On Commutative and Nonassociative Syntactic Calculi and Categorial Grammars

Two axiomatizations of the nonassociative and commutative Lambek syntactic calculus are given and their equivalence is proved. The first axiomatization employs Permutation as the only structural rule, the second one, with no Permutation rule, employs only unidirectional types. It is also shown that in the case of the Ajdukiewicz calculus an analogous equivalence is valid only in the case of a restricted set of formulas. Unidirectional axiomatizations are employed in order to establish the generative power of categorial grammars based on the nonassociative and commutative Lambek calculus with product. Those grammars produce CF-languages of finite degree generated by CF-grammars closed with respect to permutations.     

两个分段函数卷积的数值算法

本文推广了文［１］中卷积的数值计算方法，使之适用于更广的范围，并用Ｃ语言编程举例说明．     

MODLER: Modeling by object-driven linear elemental relations

This paper describes a system to represent linear programming models and their instances. In addition to a modeling language, MODLER has an extensive query capability which includes a multi-view architecture. Further, randomization options provide rapid prototyping. The MODLER system is part of a workbench for building and managing decision support systems that are based on linear programming.This research was supported by a consortium of industries: Amoco Oil Company, Shell Development Company, Chesapeake Decision Science, GAMS Development Corp., Ketron Management Science, MathPro, Inc., Optimal Methods, Inc., and XMP Software, Inc. Partial support was also provided by the Office of Naval Research (Contract No. N-00014-88-K-0104).     

极大前缀码的刻划

设X*是字母表X上的自由幺半群,本文通过以X*为顶点集构造一个语言图Γ(X*),引入语言图Γ(X*)的横截集的概念,给出了极大前缀码的一个刻划.同时,证明了满足含有X中字母且长度有限的极大前缀码必是极大码.     

Observing mathematical fluency through students’ oral responses

‘Procedural’ fluency in mathematics is often judged solely on numerical representations. ‘Mathematical’ fluency incorporates explaining and justifying as well as producing correct numerical solutions. To observe mathematical fluency, representations additional to a student’s numerical work should be considered. This paper presents analysis of students’ oral responses. Findings suggested oral responses are important vantage points from which to view fluency – particularly characteristics harder to notice through numerical work such as reasoning. Students’ oral responses were particularly important when students’ written (language) responses were absent/inconsistent. Findings also revealed the importance of everyday language alongside technical terms for observing reasoning as a fluency characteristic. Students used high modality verbs and language features, such as connectives, to explain concepts and justify their thinking. The results of this study purport that to gain a fuller picture of students’ fluency, specifically their explanations or reasoning, students’ oral responses should be analyzed, not simply numerical work.     

基于AI-ESTATE标准的贝叶斯网络诊断模型研究

贝叶斯网络在解决复杂装备中不确定性和关联性引起的故障中具有很大优势,建立符合AI-ESTATE标准的贝叶斯网络模型,对实现其通用性至关重要;首先介绍了AI-ESTATE标准的主要内容、体系结构和六种信息模型;其次,在对贝叶斯网络进行分析的基础上,研究如何将公共元素模型扩展为贝叶斯网络模型,详细介绍了拓展过程并给出了拓展框图,同时对各实体和属性进行了说明;最后,针对标准中采用的EXPRESS描述语言编辑工具少、通用性差等问题,采用XML语言对其交换文件进行描述,使得诊断信息具备更好的可移植性和互操作性。     

Lattice-valued fuzzy Turing machines: Computing power, universality and efficiency

In this paper we study fuzzy Turing machines with membership degrees in distributive lattices, which we called them lattice-valued fuzzy Turing machines. First we give several formulations of lattice-valued fuzzy Turing machines, including in particular deterministic and non-deterministic lattice-valued fuzzy Turing machines (l-DTMcs and l-NTMs). We then show that l-DTMcs and l-NTMs are not equivalent as the acceptors of fuzzy languages. This contrasts sharply with classical Turing machines. Second, we show that lattice-valued fuzzy Turing machines can recognize n-r.e. sets in the sense of Bedregal and Figueira, the super-computing power of fuzzy Turing machines is established in the lattice-setting. Third, we show that the truth-valued lattice being finite is a necessary and sufficient condition for the existence of a universal lattice-valued fuzzy Turing machine. For an infinite distributive lattice with a compact metric, we also show that a universal fuzzy Turing machine exists in an approximate sense. This means, for any prescribed accuracy, there is a universal machine that can simulate any lattice-valued fuzzy Turing machine on it with the given accuracy. Finally, we introduce the notions of lattice-valued fuzzy polynomial time-bounded computation (lP) and lattice-valued non-deterministic fuzzy polynomial time-bounded computation (lNP), and investigate their connections with P and NP. We claim that lattice-valued fuzzy Turing machines are more efficient than classical Turing machines.     

A statistical approach to crosslingual natural language tasks

The existence of huge volumes of documents written in multiple languages on Internet leads to investigate novel algorithmic approaches to deal with information of this kind. However, most crosslingual natural language processing (NLP) tasks consider a decoupled approach in which monolingual NLP techniques are applied along with an independent translation process. This two-step approach is too sensitive to translation errors, and in general to the accumulative effect of errors. To solve this problem, we propose to use a direct probabilistic crosslingual NLP system which integrates both steps, translation and the specific NLP task, into a single one. In order to perform this integrated approach to crosslingual tasks, we propose to use the statistical IBM 1 word alignment model (M1). The M1 model may show a non-monotonic behaviour when aligning words from a sentence in a source language to words from another sentence in a different, target language. This is the case of languages with different word order. In English, for instance, adjectives appear before nouns, whereas in Spanish it is exactly the opposite. The successful experimental results reported in three different tasks - text classification, information retrieval and plagiarism analysis - highlight the benefits of the statistical integrated approach proposed in this work.     

脚本语言及其应用

介绍了脚本语言的基本组成、主要特征及其与系统编程语言的互补性,给出了使用该类语言开发应用程序的基本方法． 通过分析相关实例数据获得的结论是：脚本语言编程在减少编程工作量、提高组件重用率、缩短开发周期、降低开发费用等方面较系统编程语言具有明显的优势,并具有广阔的应用前景．     

证明策略的集成研究

讨论了ＸＹＺ／ＶＥＲＩ系统的向后推理机制,具体而言是基本策略、集成策略语言、策略的结构以及在这样的策略集成环境中的向后推理过程．