Logical analysis of data—An overview: From combinatorial optimization to medical applications

The paper presents a review of the basic concepts of the Logical Analysis of Data (LAD), along with a series of discrete optimization models associated to the implementation of various components of its general methodology, as well as an outline of applications of LAD to medical problems. The combinatorial optimization models described in the paper represent variations on the general theme of set covering, including some with nonlinear objective functions. The medical applications described include the development of diagnostic and prognostic systems in cancer research and pulmonology, risk assessment among cardiac patients, and the design of biomaterials.     

Proportions of Irreducible Diagrams

We investigate the proportion of graphs on n-vertices each of which is m-valent, that are “k-reducible”. An asymptotic formula is developed for large n and fixed values of the other variables, in terms of an n-independent parameter that is evaluated for a number of (m, k) values.     

Proportions of Irreducible Diagrams

We consider diagrams consisting of pairings among 2n integers, a₁, & , a2_n. Certain classes of such diagrams called “reducible diagrams of type k” are defined. We investigate the proportion of diagrams lying in these classes, obtaining asymptotic results for large values of n, and fixed k.     

The Percent Proportion

<正>When am I ever going to use this?The engine on the space shuttle weighs approximately 19,700 pounds.The entire space shuttle weighs 178,000 pounds.1.Write the ratio of engine weight to total weight as a fraction.2.Use a calculator to write the fraction as a decimal to the nearest hundredth.3.What percent of the space shuttle's weight is the engine?Apercent proportion compares part of a quantity to thewhole quantity,called the base,using a percent.     

Enriched Logical Connections

In the setting of enriched category theory, we describe dual adjunctions of the form $L\dashv R:{\mathsf{Spa}}^{op} \longrightarrow{\mathsf{Alg}}$ between the dual of the category Spa of “spaces” and the category Alg of “algebras” that arise from a schizophrenic object Ω, which is both an “algebra” and a “space”. We call such adjunctions logical connections. We prove that the exact nature of Ω is that of a module that allows to lift optimally the structure of a “space” and an “algebra” to certain diagrams. Our approach allows to give a unified framework known from logical connections over the category of sets and analyzed, e.g., by Hans Porst and Walter Tholen, with future applications of logical connections in coalgebraic logic and elsewhere, where typically, both the category of “spaces” and the category of “algebras” consist of “structured presheaves”.     

逻辑度量空间

取赋值格为［０,１］,用积分工具引入了公式的真度和相似度的概念,并从而在公式集Ｆ上建立了伪距离,为近似推理提供了一种可能的框架．     

Abstract Logical Constants

A possibility of defining logical constants within abstract logical frameworks is discussed, in relation to abstract definition of logical consequence. We propose using duals as a general method of applying the idea of invariance under replacement as a criterion for logicality.     

Heavy-Traffic Limits for Loss Proportions in Single-Server Queues

We establish heavy-traffic stochastic-process limits for the queue-length and overflow stochastic processes in the standard single-server queue with finite waiting room (G/G/1/K). We show that, under regularity conditions, the content and overflow processes in related single-server models with finite waiting room, such as the finite dam, satisfy the same heavy-traffic stochastic-process limits. As a consequence, we obtain heavy-traffic limits for the proportion of customers or input lost over an initial interval. Except for an interchange of the order of two limits, we thus obtain heavy-traffic limits for the steady-state loss proportions. We justify the interchange of limits in M/GI/1/K and GI/M/1/K special cases of the standard GI/GI/1/K model by directly establishing local heavy-traffic limits for the steady-state blocking probabilities.     

模糊错误逻辑分解转化词与内涵否定词的逻辑关系

在文 [1]的基础上 ,在简单分析现时中错误的传递与转化的实际存在的同时 ,介绍国内外在逻辑研究领域对事物传递与转化规律的研究现状。特别为了探索控制与防范证券风险的技术而主要研究模糊错误逻辑分解转化词与内涵否定词的逻辑关系。     

Logical omniscience as infeasibility

Logical theories for representing knowledge are often plagued by the so-called Logical Omniscience Problem. The problem stems from the clash between the desire to model rational agents, which should be capable of simple logical inferences, and the fact that any logical inference, however complex, almost inevitably consists of inference steps that are simple enough. This contradiction points to the fruitlessness of trying to solve the Logical Omniscience Problem qualitatively if the rationality of agents is to be maintained. We provide a quantitative solution to the problem compatible with the two important facets of the reasoning agent: rationality and resource boundedness. More precisely, we provide a test for the logical omniscience problem in a given formal theory of knowledge. The quantitative measures we use are inspired by the complexity theory. We illustrate our framework with a number of examples ranging from the traditional implicit representation of knowledge in modal logic to the language of justification logic, which is capable of spelling out the internal inference process. We use these examples to divide representations of knowledge into logically omniscient and not logically omniscient, thus trying to determine how much information about the reasoning process needs to be present in a theory to avoid logical omniscience.     

Inverse Proportion(2)

Example 1 If an emergency pack of food can last 10 men for 6days,how long would the food last if there were 15 men? Solution The food will last shorter for more men,implying an inverse proportion.Let the number of days be d.     

A Response to ‘A Good Enhancement with Logical Weaknesses’

Journal of the Operational Research Society -     

From Intersectors to Successors

 A geometric graph any two line segments of which intersect is called an intersector. This notion will be generalized in order to obtain new results which are not true for this (restricted) category. Received: December 8, 1997 Final version received: January 12, 2000     

From Polling to Snowplowing

We study the limiting behavior of gated polling systems, as their dimension (the number of queues) tends to infinity, while the system's total incoming workflow and total switchover time (per cycle) remain unchanged. The polling systems are assumed asymmetric, with incoming workflow obeying general Lévy statistics, and with general inter-dependent switchover times. We prove convergence, in law, to a limiting polling system on the circle. The derivation is based on an asymptotic analysis of the stochastic Poincaré maps of the polling systems. The obtained polling limit is identified as a snowplowing system on the circle—whose evolution, steady-state equilibrium, and statistics have been recently investigated and are known.