、F.4.1和F.4.2中的材料；F.4.3（形式语言）中的一些材料在这里也可能是合适的，尽管计算复杂性通常是更合适的主题领域。
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一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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英文摘要：
  The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with non-monotone inductive definitions. Such logic formally extends logic programming, abductive logic programming and datalog, and thus formalizes the view on these formalisms as logics of (generalized) inductive definitions. The goal of this paper is to study a deductive inference method for PC(ID), which is the propositional fragment of FO(ID). We introduce a formal proof system based on the sequent calculus (Gentzen-style deductive system) for this logic. As PC(ID) is an integration of classical propositional logic and propositional inductive definitions, our sequent calculus proof system integrates inference rules for propositional calculus and definitions. We present the soundness and completeness of this proof system with respect to a slightly restricted fragment of PC(ID). We also provide some complexity results for PC(ID). By developing the proof system for PC(ID), it helps us to enhance the understanding of proof-theoretic foundations of FO(ID), and therefore to investigate useful proof systems for FO(ID).
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PDF链接：
https://arxiv.org/pdf/1207.2534