STABLE THEORIES IN AUTOEPISTEMIC LOGIC
STABLE THEORIES IN AUTOEPISTEMIC LOGIC
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自认知逻辑中的稳定理论
DOI：
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发表时间：
1989
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通讯作者：
W. Marek
中科院分区：
文献类型：
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作者：
W. Marek
我们调查的运营商产生一个稳定的理论，其客观的一部分（一个稳定的理论是一组信念的理性代理）。我们描述了稳定理论的客观部分。最后，我们讨论了谓词演算的情况。第一节：介绍人工智能的最新发展，特别是对常识推理和非单调逻辑（[MC]，[Re 2]，[Li]，[MDD]）的形式化的强烈兴趣以及对知识的推理导致了逻辑领域的新的有趣发展，以前几乎只留给哲学家。这些主题现在得到了计算机科学家和数学家的关注，提高了适用性和增加数学严谨性的希望。在这些贡献之一，摩尔[莫]，成功地形式化的想法[MDD];由此产生的系统模态逻辑，称为自认知逻辑，处理的概念，信念的一个完全理性的代理。特别是，摩尔已经表明，一个稳定的自我认知理论是由它的客观部分。(The同样的结果在[HM]中得到了证明）。然而，他并没有从客观部分中提供T的明确结构。本文考察了稳定的自我认知理论的客观部分与理论本身之间的联系。特别是，我们展示了一个理论的有效建设的客观部分。我们证明，每一个命题理论下关闭命题的后果（在语言没有模态）是一个稳定的自认识理论的客观部分。这与[FHV]的结构有关。这些结果见第2节和第3节。在第4节中，我们考虑谓词演算的情况（这似乎是[MDD]和[Mo]的原始任务，尽管他们在论文中将自己限制在命题逻辑中）。我们通过强性质（类似于Godel的ω完备性）扩展了稳定性条件。这使我们能够证明巴肯公式的类比，因此，各种标准形式的公式。这反过来又允许扩展摩尔的结果（限制）谓词演算的情况下。下面我们介绍一下本文的一些基本概念。我们假定熟悉摩尔的论文，即使我们重复一些基本的定义。设L是命题演算的语言，LM是其相应的模态扩张。一个理论T 'i LM是稳定的当且仅当它满足Stalnaker的条件：1）T在命题（重言式）可证明下是闭的。
We investigate the operator producing a stable theory out of its objective part (A stable theory is a set of beliefs of a rational agent). We characterize the objective parts of stable theories. Finally, we discuss the predicate calculus case. Section 1: Introduction Recent developments in the artificial intelligence and, in particular, strong interest in the formalizations of the common sense reasonings and nonmonotonic logics ([MC], [Re2], [Li], [MDD]) and reasoning about knowledge leads to new interesting developments in the areas of logic previously left almost exclusively to philosophers. These subjects now get attention of computer scientists and mathematicians, raising hopes of applicability and of increased mathematical rigour. In one of these contributions, Moore [Mo], successfully formalizes the ideas of [MDD]; the resulting system of modal logic, called autoepistemic logic, deals with the notion of beliefs of a fully rational agent. In particular, Moore has shown that a stable autoepistemic theory is determined by its objective part. (The same result is proved in [HM]). He has not, however, provided the explicit construction of T out of its objective part. In this note, we investigate the connection between the objective part of a stable autoepistemic theory and the theory itself. In particular, we show an effective construction of a theory out of its objective part. We prove that every propositional theory closed under propositional consequence (in a language without modality) is the objective part of a stable autoepistemic theory. The construction is related to that of [FHV]. These results are shown in the Sections 2 and 3. In the Section 4, we consider the case of predicate calculus (which seems to be the original task of both [MDD] and [Mo], although they restrict themselves to the propositional logics in their papers). We extend the stability conditions by strong properties (similar to ω completeness of Godel). This allows us to prove analogons of Barkan’s formulas and, consequently, various normal forms for the formulas. This in turn allows to extend Moore’s results to the (restricted) predicate calculus case. Below we introduce some basic concepts of this paper. We presuppose the acquaintance with Moore’s paper, even though we repeat some of the basic definitions. Let L be the language of the propositional calculus and LM its corresponding modal extension. A theory T ‘i LM is stable if and only if it satisfies Stalnaker’s conditions: 1) T is closed under propositional (tautological) provability.