A Categorical Equivalence for Stonean Residuated Lattices

We follow the ideas given by Chen and Grätzer to represent Stone algebras and adapt them for the case of Stonean residuated lattices. Given a Stonean residuated lattice, we consider the triple formed by its Boolean skeleton, its algebra of dense elements and a connecting map. We define a category whose objects are these triples and suitably defined morphisms, and prove that we have a categorical equivalence between this category and that of Stonean residuated lattices. We compare our results with other works and show some applications of the equivalence.

     

Quantum Computational Structures: Categorical Equivalence for Square Root qMV -algebras

In this paper we investigate a categorical equivalence between square root qMV -algebras (a variety of algebras arising from quantum computation) and a category of preordered semigroups.     

Information Completeness in Nelson Algebras of Rough Sets Induced by Quasiorders

In this paper, we give an algebraic completeness theorem for constructive logic with strong negation in terms of finite rough set-based Nelson algebras determined by quasiorders. We show how for a quasiorder R, its rough set-based Nelson algebra can be obtained by applying Sendlewski’s well-known construction. We prove that if the set of all R-closed elements, which may be viewed as the set of completely defined objects, is cofinal, then the rough set-based Nelson algebra determined by the quasiorder R forms an effective lattice, that is, an algebraic model of the logic E ₀, which is characterised by a modal operator grasping the notion of “to be classically valid”. We present a necessary and sufficient condition under which a Nelson algebra is isomorphic to a rough set-based effective lattice determined by a quasiorder.     

On Definability of the Equality in Classes of Algebras with an Equivalence Relation

We present a finitary regularly algebraizable logic not finitely equivalential, for every similarity type. We associate to each of these logics a class of algebras with an equivalence relation, with the property that in this class, the identity is atomatically definable but not finitely atomatically definable. This revised version was published online in June 2006 with corrections to the Cover Date.     

分类数据测量等价性检验方法及其比较：项目阈值(难度)参数的组间差异性检验

测量工具满足等价性是进行多组比较的前提, 测量等价性的检验方法主要有基于CFA的多组比较法和基于IRT的DIF检验两类方法。文章比较了单维测验情境下基于CCFA的DIFFTEST检验方法和基于IRT模型的IRT-LR检验方法, 以及多维测验情境下DIFFTEST和基于MIRT的卡方检验方法的差异。通过模拟研究的方法, 比较了几种方法的检验力和第一类错误, 并考虑了样本总量、样本量的组间均衡性、测验长度、阈值差异大小以及维度间相关程度的影响。研究结果表明：(1)在单维测验下, IRT-LR是比DIFFTEST更为严格的检验方法; 多维测验下, 在测验较长、测验维度之间相关较高时, MIRT-MG比DIFFTEST更容易检验出项目阈值的差异, 而在测验长度较短、维度之间相关较小时, DIFFTEST的检验力反而略高于MIRT-MG方法。(2)随着阈值差值增加, DIFFTEST、IRT-LR和MIRT-MG三种方法的检验力均在增加, 当阈值差异达到中等或较大时, 三种方法都可以有效检验出测验阈值的不等价性。(3)随着样本总量增加, DIFFTEST、IRT-LR和MIRT-MG方法的检验力均在增加; 在总样本量不变, 两组样本均衡情况下三种方法的检验力均高于不均衡的情况。(4)违背等价性题目个数不变时, 测验越长DIFFTEST的检验力会下降, 而IRT-LR和MIRT-MG检验力则上升。(5) DIFFTEST方法的一类错误率平均值接近名义值0.05; 而IRT-LR和MIRT-MG方法的一类错误率平均值远低于0.05。     

A Proof System for Contact Relation Algebras

Contact relations have been studied in the context of qualitative geometry and physics since the early 1920s, and have recently received attention in qualitative spatial reasoning. In this paper, we present a sound and complete proof system in the style of Rasiowa and Sikorski (1963) for relation algebras generated by a contact relation.     

A Categorical Approach to Probability Theory

First, we discuss basic probability notions from the viewpoint of category theory. Our approach is based on the following four “sine quibus non” conditions: 1. (elementary) category theory is efficient (and suffices); 2. random variables, observables, probability measures, and states are morphisms; 3. classical probability theory and fuzzy probability theory in the sense of S. Gudder and S. Bugajski are special cases of a more general model; 4. a good model allows natural modifications. Second, we show that the category ID of D-posets of fuzzy sets and sequentially continuous D-homomorphisms allows to characterize the passage from classical to fuzzy events as the minimal generalization having nontrivial quantum character: a degenerated state can be transported to a nondegenerated one. Third, we describe a general model of probability theory based on the category ID so that the classical and fuzzy probability theories become special cases and the model allows natural modifications. Finally, we present a modification in which the closed unit interval [0,1] as the domain of traditional states is replaced by a suitable simplex.     

类别指称对象提取过程的发展研究

本研究选取初中二年级、高中二年级和大学二年级学生为被试,探讨了青少年对含有类别指称对象语篇心理加工过程。实验1采用命名法,实验2采用眼动记录法。结果发现,随着年级的升高,被试在单位时间内获得的信息逐渐增多,阅读能力不断提高,对类别指称概念的理解能力也不断提高;各年级被试表现出对类别指称对象激活的增强;大学生组被试还表现出对非指称对象激活的抑制;激活是立即发生的认知过程;抑制则是延缓发生的认知过程,且是一种策略性的控制加工过程。     

X—A Defence of Categorical Reasons

In this paper I offer two arguments designed to defend the existence of categorical reasons, which I define as those justifying considerations that obtain independently of their relation to an agent's commitments. The first argument is based on certain paradigm cases meant to reveal difficulties for practical instrumentalism—the view, as I define it here, that categorical reasons do not exist, because all reasons must serve the commitments of the agents to whom they apply. The second argument relies on considerations of responsibility and blame to establish the existence of categorical reasons.     

