Complete Axiomatizations for Reasoning about Knowledge and Branching Time

Sound and complete axiomatizations are provided for a number of different logics involving modalities for the knowledge of multiple agents and operators for branching time, extending previous work of Halpern, van der Meyden and Vardi [to appear, SIAM Journal on Computing] for logics of knowledge and linear time. The paper considers the system constraints of synchrony, perfect recall and unique initial states, which give rise to interaction axioms. The language is based on the temporal logic CTL*, interpreted with respect to a version of the bundle semantics.     

Proof Systems for Reasoning about Computation Errors

In the paper we examine the use of non-classical truth values for dealing with computation errors in program specification and validation. In that context, 3-valued McCarthy logic is suitable for handling lazy sequential computation, while 3-valued Kleene logic can be used for reasoning about parallel computation. If we want to be able to deal with both strategies without distinguishing between them, we combine Kleene and McCarthy logics into a logic based on a non-deterministic, 3-valued matrix, incorporating both options as a non-deterministic choice. If the two strategies are to be distinguished, Kleene and McCarthy logics are combined into a logic based on a 4-valued deterministic matrix featuring two kinds of computation errors which correspond to the two computation strategies described above. For the resulting logics, we provide sound and complete calculi of ordinary, two-valued sequents. Presented by Yaroslav Shramko and Heinrich Wansing     

Rules for Reasoning from Knowledge and Lack of Knowledge

In this paper, the traditional view that argumentum ad ignorantiam is a logical fallacy is challenged, and lessons are drawn on how to model inferences drawn from knowledge in combination with ones drawn from lack of knowledge. Five defeasible rules for evaluating knowledge-based arguments that apply to inferences drawn under conditions of lack of knowledge are formulated. They are the veridicality rule, the consistency of knowledge rule, the closure of knowledge rule, the rule of refutation and the rule for argument from ignorance. The basic thesis of the paper is that knowledge-based arguments, including the argument from ignorance, need to be evaluated by criteria for epistemic closure and other evidential rules that are pragmatic in nature, that need to be formulated and applied differently at different stages of an investigation or discussion. The paper helps us to understand practical criteria that should be used to evaluate all arguments based on knowledge and/or ignorance.

A Logic for Reasoning about Relative Similarity

A similarity relation is a reflexive and symmetric binary relation between objects. Similarity is relative: it depends on the set of properties of objects used in determining their similarity or dissimilarity. A multi-modal logical language for reasoning about relative similarities is presented. The modalities correspond semantically to the upper and lower approximations of a set of objects by similarity relations corresponding to all subsets of a given set of properties of objects. A complete deduction system for the language is presented.     

人类对知识的好奇:认识性好奇心

认识性好奇心是个体对新知识的好奇,可从状态和特质角度理解,其中特质认识性好奇心又区分为兴趣型和剥夺型两种类型。近年来众多证据表明,认识性好奇心受知道感、性别、对信息的偏好模式等因素影响,并在学习、记忆及创造性方面起到积极作用。未来研究有必要着眼于毕生发展的角度进行纵向考察,完善其测量方式,并深入考察认识性好奇心对学习的影响机制,从而为教育实践提供一定启示。     

Systems Thinking for Knowledge

The capacity to engage in systems thinking is often viewed as being a product of being able to understand complex systems due to one's facility in mastering systems theories, methods, and being able to adeptly reason. Relatively little attention is paid in the systems literature to the processes of learning from experience and creating knowledge as a direct consequence of individuals engaging systems thinking itself over time. In fact, the potential efficacy of systems thinking to improve performance normally seen as only contingent on a priori knowledge, rather than knowledge created via learning from experience. Such newly create knowledge often results from engaging in modeling efforts and systemic forms of inquiry. This article proposes a model for creating new knowledge by coupling systems modeling with a pragmatic approach to knowledge-creation. This approach is based on a foundation of the pragmatic concepts first proposed by the American philosopher/scientist Charles Sanders Peirce over a century ago. This model offers systems practitioners a framework to engage in knowledge-intensive systems thinking (KIST) for addressing complex problematic issues.     

A Map of Common Knowledge Logics

In order to capture the concept of common knowledge, various extensions of multi-modal epistemic logics, such as fixed-point ones and infinitary ones, have been proposed. Although we have now a good list of such proposed extensions, the relationships among them are still unclear. The purpose of this paper is to draw a map showing the relationships among them. In the propositional case, these extensions turn out to be all Kripke complete and can be comparable in a meaningful manner. F. Wolter showed that the predicate extension of the Halpern-Moses fixed-point type common knowledge logic is Kripke incomplete. However, if we go further to an infinitary extension, Kripke completeness would be recovered. Thus there is some gap in the predicate case. In drawing the map, we focus on what is happening around the gap in the predicate case. The map enables us to better understand the common knowledge logics as a whole.     

