悖论逻辑的表演算

悖论逻辑ＬＰ是一个超协调逻辑，发展超协调逻辑（ＬＰ）的目的是使得不会从矛盾推出任一命题，但它有一个主要缺点：就是一些在经典逻辑中有效的推理在ＬＰ中不再有效；极小悖论逻辑ＬＰｍ能克服这个缺点，使得在没有矛盾的直接影响下超协调逻辑等价于经典逻辑．ＬＰ和ＬＰｍ原来都只给出语义定义，虽然已有ＬＰ的证明论，但如何得到一个ＬＰｍ的证明论仍是一个未解问题．本文提出了一种可靠与完全的表演算作为ＬＰ与ＬＰｍ的证明论．     

一个经典悖论在类比学习中的解决

自动知识获取的知识库一直面临因不协调引起的知识不一致问题.经典逻辑不具备处理不协调性的能力,而次协调逻辑是一个能够在不协调的情况下进行正常推理的逻辑.本文试图通过将经典悖论的一个例子转成类比学习中的模型,用次协调的思想对在类比学习中解决知识前后不一致性问题作一些探讨.     

基于模糊逻辑的不确定知识处理（Ⅱ）─—模糊逻辑的TABLEAU推理

本文基于ＴＡＢＬＥＡＵ方法，给出了模糊逻辑中一些至今缺少有效证明论的推理关系的证明论，也给出了作者提出的模糊择优蕴涵的判定过程．据此说明了Ｙａｇｅｒ所给出的推理规则对其所讨论的模糊推理关系是不完备的．分析了本文对前提和结论分别构造ＴＡＢＬＥＡＵ推理树的方法在研究推理关系的相关性等方面的直观语义和作为模糊Ｐｒｏｌｏｇ的推理机所具有的优越性．     

一个在弗协调逻辑中的限制

本文通过应用限制到一个弗协调逻辑给出一种弗协调限制，弗协调限制是一种弗协调非单调逻辑，它能被极小化语义所刻划，并具有两方面优点：非单调逻辑在包含矛盾时是不平凡的；弗协调逻辑在矛盾没有影响时等价于经典逻辑．     

基于四值语义的缺省逻辑

基于公式变换，给出一组缺省理论的变换方法，将命题语言L中的缺省理论变换到对应的命题语言L^-＋中，保证了所得到的缺省理论的所有扩张均不平凡，并通过一种弱变换可同时保证缺省扩张的存在性．为缺省理论定义了各种四值模型，使得缺省逻辑具有非单调超协调推理能力，并证明了L^-＋中的缺省扩张与L中缺省理论的四值模型之间具有一一对应关系．四值模型描述了公式变换的语义，基于四值语义的缺省推理通过缺省理论的变换技术能在标准的缺省逻辑中实现．     

超协调限制逻辑

本文给出了一阶超协调限制逻辑ＬＰｓ的定义，并证明了它与悖论逻辑（ＬＰ与ＬＰｍ）和限制逻辑（ＣＩＲＣ）的关系，ＬＰ作为一种非单调超协调逻辑具有非单逻辑和超协调逻辑的优点，而用能解决非单调逻辑和超协调逻辑存在的问题，它可作为在不完全与不协调知识下常识推理的形式化，因此它的知识表示中具有广泛的应用。     

超协调逻辑（Ⅲ）—超协调性的逻辑基础

这是关于超协调逻辑研究的第三篇，文中将给出一种优先语义作为超协调性的模型论基础，并给出一种表演算系统作为超协调性的证明论基础，这种优先语义和表演算系统，不仅可以包括名种超协调逻辑，而且能够导出新的超协调逻辑，在一定意义上，是超协调逻辑的统一基础，容易统一地刻画非单调性。     

基于模糊逻辑的不确定知识处理（Ⅱ）：模糊逻辑的TABLEAU推理

本文基于ＴＡＢＬＥＡＵ方法，给出了模糊逻辑中一些至今缺少有效证明论的推理关系的证明论，也给出了作者提出的模糊择优蕴 的判定过程，据此说明了Ｙａｇｅｒ所给出的推理规则对其所讨论的模糊推理关系是不完备的。     

一个在费协调逻辑中的限制

本通过应用限制到一个费协调逻辑给出一种费协调限制，费协调限制是一种费协调非单调逻辑，它能被极小化语义所刻划，并具有两方面优点：非单调逻辑在包含矛盾时是不平凡的；费协调逻辑在矛盾没有影响时等介于经典逻辑。     

OWL DL的形式化基础研究

W3C正在制定的OWL DL是一种面向语义Web的知识表示标记语言，具有较强的知识表达能力并适合大规模应用的推理效率，是语义Web领域对适合语义Web应用的知识表示标记语言进行研究的最新综合．在知识表示领域，为了对知识表达能力和推理效率做合适的折衷，进行了大量关于描述逻辑的研究，本文以描述逻辑作为OWL DL的形式化基础，详细分析了OWL DL和描述逻辑间的对应关系，用描述逻辑的语义解释了OWL DL的各个基本元素，从而可以将描述逻辑领域研究的大量成果应用到OWL DL上来，为进一步研究OWL DL的知识表示、推理等问题奠定了基础．     