Categorical Equivalence Between $$\varvec{PMV}_{\varvec{f}}$$ PMV f -Product Algebras and Semi-Low $$\varvec{f}_{\varvec{u}}$$ f u -Rings

Studia Logica - An explicit categorical equivalence is defined between a proper subvariety of the class of $${ PMV}$$ -algebras, as defined by Di Nola and Dvure?enskij, to be called $${...     

A Note on the Interpolation Property in Tense Logic

It is proved that all bimodal tense logics which contain the logic of the weak orderings and have unbounded depth do not have the interpolation property.     

Combinations of Tense and Modality for Predicate Logic

In recent years combinations of tense and modality have moved into the focus of logical research. From a philosophical point of view, logical systems combining tense and modality are of interest because these logics have a wide field of application in original philosophical issues, for example in the theory of causation, of action, etc. But until now only methods yielding completeness results for propositional languages have been developed. In view of philosophical applications, analogous results with respect to languages of predicate logic are desirable, and in this paper I present two such results. The main developments in this area can be split into two directions, differing in the question whether the ordering of time is world-independent or not. Semantically, this difference appears in the discussion whether T×W-frames or Kamp-frames (resp. Ockham-frames) provide a suitable semantics for combinations of tense and modality. Here, two calculi are presented, the first adequate with respect to Kamp-semantics, the second to T×W-semantics. (Both calculi contain an appropriate version of Gabbay's irreflexivity rule.) Furthermore, the proposed constructions of canonical frames simplify some of those which have hitherto been discussed.     

A Latent Block Distance-Association Model for Profile by Profile Cross-Classified Categorical Data

Abstract

Distance association models constitute a useful tool for the analysis and graphical representation of cross-classified data in which distances between points inversely describe the association between two categorical variables. When the number of cells is large and the data counts result in sparse tables, the combination of clustering and representation reduces the number of parameters to be estimated and facilitates interpretation. In this article, a latent block distance-association model is proposed to apply block clustering to the outcomes of two categorical variables while the cluster centers are represented in a low dimensional space in terms of a distance-association model. This model is particularly useful for contingency tables in which both the rows and the columns are characterized as profiles of sets of response variables. The parameters are estimated under a Poisson sampling scheme using a generalized EM algorithm. The performance of the model is tested in a Monte Carlo experiment, and an empirical data set is analyzed to illustrate the model.     

Categorical effects in visual search for colour

The role of categorization in visual search was studied in 3 colour search experiments where the target was or was not linearly separable from the distractors. The linear separability effect refers to the difficulty of searching for a target that falls between the distractors in CIE colour space (Bauer, Jolicoeur, & Cowan, 1996b Bauer, B., Jolicoeur, P. and Cowan, W. B. 1996b. Visual search for colour targets that are or are not linearly separable from distractors. Vision Research, 36: 1439–1465. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Observers performed nonlinearly separable searches where the target fell between the two types of distractors in CIE colour space. When the target and distractors fell within the same category, search was difficult. When they fell within three distinct categories, response times and search slopes were significantly reduced. The results suggest that categorical information, when available, facilitates search, reducing the linear separability effect.     

A Connectionist Model of English Past Tense and Plural Morphology

The acquisition of English noun and verb morphology is modeled using a single-system connectionist network. The network is trained to produce the plurals and past tense forms of a large corpus of monosyllabic English nouns and verbs. The developmental trajectory of network performance is analyzed in detail and is shown to mimic a number of important features of the acquisition of English noun and verb morphology in young children. These include an initial error-free period of performance on both nouns and verbs followed by a period of intermittent over-regularization of irregular nouns and verbs. Errors in the model show evidence of phonological conditioning and frequency effects. Furthermore, the network demonstrates a strong tendency to regularize denominal verbs and deverbal nouns and masters the principles of voicing assimilation. Despite their incorporation into a single-system network, nouns and verbs exhibit some important differences in their profiles of acquisition. Most importantly, noun inflections are acquired earlier than verb inflections. The simulations generate several empirical predictions that can be used to evaluate further the suitability of this type of cognitive architecture in the domain of inflectional morphology.     

A Proof-Theoretic Approach to Negative Translations in Intuitionistic Tense Logics

Studia Logica - A cut-free Gentzen sequent calculus for Ewald’s intuitionistic tense logic $$\mathsf {IK}_t$$ is established. By the proof-theoretic method, we prove that, for every set of...     

A Note on Algebras of Substitutions

We will study the class RSA of -dimensional representable substitution algebras. RSA is a sub-reduct of the class of representable cylindric: algebras, and it was an open problem in Andréka [1] that whether RSA can be finitely axiomatized. We will show, that the answer is positive. More concretely, we will prove, that RSA is a finitely axiomatizable quasi-variety. The generated variety is also described. We note that RSA is the algebraic counterpart of a certain proportional multimodal logic and it is related to a natural fragment of first order logic, as well.