n值Lukasiewicz命题逻辑系统中公式的随机真度及近似推理

利用赋值集的随机化方法,在n值Lukasiewicz命题逻辑系统中引入公式的随机真度,证明了随机真度的MP规则、HS规则及交推理规则;同时引入公式间的随机相似度和随机伪距离,建立了随机逻辑度量空间,推导出随机相似度的若干性质,证明了随机逻辑度量空间中逻辑运算的连续性;并在随机逻辑度量空间中提出了三种不同类型的近似推理模式,证明了三种近似推理模式的等价性.     

Validating a concept inventory for measuring students’ probabilistic reasoning: The case of reasoning within the context of a raffle

Assessing students’ conceptions related to independence of events and determining probabilities from a sample space has been the focus of research in probability education for over 40 years. While we know a lot from past studies about predictable ways students may reason with well-known tasks, developing a diagnostic assessment that can be used by teachers to inform instruction demands the use of familiar and unfamiliar contexts. This paper presents the current work of a research team whose aim is to create a formative concept inventory with strong evidence of validity that uses a psychometric model to confidently predict whether a student exhibits one or more misconception across many items. We illustrate this process in this paper using a particular item with a context of a raffle aimed to measure whether a student reasons with misconceptions related to independence or equiprobability. The results of two aspects of the validity process: cognitive interviews to assess response processes on individual items, and a large-scale administration to examine internal structure of the concept inventory revealed difficulties in assessing students’ reasoning about these key probability concepts and trends in the prevalence of misconceptions across grades. Results can provide guidance for others aiming to develop assessments in mathematics education and also support further possibilities for research into understanding students’ reasoning about independence and sample space.     

基于系统L（X）的几种近似推理

本文在格值命题逻辑系统Ｌ（Ｘ）研究工作的基础上，借助于Ｌ（Ｘ）的语法推演规则，针对四种近似推理模型分别提出了几种近似推理方法。     

A Kind of Approximate Reasoning Principles

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A computer program for fuzzy reasoning

An interactive computer program is described which implements the procedure proposed in “A Formal System for Fuzzy Reasoning” [1]. The problem in question is that of deciding what conclusions may be drawn in the presence of (posibly conflicting) evidence provided, generally with associated partial degrees of belief, by several sources of differing reliability. In using the program, each piece of evidence is entered as a sentence (using the terms NOT, AND, OR, IMPLIES as necessary), with an associated ‘degree of belief’ and ‘weight’; followed by a tentative conclusion. The system returns the degree(s) of belief and weight(s) which may rationally be attached to the conclusion. Copies of the program, written in FORTRAN IV (870 lines) have been lodged with the program libraries CUBE, DECUS, and SHARE, or may be obtained by writing to the author.     

Generating possible intentions with constrained argumentation systems

Practical reasoning (PR), which is concerned with the generic question of what to do, is generally seen as a two steps process: (1) deliberation, in which an agent decides what state of affairs it wants to reach - that is, its desires; and (2) means-ends reasoning, in which the agent looks for plans for achieving these desires. The agent’s intentions are a consistent set of desires that are achievable together.This paper proposes the first argumentation system for PR that computes in one step the possible intentions of an agent, avoiding thus the drawbacks of the existing systems. The proposed system is grounded on a recent work on constrained argumentation systems, and satisfies the rationality postulates identified in argumentation literature, namely the consistency and the completeness of the results.     

The Place of Logic in Reasoning

Reasoning is a goal-oriented activity. The logical steps are at best the median part of a full reasoning: before them, a language has to be defined, and a model of the goal in this language has to be developed; after them, their result has to be checked in the real world with respect to the goal. Both the prior and the subsequent steps can be conducted rationally; none of them has a logical counterpart. Furthermore, Logic aims at prescribing what a correct reasoning is. But correct with respect to what? If the answer is: with respect to truth, the next question is whether the truth in everyday life, physics, economy, is the same as the truth that logicians have in mind. Resorting to Logic is justified only if an idealization in terms of true propositions in the logical sense is compatible with the goal. If such an idealization is legitimate, so is the use of classical Logic. If not, there is no authority forbidding to skew Logic in order to better reflect the nature of the reasoning required for the task.     

浅谈合情推理的教学

论述了合情推理与逻辑推理的关系、在高等数学教学中渗透合情推理的意义 ,并结合教学实践就通过合情推理引入数学理论 ,探求问题结论 ,探索解题方法作了初步探讨     

Reasoning about sequences of memory states

Motivated by the verification of programs with pointer variables, we introduce a temporal logic whose underlying assertion language is the quantifier-free fragment of separation logic and the temporal logic on the top of it is the standard linear-time temporal logic LTL. We analyze the complexity of various model-checking and satisfiability problems for , considering various fragments of separation logic (including pointer arithmetic), various classes of models (with or without constant heap), and the influence of fixing the initial memory state. We provide a complete picture based on these criteria. Our main decidability result is pspace-completeness of the satisfiability problems on the record fragment and on a classical fragment allowing pointer arithmetic. -completeness or -completeness results are established for various problems by reducing standard problems for Minsky machines, and underline the tightness of our decidability results.     

