Normative KGP agents

We extend the logical model of agency known as the KGP model, to support agents with normative concepts, based on the roles an agent plays and the obligations and prohibitions that result from playing these roles. The proposed framework illustrates how the resulting normative concepts, including the roles, can evolve dynamically during the lifetime of the agent. Furthermore, we illustrate how these concepts can be combined with the existing capabilities of KGP agents in order to plan for their goals, react to changes in the environment, and interact with other agents. Our approach gives an executable specification of normative concepts that can be used directly for prototyping applications. Fariba Sadri is a senior lecturer at Imperial College London, from where she received her PhD. Her earlier work concentrated on integrity of deductive databases and temporal reasoning, in particular using the event calculus. In more recent years her work has been on agent technologies and multi-agent systems. She has worked on logic-based agent models, reasoning, dynamic belief revision, and inter-agent communication and negotiation for resources. She was co-awarded an EPSRC grant for research into logic-based multi-agents and was co-investigator in the EU SOCS project. Kostas Stathis is a senior lecturer at Royal Holloway, University of London and he holds a PhD from Imperial College London. His research interests are in the area of computational intelligence in general and in the intersection of computational logic and cognitive systems for social computing applications in particular. His research interests include: representation of human-computer (or computer-computer) interaction as a game; cognitive & autonomous agents; artificial agent societies; agent communication; programmable agents and agent platforms. He is a co-investigator of the EU ArguGRID project and was a co-investigator of the EU SOCS project. Francesca Toni is a senior lecturer at Imperial College London, from where she received her PhD. Her earlier work focused on abductive reasoning. In more recent years, she focused on argumentation, agent models and multi-agent systems. She has worked on computational logic-based agent models, agent reasoning, dynamic belief revision, and inter-agent communication and negotiation for resources. She has been co-ordinator of the EU SOCS project, which developed the KGP model of agency, and is coordinator of the EU ArguGRID project, on the application of argumentative agents within grid systems.     

Approximation of Matrices and a Family of Gander Methods for Polar Decomposition

Two matrix approximation problems are considered: approximation of a rectangular complex matrix by subunitary matrices with respect to unitarily invariant norms and a minimal rank approximation with respect to the spectral norm. A characterization of a subunitary approximant of a square matrix with respect to the Schatten norms, given by Maher, is extended to the case of rectangular matrices and arbitrary unitarily invariant norms. Iterative methods, based on the family of Gander methods and on Higham’s scaled method for polar decomposition of a matrix, are proposed for computing subunitary and minimal rank approximants. Properties of Gander methods are investigated in details. AMS subject classification (2000) 65F30, 15A18     

ON SOME INTERPRETATIONS OF CLASSICAL LOGIC

In distinction from the well-known double-negation embeddings of the classical logic we consider some variants of single-negation embeddings and describe some classes of superintuitionistic first-order predicate logics in which the classical first-order calculus is interpretable in such a way. Also we find the minimal extensions of Heyting's logic in which the classical predicate logic can be embedded by means of these translations.     

ON THE INADEQUACY OF THE RELATIONAL SEMANTIC FOR THE “UNTIL” OPERATOR

Modal logics with the binary operator Until are considered. It is shown that there exists a continuum of consistent U-logics without Kripke frames, and that each U-logic whose class of order does not have the finite frame property.     

There exist no 2-type surfaces in E 3 which are images under stereographic projection of minimal surfaces in S 3

In this paper we deal with the following particular case of a weaker conjecture by B. Y. Chen: Are there 2-type Willmore surfaces in E ³? In particular we prove that the above question has a negative answer when the surface is the image under stereographic projection of a minimal surface in S ³.     

Preservativity logic: An analogue of interpretability logic for constructive theories

In this paper we study the modal behavior of Σ‐preservativity, an extension of provability which is equivalent to interpretability for classical superarithmetical theories. We explain the connection between the principles of this logic and some well‐known properties of HA, like the disjunction property and its admissible rules. We show that the intuitionistic modal logic given by the preservativity principles of HA known so far, is complete with respect to a certain class of frames.     

带有边集限制的最均匀支撑树问题

本在无向网络中，建立了带有边集限制的最均匀支撑树问题的网络模型．中首先解决最均匀支撑树问题，并给出求无向网络中最均匀支撑树的多项式时间算法；然后，给出了求无向网络中带有边集限制的最小树多项式时间算法；最后，在已解决的两个问题的基础上解决了带有边集限制的最均匀支撑树问题．     

复制受限的环境演算中模态逻辑的内涵性

环境演算(MA)的模态逻辑AL进行了研究．在考虑了复制操作和限制操作的情况下，提出了逻辑等价的协归纳操作描述，并利用协归纳关系与进程结构同余关系进行比较，证明了若对MA加上约束条件得到子集MAIF^syn，此时逻辑等价(=L)与结构同余关系是等价的，即AL在MAIF^syn中是内涵的．同时发现由于复制操作的存在，AL的内涵性受到了影响，使得AL的区分能力被削弱，但通过对复制公式的构造验证了AL的表达能力．     

A Theta Lift for Spin7

We establish an example of a functorial lift from generic cuspidal representations of a similitude group of the type A ₁×C ₂ to generic representations of Spin₇. Our construction uses the theta correspondence associated to the dual pair of the type (A ₁×C ₂ B ₃) inside E ₇. We also consider another theta correspondence associated to the dual pair of type (A ₁×C ₂ A ₁×A ₁) in D ₆ and show that these two pairs fit into a tower and the standard properties of a tower of theta correspondences hold.