Propositional and situational representations of text

Two informationally equivalent texts were constructed which described a fictitious town, emphasizing its spatial layout. In one version (Survey text), spatial information was in geographic terms, while in the other version (Route text), the equivalent information was provided in the form of directions for driving through the town. Subjects recalled these texts and verified old as well as inference statements. In Experiment I, subjects were able to recall the texts quite well, while showing little ability to use the information they had acquired to make inferences about spatial relations in the town which had not been directly stated in the text. With simpler texts, subjects in Experiment II were able to make infereces, especially when the form of the question corresponded to the version of the text they had read. It was concluded that free recall depended on the construction of a propositional textbase during comprehension, while inferences required a situation model, either in the form of a mental map or a procedural representation of the town. It could be shown that the form of the situation model depended on both the representation invited by the text and subject biases.

Sensory and conceptual representations in memory: Motor images which cannot be imaged

The paper argues for a distinction between sensory-and conceptual-information storage in the human information-processing system. Conceptual information is characterized as meaningful and symbolic, while sensory information may exist in modality-bound form. Furthermore, it is assumed that sensory information does not contribute to conscious remembering and can be used only in data-driven process reptitions, which can be accompanied by a kind of vague or intuitive feeling. Accordingly, pure top-down and willingly controlled processing, such as free recall, should not have any access to sensory data. Empirical results from different research areas and from two experiments conducted by the authors are presented in this article to support these theoretical distinctions. The experiments were designed to separate a sensory-motor and a conceptual component in memory for two-digit numbers and two-letter items, when parts of the numbers or items were imaged or drawn on a tablet. The results of free recall and recognition are discussed in a theoretical framework which distinguishes sensory and conceptual information in memory.

Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality

We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.

Development of meta-representations: Procedural metacognition and the relationship to Theory of Mind

In several studies it was shown that metacognitive ability is crucial for children and their success in school. Much less is known about the emergence of that ability and its relationship to other meta-representations like Theory of Mind competencies. In the past years, a growing literature has suggested that metacognition and Theory of Mind could theoretically be assumed to belong to the same developmental concept. Since then only a few studies showed empirically evidence that metacognition and Theory of Mind are related. But these studies focused on declarative metacognitive knowledge rather than on procedural metacognitive monitoring like in the present study: N = 159 children were first tested shortly before making the transition to school (aged between 5 1/2 and 7 1/2 years) and one year later at the end of their first grade. Analyses suggest that there is in fact a significant relation between early metacognitive monitoring skills (procedural metacognition) and later Theory of Mind competencies. Notably, language seems to play a crucial role in this relationship. Thus our results bring new insights in the research field of the development of meta-representation and support the view that metacognition and Theory of Mind are indeed interrelated, but the precise mechanisms yet remain unclear.

Explicit description of generic representations for quivers of type An or Dn

We describe explicitly a generic representation for Dynkin quivers of type An or Dn for any dimension vector.

A Mathematical Model for Simplifying Representations of Objects in a Geographic Information System

The study of operations on representations of objects is well documented in the realm of spatial engineering. However, the mathematical structure and formal proof of these operational phenomena are not thoroughly explored. Other works have often focused on query-based models that seek to order classes and instances of objects in the form of semantic hierarchies or graphs. In some models, nodes of graphs represent objects and are connected by edges that represent different types of coarsening operators. This work, however, studies how the coarsening operator "simplification" can manipulate partitions of finite sets, independent from objects and their attributes. Partitions that are "simplified first have a collection of elements filtered (removed), and then the remaining partition is amalgamated (some sub-collections are unified). Simplification has many interesting mathematical properties. A finite composition of simplifications can also be accomplished with some single simplification. Also, if one partition is a simplification of the other, the simplified partition is defined to be less than the other partition according to the simp relation. This relation is shown to be a partial-order relation based on simplification. Collections of partitions can not only be proven to have a partial- order structure, but also have a lattice structure and are complete. In regard to a geographic information system (GIs), partitions related to subsets of attribute domains for objects are called views. Objects belong to different views based whether or not their attribute values lie in the underlying view domain. Given a particular view, objects with their attribute n-tuple codings contained in the view are part of the actualization set on views, and objects are labeled according to the particular subset of the view in which their coding lies. Though the scope of the work does not mainly focus on queries related directly to geographic objects, it provides verification for the existence of particular views in a system with this underlying structure. Given a finite attribute domain, one can say with mathematical certainty that different views of objects are partially ordered by simplification, and every collection of views has a greatest lower bound and least upper bound, which provides the validity for exploring queries in this regard.

Emerging Identities in Colonial Tunisia: "Alliancist" and Zionist Representations in Tunis prior to World War I

By 1900 the Jewish community of Tunisia witnessed the emergence of new competing identities: “assimilationist” of the Alliance Israelite Universelle, termed “Alliancist,” and Zionist. Strikingly, two members of the same family in Tunis, Raymond Valensi, President of the AIU Regional Committee, and Alfred Valensi, President of the Zionist Federation, led the struggle for their separate causes. In his discussion of identity in the modern world, Homi Bhabha asks, "How do strategies of representation or empowerment come to be formulated in the competing claims of communities…where, despite shared histories of …discrimination, the exchange of values, meanings and priorities…may be profoundly antagonistic…?" It is in this context that the claims of the Alliance and Zionism will be examined prior to World War I, based on the Archives of the AIU and on such secondary sources as the indispensable work of Paul Sebag. The tensions between the Alliancists and Zionists continued until the outbreak of World War II, as the French-speaking Jews of Tunisia sought to define their individual and collective identities.