基于神经网络的模糊推理

为了使模糊推理符合推理原则，目前已定义了１０多种模糊关系，但各种模糊关系定义都存在一定的缺陷。本文提出的基于神经网络的模糊推理，能很好地符合模糊推理原则。     

基于经典逻辑系统的模糊推理方法

给出了一种基于经典二值逻辑系统的模糊推理方法.由于经典二值逻辑系统和我们提出的一种新的三段论原则是比较令人信服的,故我们的算法的基础是较为坚实的;同时在新的推理方法中避免了蕴合算子的选择,使得本算法不存在选择蕴含算子的困难;本算法具有还原性且计算简单;通过实例的计算结果与三Ⅰ算法和CRI算法的计算结果相比较,说明由新算法计算出的结果也是较为令人信服的,因此新算法是一种较好的算法.     

关于模糊逻辑的—场争论

本文介绍最近发生的关于模糊逻辑的意义和应用的一场争论。并提出笔者的见解。     

Inconsistency as qualified truth: A probability logic approach

We treat the sentences in a finite inconsistent knowledge base as assertions that are true with probability at least some primary threshold η and consider as consequences those assertions entailed to have probability at least some secondary threshold ζ.     

应急决策知识发现的推理方法研究

在复杂多变的应急决策环境中,如何根据已有的决策背景知识和当前发生的应急问题,进行有效的知识推理是在应急处置过程中实现知识发现的重要途径。本文基于范畴论和定型范畴论,提出了一种从联想和推演两个角度实现的知识推理方法。这种方法是通过类推定型函子(Functor)和推出(Pushout)来实现的,它将推理形式转变成一种范畴化知识结构上的计算过程。该方法能够通过有效的知识推理,从已知的决策背景知识中获得新知识,以辅助决策者进行有效的决策。     

概率逻辑学基本定理在多值命题逻辑系统中的推广

通过引入概率测度空间,在n值Lukasiewicz命题逻辑系统中提出了满足Kolmogorov公理的命题公式的概率;证明了概率逻辑学基本定理,并将概率逻辑学基本定理推广到了更一般的形式,改进了对推理结论的不可靠度上界的估计;将概率逻辑学的基本方法引入计量逻辑学,建立了更一般的逻辑度量空间;通过概率逻辑学基本定理,证明了逻辑度量空间中概率MP,HS规则,它是真度MP,HS规则的推广.     

Gainse-Rescher逻辑系统中的一种降级算法及其性质

在Gainse-Rescher逻辑系统^-C，Gr,Sn中的广义矛盾式之间建立了一种降级算法，并讨论了该降级算法的基本性质。主要结果是：在逻辑系统^-Gr(Gr)中，矛盾式不可能由对非矛盾式进行有限次降级算法得到，在逻辑系统Sn中，对任一公式最多次行n-1次降级算法即可得到矛盾式。     

Reasoning about variation in the intensity of change in covarying quantities involved in rate of change

This paper extends work in the area of quantitative reasoning related to rate of change by investigating numerical and nonnumerical reasoning about covarying quantities involved in rate of change via tasks involving multiple representations of covarying quantities. The findings suggest that by systematically varying one quantity, an individual could simultaneously attend to variation in the intensity of change in a quantity indicating a relationship between covarying quantities. The results document how a secondary student, prior to formal instruction in calculus, reasoned numerically and nonnumerically about covarying quantities involved in rate of change in a way that was mathematically powerful and yet not ratio-based. I discuss how coordinating covariational and transformational reasoning supports attending to variation in the intensity of change in quantities involved in rate of change.     

A Functorial Framework for Constraint Normal Logic Programming

The semantic constructions and results for definite programs do not extend when dealing with negation. The main problem is related to a well-known problem in the area of algebraic specification: if we fix a constraint domain as a given model, its free extension by means of a set of Horn clauses defining a set of new predicates is semicomputable. However, if the language of the extension is richer than Horn clauses its free extension (if it exists) is not necessarily semicomputable. In this paper we present a framework that allows us to deal with these problems in a novel way. This framework is based on two main ideas: a reformulation of the notion of constraint domain and a functorial presentation of our semantics. In particular, the semantics of a logic program P is defined in terms of three functors: that apply to constraint domains and provide the operational, the least fixpoint and the logical semantics of P, respectively. To be more concrete, the idea is that the application of to a specific constraint solver provides the operational semantics of P that uses this solver; the application of to a specific domain provides the least fixpoint of P over this domain; and, the application of to a theory of constraints provides the logic theory associated to P. In this context, we prove that these three functors are in some sense equivalent.      

模糊推理中的规则约简

为避免模糊推理中出现复合规则爆炸的情况,研究了方程pΛq→r=(p→r)V(q→r)关于uninorm诱导蕴涵所有解的情况.选用uninorm诱导的R-蕴涵作为上述方程中蕴涵时,证明了没有新的非平凡解出现;选用uninorm诱导的S-蕴涵作为上述方程中蕴涵时,获得了uninorm满足该方程的充要条件.