Essential unifiers

A substitution δ is less general than a substitution σ if there exists λ such that δ=σλ, which induces a notion of generality in the algebra of substitutions. We propose to look at this well known concept of generality again, and to impose a new quasi ordering on substitutions as a natural result of a stronger notion of the composition of substitutions. This new generality ordering has important consequences for the theory of E-unification (unification in equational theories) and changes the basic notion of the most general unifiers, now called essential unifiers, as well as the unification hierarchy. In particular we show that for idempotent Semigroups (associativity and idempotency), also known as Bands, the set of essential unifiers always exists and is finite.     

A non-finitely based quasi-variety of De Morgan algebras

In this paper we exhibit a non-finitely based, finitely generated quasi-variety of De Morgan algebras and determine the bottom of the lattices of sub-quasi-varieties of Kleene and De Morgan algebras.Supported by Vicerrectoría Académica de la Facultad de Ciencias and by División de Investigación, Sede Bogotá of the Universidad Nacional de Colombia.Special issue of Studia Logica: Algebraic Theory of Quasivarieties Presented by M. E. Adams, K. V. Adaricheva, W. Dziobiak, and A. V. Kravchenko     

A Necessary Relation Algebra for Mereotopology

The standard model for mereotopological structures are Boolean subalgebras of the complete Boolean algebra of regular closed subsets of a nonempty connected regular T ₀ topological space with an additional "contact relation" C defined by xCy x ØA (possibly) more general class of models is provided by the Region Connection Calculus (RCC) of Randell et al. We show that the basic operations of the relational calculus on a "contact relation" generate at least 25 relations in any model of the RCC, and hence, in any standard model of mereotopology. It follows that the expressiveness of the RCC in relational logic is much greater than the original 8 RCC base relations might suggest. We also interpret these 25 relations in the the standard model of the collection of regular open sets in the two-dimensional Euclidean plane.     

Division by zero in non-involutive meadows

Meadows have been proposed as alternatives for fields with a purely equational axiomatization. At the basis of meadows lies the decision to make the multiplicative inverse operation total by imposing that the multiplicative inverse of zero is zero. Thus, the multiplicative inverse operation of a meadow is an involution. In this paper, we study ‘non-involutive meadows’, i.e. variants of meadows in which the multiplicative inverse of zero is not zero, and pay special attention to non-involutive meadows in which the multiplicative inverse of zero is one.     

数学学业不良初中生的工作记忆特点：领域普遍性还是特殊性?

研究选取上海111名(男生48名, 女生63名, 平均年龄11.97岁)初中学生(数学学业不良学生55名与数学学业优秀学生56名), 根据国家数学课程标准, 将数学划分为数与代数、空间与几何两部分, 又从空间与几何领域中选取初一数学学业知识点—— 轴对称和中心对称图形, 分析在不同内容知识领域的解答过程中所涉及的工作记忆成分。结果发现：(1)数与代数学习需要中央执行系统、视觉-空间模板、语音环路三个成分的共同作用; 空间与几何学习主要受到视觉-空间模板和中央执行系统的影响, 但不存在语音环路的影响。(2)对轴对称与中心对称图形任务的成绩影响最大的是视觉-空间模板, 其次是中央执行系统, 语音环路对该任务作用不明显。两个研究说明工作记忆在初中不同年级的各类数学学业任务中具有不同的作用, 中央执行系统和视觉-空间模板相对更具有普遍性作用, 语音环路具有特殊性作用, 并且随着年龄增高, 视觉－空间模板对数学学业任务的作用更为突显。     

含有新算符的代数运算规则学习的有效样例设计

为了探索含有新算符的代数运算规则学习的有效样例设计方式,分别采用“转换标记法”和“解释法”设计“指-对数转换”运算和对数运算的样例,考察了初中三年级学生代数运算规则样例学习的迁移效果。结果显示：(1)采用“转换标记法”设计的样例可以明显提高“指-对数转换”规则样例学习的迁移效果;(2)采用“解释法”设计的运算样例,能够明显促进“对数运算规则”的样例学习迁移效果,并与被试的基础知识有关。     

Ordered domain algebras

We give a finite axiomatisation to representable ordered domain algebras and show that finite algebras are representable on finite bases.