The Nature of Nonmonotonic Reasoning

Conclusions reached using common sense reasoning from a set of premises are often subsequently revised when additional premises are added. Because we do not always accept previous conclusions in light of subsequent information, common sense reasoning is said to be nonmonotonic. But in the standard formal systems usually studied by logicians, if a conclusion follows from a set of premises, that same conclusion still follows no matter how the premise set is augmented; that is, the consequence relations of standard logics are monotonic. Much recent research in AI has been devoted to the attempt to develop nonmonotonic logics. After some motivational material, we give four formal proofs that there can be no nonmonotonic consequence relation that is characterized by universal constraints on rational belief structures. In other words, a nonmonotonic consequence relation that corresponds to universal principles of rational belief is impossible. We show that the nonmonotonicity of common sense reasoning is a function of the way we use logic, not a function of the logic we use. We give several examples of how nonmonotonic reasoning systems may be based on monotonic logics.     

逻辑函数的双逻辑综合与优化

针对传统布尔逻辑在电路面积优化中存在的不足,提出了一种用传统布尔逻辑和Reed-Muller(RM)逻辑相结合的双逻辑优化算法.通过将原逻辑函数的乘积项转化为不相交乘积项,并利用不相交乘积项的位操作,将逻辑函数的覆盖分成2个部分,使之分别适合布尔逻辑综合和RM逻辑综合;同时提出了适合双逻辑函数的逻辑功能验证方法.双逻辑优化算法用C语言编程实现并用MCNC标准电路进行测试.实验结果表明,与单一的布尔逻辑综合结果相比,在绝大多数情况下文中算法可使电路面积获得进一步优化.     

Intuitionistic hybrid logic: Introduction and survey

Intuitionistic hybrid logic is hybrid modal logic over an intuitionistic logic basis instead of a classical logical basis. In this short paper we introduce intuitionistic hybrid logic and we give a survey of work in the area.     

Naming Worlds in Modal and Temporal Logic

In this paper we suggest adding to predicate modal and temporal logic a locality predicate W which gives names to worlds (or time points). We also study an equal time predicate D(x, y)which states that two time points are at the same distance from the root. We provide the systems studied with complete axiomatizations and illustrate the expressive power gained for modal logic by simulating other logics. The completeness proofs rely on the fairly intuitive notion of a configuration in order to use a proof technique similar to a Henkin completion mixed with a tableau construction. The main elements of the completeness proofs are given for each case, while purely technical results are grouped in the appendix. This revised version was published online in August 2006 with corrections to the Cover Date.     

Temporal Languages for Epistemic Programs

This paper adds temporal logic to public announcement logic (PAL) and dynamic epistemic logic (DEL). By adding a previous-time operator to PAL, we express in the language statements concerning the muddy children puzzle and sum and product. We also express a true statement that an agent’s beliefs about another agent’s knowledge flipped twice, and use a sound proof system to prove this statement. Adding a next-time operator to PAL, we provide formulas that express that belief revision does not take place in PAL. We also discuss relationships between announcements and the new knowledge agents thus acquire; such relationships are related to learning and to Fitch’s paradox. We also show how inverse programs and hybrid logic each can be used to help determine whether or not an arbitrary structure represents the play of a game. We then add a past-time operator to DEL, and discuss the importance of adding yet another component to the language in order to prove completeness.     

人工智能中概率逻辑的研究

概率论是在不完备的、不确定的数据中进行推理的,它是度量不确定性的重要手段。在人工智能中,研究者结合概率和逻辑各自的优点,进行概率逻辑的研究。本文介绍了传统概率逻辑的三大派别,阐述了二值逻辑概率和三值逻辑概率的发展;最后介绍了泛逻辑,通过对概率逻辑和泛逻辑学的研究,将概率逻辑纳入泛逻辑学的框架内。     

Synthesis of quaternary reversible/quantum comparators

Multiple-valued quantum circuits are promising choices for future quantum computing technology, since they have several advantages over binary quantum circuits. Quaternary logic has the advantage that classical binary functions can be very easily represented as quaternary functions by grouping two bits together into quaternary values. Grover’s quantum search algorithm requires a sub-circuit called oracle, which takes a set of inputs and gives an output stating whether a given search condition is satisfied or not. Equality, less-than, and greater-than comparisons are widely used as search conditions. In this paper, we show synthesis of quaternary equality, less-than, and greater-than comparators on the top of ion-trap realizable 1-qudit gates and 2-qudit Muthukrishnan–Stroud gates.     

Mediative fuzzy logic: a new approach for contradictory knowledge management

In this paper we are proposing a novel fuzzy method that can handle imperfect knowledge in a broader way than Intuitionistic (in the sense of Atanassov) fuzzy logic does (IFL). This fuzzy method can manage non- contradictory, doubtful, and contradictory information provided by experts, providing a mediated solution, so we called it Mediative Fuzzy Logic (MFL). We are comparing results of MFL, with IFL and traditional Fuzzy logic (FL).