A Sound and Complete Tableau Calculus for Reasoning about only Knowing and Knowing at Most

We define a tableau calculus for the logic of only knowing and knowing at most ON, which is an extension of Levesque's logic of only knowing O. The method is based on the possible-world semantics of the logic ON, and can be considered as an extension of known tableau calculi for modal logic K45. From the technical viewpoint, the main features of such an extension are the explicit representation of "unreachable" worlds in the tableau, and an additional branch closure condition implementing the property that each world must be either reachable or unreachable. The calculus allows for establishing the computational complexity of reasoning about only knowing and knowing at most. Moreover, we prove that the method matches the worst-case complexity lower bound of the satisfiability problem for both ON and O. With respect to [22], in which the tableau calculus was originally presented, in this paper we both provide a formal proof of soundness and completeness of the calculus, and prove the complexity results for the logic ON.     

Reasoning about cooperation,actions and preferences

In this paper, a logic for reasoning about coalitional power is developed which explicitly represents agents’ preferences and the actions by which the agents can achieve certain results. A complete axiomatization is given and its satisfiability problem is shown to be decidable and EXPTIME-hard.     

Analytic Tableau Systems and Interpolation for the Modal Logics KB, KDB, K5, KD5

We give complete sequent-like tableau systems for the modal logics KB, KDB, K5, and KD5. Analytic cut rules are used to obtain the completeness. Our systems have the analytic superformula property and can thus give a decision procedure. Using the systems, we prove the Craig interpolation lemma for the mentioned logics.     

Knowledge on Treelike Spaces

This paper presents a bimodal logic for reasoning about knowledge during knowledge acquisitions. One of the modalities represents (effort during) non-deterministic time and the other represents knowledge. The semantics of this logic are tree-like spaces which are a generalization of semantics used for modeling branching time and historical necessity. A finite system of axiom schemes is shown to be canonically complete for the formentioned spaces. A characterization of the satisfaction relation implies the small model property and decidability for this system.     

Knowledge and availability

The mentioning of error-possibilities makes us less likely to ascribe knowledge. This paper offers a novel psychological account of this data. The account appeals to “subadditivity,” a well-known psychological tendency to judge possibilities as more likely when they are disjunctively described.     

Correspondence Results for Relational Proof Systems with Application to the Lambek Calculus

We present a general framework for proof systems for relational theories. We discuss principles of the construction of deduction rules and correspondences reflecting relationships between semantics of relational logics and the rules of the respective proof systems. We illustrate the methods developed in the paper with examples relevant for the Lambek calculus and some of its extensions.     

Toward an Ethics of Knowledge

Abstract. Modern science is one form of knowledge, demarcated by its time (modernity) and by other “knowledges.” There is a fair amount of clarity as to what does not count as scientific, but there is a twilight zone of knowledges whose scientific status is ambivalent. In this zone the encounter between science and religion takes place. The particular contribution of religion and theology in this encounter is to call for an ethics of knowledge in the epistemological endeavors of science.     

A Logic for Multiple-source Approximation Systems with Distributed Knowledge Base

The theory of rough sets starts with the notion of an approximation space, which is a pair (U,R), U being the domain of discourse, and R an equivalence relation on U. R is taken to represent the knowledge base of an agent, and the induced partition reflects a granularity of U that is the result of a lack of complete information about the objects in U. The focus then is on approximations of concepts on the domain, in the context of the granularity. The present article studies the theory in the situation where information is obtained from different sources. The notion of approximation space is extended to define a multiple-source approximation system with distributed knowledge base, which is a tuple (U,R_P)_{Pßf N}(U,R_P)_{P\ss_f N}, where N is a set of sources and P ranges over all finite subsets of N. Each R _P is an equivalence relation on U satisfying some additional conditions, representing the knowledge base of the group P of sources. Thus each finite group of sources and hence individual source perceives the same domain differently (depending on what information the group/individual source has about the domain), and the same concept may then have approximations that differ with the groups. In order to express the notions and properties related with rough set theory in this multiple-source situation, a quantified modal logic LMSAS ^D is proposed. In LMSAS ^D , quantification ranges over modalities, making it different from modal predicate logic and modal logic with propositional quantifiers. Some fragments of LMSAS ^D are discussed and it is shown that the modal system KTB is embedded in LMSAS ^D . The epistemic logic S5^D_nS5^D_n is also embedded in LMSAS ^D , and cannot replace the latter to serve our purpose. The relationship of LMSAS ^D with first and second-order logics is presented. Issues of expressibility, axiomatization and decidability are addressed.     

异步异构分层并行演化算法及其在串并系统可靠性优化中的应用(英文)

本文提出了一种新的并行演化算法――异步异构分层并行演化算法(AHHPGA),用于求解串并系统可靠性分配的多目标优化问题(RAP)。AHHPGA采用分层结构,上层由粗粒度模型构成,下层由细粒度模型构成。在AHHPGA的每个子种群中,采用不同的全局/局部搜索度和拓扑结构,构成异构模型。AHHPGA的迁移方式包括异步接收和异步迁出。采用基于模型的复杂系统可靠性评价工具(HiP-HOPS),以克服可靠性框图方法(RBD)的缺点。仿真结果表明,基于异步异构分层并行演化算法和HiP-HOPS工具的串并系统可靠性分配的多目标优化方法,优于传统的基于遗传算法的优化方法。