42852449
A Formal System of Logic
The main purpose of this paper is to present a formal system P in which we enjoy a smooth-running technique and which countenances a universe of classes which is symmetrical as between large and small. More exactly, P is a system which differs from the inconsistent system of [ 1 ] only in the introduction of a rather natural new restrictive condition on the defining formulas of the elements (sets, membership-eligible classes). It will be proved that if the weaker system of [ 2 ] is consistent, then P is also consistent. After the discovery of paradoxes, it may be recalled, Russell and Zermelo in the same year proposed two different ways of safeguarding logic against contradictions (see [ 3 ], [ 4 ]). Since then various simplifications and refinements of these systems have been made. However, in the resulting systems of Zermelo set theory, generation of classes still tends to be laborious and uncertain; and in the systems of Russell's theory of types, complications in the matter of reduplication of classes and meaningfulness of formulas remain. In [ 2 ], Quine introduced a system which seems to be free from all these complications. But later it was found out that in it there appears to be an unavoidable difficulty connected with mathematical induction. Indeed, we encounter the curious situation that although we can prove in it the existence of a class V of all classes, and we can also prove particular existence theorems for each of infinitely many classes, nobody has so far contrived to prove in it that V is an infinite class or that there exists an infinite class at all.
26896458
The Axiomatization of Arithmetic
21405683
Set-Theoretical Basis for Real Numbers
twenty axioms used by Tarski which are sufficient for the arithmetic of real numbers and are to the effect that real numbers form a complete ordered field.2 Indeed, we cannot prove in L all Tarski's twenty axioms in their full generality. One of them, stating in effect that every bounded class of real numbers possesses a least upper bound, can only be proved as a metatheorem which states that every bounded nameable class of real numbers possesses a least upper bound. However, all the other nineteen axioms can be proved in L without any modification. This result may be of some interest because the axioms of L are considerably weaker than those commonly employed for the same purpose. In L variables need to take as values only classes each of whose members has no more than two members. In other words, only classes each with no more than two members are to be elements. On the other hand, it is usual to assume for the purpose of natural arithmetic that all finite classes are elements, and, for the purpose of real arithmetic, that all enumerable classes are elements. 2. The system L. In developing L, elementary logic (viz., the theory of truth functions and quantifiers) is assumed from the beginning. The single additional primitive is the two place predicate e with which we can generate formulas of L from variables and logical operators in the usual manner. The usual definitions (e.g., D9-D35 of [21) of the theory of classes and relations are assumed. In particular, let tx denote the unit class of x, x u y denote the sum class of x and y, and V denote the class of all elements. The axioms of L are given by the following three statements: Mi. tx U by f V. M2. x = y D . x e z D y e z. M3. If q is any formula of L in which y is not free, then . (3y)(x)(x e yW
33404030
Some Facts About Kurt Godel
34944417
Logic of Many-Sorted Theories
Certain axiomatic systems involve more than one category of fundamental objects; for example, points, lines, and planes in geometry; individuals, classes of individuals, etc. in the theory of types or in predicate calculi of orders higher than one. It is natural to use variables of different kinds with their ranges respectively restricted to different categories of objects, and to assume as substructure the usual quantification theory (the restricted predicate calculus) for each of the various kinds of variables together with the usual theory of truth functions for the formulas of the system. An axiomatic theory set up in this manner will be called many-sorted. We shall refer to the theory of truth functions and quantifiers in it as its (many-sorted) elementary logic, and call the primitive symbols and axioms (including axiom schemata) the proper primitive symbols and proper axioms of the system. Our purpose in this paper is to investigate the many-sorted systems and their elementary logics. Among the proper primitive symbols of a many-sorted system T n ( n = 2, …, ω ) there may be included symbols of some or all of the following kinds: (1) predicates denoting the properties and relations treated in the system; (2) functors denoting the functions treated in the system; (3) constant names for certain objects of the system. We may either take as primitive or define a predicate denoting the identity relation in T n .
29040872
A Variant to Turing's Theory of Computing Machines
The principal purpose of this paper is to offer a theory which is closely related to Turing's [1] but is more economical in the basic operations. I t will be proved that a theoretically simple basic machine can be imagined and specified such tha t all partial recursive functions (and hence all solvable computation problems) can be computed by it and tha t only four basic types of instruction are employed for the programs: shift left one space, shift right one space, mark a blank space, conditional transfer. In particular, erasing is dispensable, one symbol for marking is sufficient, and one kind of transfer is enough. The reduction is somewhat similar to the realization of, for instance, the definability of conjunction and implication in terms of negation and disjunction, or of the definability of all these in terms of Sheffer's stroke function. As a result, i t becomes less direct to prove that certain things can be done by the machines, but a little easier to prove that certain things cannot be done. This serf-contained theory will b e presented, as far as possible, in a language which is familiar to those who are engaged in the use and construction of largescale computers. Turing's theory of computable functions antedated but has not much influenced the extensive actual construction of digital computers. These two aspects of theory and practice have been developed almost entirely independently of each other. The main reason is undoubtedly that logicians are interested in questions radically different from those with which the applied mathematicians and electrical engineers are primarily concerned. I t cannot, however, fail to strike one as rather strange that often the same concepts are expressed by very different terms in the two developments. One is even inclined to ask whether a rapprochement might not produce some good effect. This paper wiU, it is believed, be of use to those who wish to compare and connect the two approaches. Extensive use of Turing [1] and Kleene [2] (Chapter XI I I ) will be made, although the exposition is sufficient in itself.
