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.     

Nonparametric polytomous IRT models for invariant item ordering, with results for parametric models

It is often considered desirable to have the same ordering of the items by difficulty across different levels of the trait or ability. Such an ordering is an invariant item ordering (IIO). An IIO facilitates the interpretation of test results. For dichotomously scored items, earlier research surveyed the theory and methods of an invariant ordering in a nonparametric IRT context. Here the focus is on polytomously scored items, and both nonparametric and parametric IRT models are considered.The absence of the IIO property in twononparametric polytomous IRT models is discussed, and two nonparametric models are discussed that imply an IIO. A method is proposed that can be used to investigate whether empirical data imply an IIO. Furthermore, only twoparametric polytomous IRT models are found to imply an IIO. These are the rating scale model (Andrich, 1978) and a restricted rating scale version of the graded response model (Muraki, 1990). Well-known models, such as the partial credit model (Masters, 1982) and the graded response model (Samejima, 1969), do no imply an IIO.     

Grading distractor-identification tests

On distractor-identification tests students mark as many distractors as possible on each test item. A grading scale is developed for this type testing. The scale is optimal in that it is the unique scale giving an unbiased estimate of the student's true score, i.e., the score that would result if no guessing occurred. If the test is administered as a usual multiple choice test and graded using the usual correction for guessing scale, the expected item score is the same as for the distractor-identification testing using the optimal grading scale. However, the variance of the item score is shown to be less for distractor-identification testing than for usual multiple choice testing under certain conditions.     

A Set Theory with Support for Partial Functions

Partial functions can be easily represented in set theory as certain sets of ordered pairs. However, classical set theory provides no special machinery for reasoning about partial functions. For instance, there is no direct way of handling the application of a function to an argument outside its domain as in partial logic. There is also no utilization of lambda-notation and sorts or types as in type theory. This paper introduces a version of von-Neumann-Bernays-Gödel set theory for reasoning about sets, proper classes, and partial functions represented as classes of ordered pairs. The underlying logic of the system is a partial first-order logic, so class-valued terms may be nondenoting. Functions can be specified using lambda-notation, and reasoning about the application of functions to arguments is facilitated using sorts similar to those employed in the logic of the IMPS Interactive Mathematical Proof System. The set theory is intended to serve as a foundation for mechanized mathematics systems.     

The use of partial information on weights in multicriteria decision problems

This paper addresses multicriteria decision problems in which only partial information is given in the decision-making process. We generalize existing results about preference relations induced by nonnegative inverse matrices, allowing linear relations on weights with upper and lower bounds. In addition we develop conditions for additional information that preserve the special properties studied and show how to incorporate the new information to the model. © 1998 John Wiley & Sons, Ltd.     

Priorean Strict Implication, Q and Related Systems

We introduce a system PSI for a strict implication operator called Priorean strict implication. The semantics for PSI is based on partial Kripke models without accessibility relations. PSI is proved sound and complete with respect to that semantics, and Prior's system Q and related systems are shown to be fragments of PSI or of a mild extension of it.     

Temporal Interaction of Information and Belief

The temporal updating of an agent’s beliefs in response to a flow of information is modeled in a simple modal logic that, for every date t, contains a normal belief operator B _t and a non-normal information operator I _t which is analogous to the ‘only knowing’ operator discussed in the computer science literature. Soundness and completeness of the logic are proved and the relationship between the proposed logic, the AGM theory of belief revision and the notion of plausibility is discussed. A first draft of this paper was presented at the Workshop on Belief Change in Rational Agents: Perspectives from Artificial Intelligence, Philosophy and Economics, Dagstuhl (Germany), August 2005. Special Issue Formal Epistemology II. Edited by Branden Fitelson     

声旁部分信息在儿童学习和记忆汉字中的作用

采用类似课堂教学的学习－测验任务,通过3个实验探讨了声旁提供的部分读音信息在儿童学习和记忆汉字中的作用。被试来自北京市两所小学260名四年级学生。实验中要求学生学习和记忆3种生字：（1）声旁提供汉字读音的全部信息,如规则一致字;（2）声旁提供汉字读音的部分信息,如声调不同字或声母不同字;（3）声旁不提供汉字读音的信息,如声旁不知字。要求学生学习所有的字一遍后回忆生字的读音,共学习3遍。实验发现,儿童学习和记忆汉字的正确率随声旁提供的整字读音信息不同而不同：当声旁提供全部信息时正确率最高,当声旁提供部分信息时其次,当声旁没有提供信息时最低;而且声旁提供的部分信息越多,正确率越高。结果表明,儿童对声旁提供的部分读音信息敏感,发展声旁意识对学习和记忆汉字有积极作用     

Principles for The Law of Peoples

In The Law of Peoples John Rawls gives a list of eight principles for the law of peoples. I argue that the force of the principles depends in large part upon their being lexically ordered, and I attempt such an ordering. However, the lexically ordered list makes it clear that the duty of non-intervention obtains only after the duty to honor human rights is satisfied. Also, I point to certain “practical” difficulties with intervention on behalf of human rights. Rawls writes that additional principles are needed, and I make two suggestions. I conclude that the problems arising from intervention and the need for additional principles show that the “second Original Position” is like the first Original Position: both involve, Rawls notwithstanding, the selection and ordering of principles of justice.