A modal proof theory for final polynomial coalgebras

An infinitary proof theory is developed for modal logics whose models are coalgebras of polynomial functors on the category of sets. The canonical model method from modal logic is adapted to construct a final coalgebra for any polynomial functor. The states of this final coalgebra are certain “maximal” sets of formulas that have natural syntactic closure properties.

The syntax of these logics extends that of previously developed modal languages for polynomial coalgebras by adding formulas that express the “termination” of certain functions induced by transition paths. A completeness theorem is proven for the logic of functors which have the Lindenbaum property that every consistent set of formulas has a maximal extension. This property is shown to hold if the deducibility relation is generated by countably many inference rules.

A counter-example to completeness is also given. This is a polynomial functor that is not Lindenbaum: it has an uncountable set of formulas that is deductively consistent but has no maximal extension and is unsatisfiable, even though all of its countable subsets are satisfiable.     

我国海事法律体系存在的缺陷

本文通过笔者多年的实践,指出了海事法律体系存在的多方面缺陷.     

哥德尔不完全性定理的证明过程有误

简述了哥德尔第一不完全性定理和哥德尔第二不完全性定理，通过论证证明哥德尔的两个不完全性定理的证明过程有误。     

A refutation of Penrose's Gödelian case against artificial intelligence

Having, as it is generally agreed, failed to destroy the computational conception of mind with the Godelian attack he articulated in his The Emperor's New Mind, Penrose has returned, armed with a more elaborate and more fastidious Gödelian case, expressed in Chapters 2 and 3 of his Shadows of the Mind. The core argument in these chapters is enthymematic, and when formalized, a remarkable number of technical glitches come to light. Over and above these defects, the argument, at best, is an instance of either the fallacy of denying the antecedent, the fallacy of petitio principii, or the fallacy of equivocation. More recently, writing in response to his critics in the electronic journal Psyche, Penrose has offered a Gödelian case designed to improve on the version presented in SOTM. But this version is yet again another failure. In falling prey to the errors we uncover, Penrose's new Gödelian case is unmasked as the same confused refrain J. R. Lucas initiated 35 years ago.     

重新想象建筑,倾斜现实评BAU建筑与城市设计事务所的建筑与城市设计

文章关注的是BAU这家澳大利亚 中国的建筑、城市设计与景观设计公司的作品。这些作品反映了这家从事各种规模设计,关注不同环境因素的公司对研究的重视。4个刊登的项目显示了在现代城市环境中如何拓展建筑的语汇,建筑的复杂性反射出文化的多元交汇性;可持续的理念在功能与形式等各个层面的实践;以及对建筑设计流于形态设计机器的抵制。     

Some specially formulated axiomizations for I manage to evade the Herbrandized version of the Second Incompleteness Theorem

In 1981, Paris and Wilkie indicated it was an open question whether IΣ₀ would satisfy the Second Incompleteness Theorem for Herbrand deduction. We will show that some specially formulated axiomizations for IΣ₀ can evade the Herbrandized version of the Second Incompleteness Theorem.     

Handling non-canonical software requirements based on Annotated Predicate Calculus

Eliciting requirements for a proposed system inevitably involves the problem of handling undesirable information about customer's needs, including inconsistency, vagueness, redundancy, or incompleteness. We term the requirements statements involved in the undesirable information non-canonical software requirements. In this paper, we propose an approach to handling non-canonical software requirements based on Annotated Predicate Calculus (APC). Informally, by defining a special belief lattice appropriate for representing the stakeholder's belief in requirements statements, we construct a new form of APC to formalize requirements specifications. We then show how the APC can be employed to characterize non-canonical requirements. Finally, we show how the approach can be used to handle non-canonical requirements through a case study. Kedian Mu received B.Sc. degree in applied mathematics from Beijing Institute of Technology, Beijing, China, in 1997, M.Sc. degree in probability and mathematical statistics from Beijing Institute of Technology, Beijing, China, in 2000, and Ph.D. in applied mathematics from Peking University, Beijing, China, in 2003. From 2003 to 2005, he was a postdoctoral researcher at Institute of Computing Technology, Chinese Academy of Sciences, China. He is currently an assistant professor at School of Mathematical Sciences, Peking University, Beijing, China. His research interests include uncertain reasoning in artificial intelligence, knowledge engineering and science, and requirements engineering. Zhi Jin was awarded B.Sc. in computer science from Zhejiang University, Hangzhou, China, in 1984, and studied for her M.Sc. in computer science (expert system) and her Ph.D. in computer science (artificial intelligence) at National Defence University of Technology, Changsha, China. She was awarded Ph.D. in 1992. She is a senior member of China Computer Federation. She is currently a professor at Academy of Mathematics and System Sciences, Chinese Academy of Science. Her research interests include knowledge-based systems, artificial intelligence, requirements engineering, ontology engineering, etc. Her current research focuses on ontology-based requirements elicitation and analysis. She has got about 60 papers published, including co-authoring one book. Ruqian Lu is a professor of computer science of the Institute of Mathematics, Chinese Academy of Sciences. His research interests include artificial intelligence, knowledge engineering and knowledge based software engineering. He designed the “Tian Ma” software systems that have been widely applied in more than 20 fields, including the national defense and the economy. He has won two first class awards from Chinese Academy of Sciences and a National second class prize from the Ministry of Science and Technology. He has also won the sixth Hua Lookeng Prize for Mathematics. Yan Peng received B.Sc. degree in software from Jilin University, Changchun, China, in 1992. From June 2002 to December 2005, he studied for his M.E. in software engineering at College of Software Engineering, Graduate School of Chinese Academy of Sciences, Beijing, China. He was awarded M.E degree in 2006. He is currently responsible for CRM (customer relationship management) and BI (business intelligence) project in the BONG. His research interests include customer relationship management, business intelligence, data ming, software engineering and requirements engineering.