21956342
Architectural design and implementation of highly available and scalable medical system with IBM Websphere middleware
Medical systems require the end-to-end high availability and scalability. There are many components in a medical system, and each individual component contributes to the overall system availability and scalability. We present the formulas to assess the overall system availability and capacity planning, and we architect approaches and technologies to make all components highly available in all tiers by clustering, workload management, and replication. We discuss how to unify all medical systems and design the uniform framework for different kinds of medical systems to hook up with this framework so that we can maintain a highly available and highly scalable system with ease. We use the n-tier distributed component based architecture and J2EE technologies as well as Web services to interact with .NET and others. We discuss how to program in the framework for high availability and scalability and how to upgrade application software without service interruption to achieve continuous availability. We show how to add or reduce hardware capacity in each tier and how to maintain hardware and software without service interruption as well as how to balance the capacity and availability among tiers.
18424476
Proving theorems by pattern recognition I
Certain preliminary results on doing mathematics by machines (“mechanical mathematics”) were reported in an earlier paper [20]. The writer suggested developing inferential analysis as a branch of applied logic and as a sister discipline of numerical analysis. This analogy rests on the basic distinction of pure existence proofs, elegant procedures which in theory always terminate, and efficient procedures which are more complex to describe but can more feasibly be carried out in practice. In contrast with pure logic, the chief emphasis of inferential analysis is on the efficiency of algorithms, which is usually attained by paying a great deal more attention to the detailed structures of the problems and their solutions, to take advantage of possible systematic short cuts. The possibilities of much more elaborate calculations by machines provide an incentive to studying a group of rather minute questions which were formerly regarded as of small theoretical interest. When the range of actual human computation was narrow, there seemed little point in obtaining faster procedures which were still far beyond what was feasible. Furthermore, on account of the versatility of machines, it now appears that as more progress is made, strategies in the search for proofs, or what are often called heuristic methods, will also gradually become part of the subject matter of inferential analysis. An analogous situation in numerical analysis would be, for example, to make the machine choose to apply different tricks such as taking the Fourier transform to obtain a solution of some differential equation.
16868039
Automatic text discovering through stroke-based segmentation and text string combination
In this paper we present a novel framework of automatic text discovering for content-based multimedia application. For single image, the stroke-based binarization and the coarse-to-fine text extraction will collaborate to generate a clean text image for recognition. For image sequence, multi-frame text enhancement is adopted to increase the text/background contrast, and the recognition results are finally refined by the text string combination algorithm to get more precise semantic information. Two prototype demos have been successfully developed on mobile phones. The experimental results on different platforms show the superior performance of the proposed method.
11622519
Applying Knowledge Sharing for Business Intelligence Collaboration
IT services need an automatic and flexible ability to react to dynamic changes in their environment. Managing change effectively and reducing the negative effects of day-to-day operations has become one of the most important tasks in IT service management, which require hiring highly skilled IT professionals with correspondingly high labor costs. There is a challenge to select, implement and integrate the right resources quickly and effectively. Although there is a growing body of research into IT management, many techniques are either too narrow (focusing on a single component rather than the entire system), or they address only configuration data collection and integration. Instead, one needs to scale or respond to special domain knowledge, collaboration and the right data for helping IT professionals to improve their work. In this paper, we propose a knowledge-sharing based collaborating management system for IT service management. It aims to bridge the gap between domain experts’ knowledge and manageable systems. We developed a proof-of-concept of an impact analysis service based on knowledge-sharing; it establishes an IT service management collaboration paradigm and ecosystem, leveraging the expert’s rich knowledge and experience to improve the management quality and reduce the cost. A case study driven by customers demonstrates that collaboration with knowledge sharing is effective both at constructing useful system analysis services and in using those services to improve system management.
5494803
Wireless Network Dynamic Topology Routing Protocol Based on Aggregation Tree Model
As the scale of the network increases, especially wireless and mobile networks comes into fashion, the problem of network dynamic topology management turns into a focus topic in the network world. When network information changes, frequent route computing and network state updates can cause computing and traffic overhead, respectively. Therefore, minimum of influence to network structure has been identified as one of the key issues in designing dynamic network routing protocols. A novel protocol, which is based on Aggregation Tree Routing Model (ATRM) as well as an effective ball-and-string algorithm, is introduced in this paper which aims to minimize the alteration of network topology and to speed up the minimum cost route computation. This routing protocol is applicable to all kinds of networks, including Internet, ad hoc and wireless sensor networks. The simulations show that our protocol not only results in significantly lower overhead, but also gives high levels of dynamic network topology management performance while keeping practical.