Products of modal logics and tensor products of modal algebras

One of natural combinations of Kripke complete modal logics is the product, an operation that has been extensively investigated over the last 15 years. In this paper we consider its analogue for arbitrary modal logics: to this end, we use product-like constructions on general frames and modal algebras. This operation was first introduced by Y. Hasimoto in 2000; however, his paper remained unnoticed until recently. In the present paper we quote some important Hasimoto's results, and reconstruct the product operation in an algebraic setting: the Boolean part of the resulting modal algebra is exactly the tensor product of original algebras (regarded as Boolean rings). Also, we propose a filtration technique for Kripke models based on tensor products and obtain some decidability results.     

Fuzzy Identities for an Inclusive Anglohispanic Dialogue

When constructed in linear terms, cultures and identities misrepresent other people, constructing crisp boundaries that separate groups as if completely different. To demonstrate the negative impact of such views, I analyze cultural texts such as songs, films, and Web pages, showing the intercultural complexity existing in different constructions of Mexicanness as part of the dialogue arising in the political, social, and cultural interaction between Mexico and the United States. I emphasize the contrast between examples that reinforce identities that can be interpreted as fuzzy and inclusive, against those promoting and generating discrimination and exclusion.     

Global problems,globalization, and predictability

The term globalization is questioned in its validity and applicability to structures other than verbal. Globalization is a historical term which changes its meaning with time and culture. It is not only that its content changes but the validity of a globalization concept changes with the historical perspective. Morever, solution of global problems depends heavily on the correct analysis of the problem. Without such an analysis there is no possibility to find even an approximate solution. Hence, predictability is impossible. There is no trend which is sufficiently long to make any reliable prediction for global problems other than the most simple ones.     

A Note on Prototypes,Convexity and Fuzzy Sets

The work on prototypes in ontologies pioneered by Rosch [10] and elaborated by Lakoff [8] and Freund [3] is related to vagueness in the sense that the more remote an instance is from a prototype the fewer people agree that it is an example of that prototype. An intuitive example is the prototypical “mother”, and it is observed that more specific instances like ”single mother”, “adoptive mother”, “surrogate mother”, etc., are less and less likely to be classified as “mothers” by experimental subjects. From a different direction Gärdenfors [4] provided a persuasive account of natural predicates to resolve paradoxes of induction like Goodman’s “Grue” predicate [5]. Gärdenfors proposed that “quality dimensions” arising from human cognition and perception impose topologies on concepts such that the ones that appear “natural” to us are convex in these topologies. We show that these two cognitive principles — prototypes and predicate convexity — are equivalent to unimodal (convex) fuzzy characteristic functions for sets. Then we examine the case when the fuzzy set characteristic function is not convex, in particular when it is multi-modal. We argue that this is an indication that the fuzzy concept should really be regarded as a super concept in which the decomposed components are subconcepts in an ontological taxonomy.     

A Model of Tolerance

According to the naive theory of vagueness, the vagueness of an expression consists in the existence of both positive and negative cases of application of the expression and in the non-existence of a sharp cut-off point between them. The sorites paradox shows the naive theory to be inconsistent in most logics proposed for a vague language. The paper explores the prospects of saving the naive theory by revising the logic in a novel way, placing principled restrictions on the transitivity of the consequence relation. A lattice-theoretical framework for a whole family of (zeroth-order) “tolerant logics” is proposed and developed. Particular care is devoted to the relation between the salient features of the formal apparatus and the informal logical and semantic notions they are supposed to model. A suitable non-transitive counterpart to classical logic is defined. Some of its properties are studied, and it is eventually shown how an appropriate regimentation of the naive theory of vagueness is consistent in such a logic.     

刻板印象的自动激活实验研究

本研究应用模糊主次评判方法配合语义启动技术进行实验。结果表明;在年龄刻板印象上存在自动激活,而且没有性别差异;用不同性质的启动词来激活与年龄有关的刻板印象,激活后的刻板印象对年龄的判断有不同的影响,而且被试没有一个人意识到这点,表明内隐刻板印象的存在;人的判断具有模糊性,模糊主次评判方法有助于社会认知领域的量化研究,这是一个全新的尝试。     

Algebraic Aspects of Cut Elimination

We will give here a purely algebraic proof of the cut elimination theorem for various sequent systems. Our basic idea is to introduce mathematical structures, called Gentzen structures, for a given sequent system without cut, and then to show the completeness of the sequent system without cut with respect to the class of algebras for the sequent system with cut, by using the quasi-completion of these Gentzen structures. It is shown that the quasi-completion is a generalization of the MacNeille completion. Moreover, the finite model property is obtained for many cases, by modifying our completeness proof. This is an algebraic presentation of the proof of the finite model property discussed by Lafont [12] and Okada-Terui [17].     

模糊分组的时间层次网络结构研究

本研究通过两个实验来对连续性的时间顺序标码的层次网络结构的性质进行了探讨。研究结果表明,连续性的时间顺序标码是按照层次网络的结构组织起来的,若干项目组成一个小组,若干小组组成更大的组。连续性的时间标码层次网络的形成具有自动性、内隐性的特点。连续性的时间顺序标码的层次网络结构是主观的、模糊的。两个相邻的小组的项目之间出现了距离效应,而两个相邻的大组的项目之间则出现了越界效应,由于两个大组的项目的平均距离大于两个小组的项目的平均距离,越界效应大于距离效应。