The link between logic, mathematics and imagination: evidence from children with developmental dyscalculia and mathematically gifted children

This study examined performance on transitive inference problems in children with developmental dyscalculia (DD), typically developing controls matched on IQ, working memory and reading skills, and in children with outstanding mathematical abilities. Whereas mainstream approaches currently consider DD as a domain-specific deficit, we hypothesized that the development of mathematical skills is closely related to the development of logical abilities, a domain-general skill. In particular, we expected a close link between mathematical skills and the ability to reason independently of one's beliefs. Our results showed that this was indeed the case, with children with DD performing more poorly than controls, and high maths ability children showing outstanding skills in logical reasoning about belief-laden problems. Nevertheless, all groups performed poorly on structurally equivalent problems with belief-neutral content. This is in line with suggestions that abstract reasoning skills (i.e. the ability to reason about content without real-life referents) develops later than the ability to reason about belief-inconsistent fantasy content.A video abstract of this article can be viewed at http://www.youtube.com/watch?v=90DWY3O4xx8.

Merging Knowledge Bases in Possibilistic Logic by Lexicographic Aggregation

Belief merging is an important but difficult problem in Artificial Intelligence, especially when sources of information are pervaded with uncertainty. Many merging operators have been proposed to deal with this problem in possibilistic logic, a weighted logic which is powerful for handling inconsistency and deal-ing with uncertainty. They often result in a possibilistic knowledge base which is a set of weighted formulas. Although possibilistic logic is inconsistency tolerant, it suffers from the well-known "drowning effect". Therefore, we may still want to obtain a consistent possibilistic knowledge base as the result of merging. In such a case, we argue that it is not always necessary to keep weighted information after merging. In this paper, we define a merging operator that maps a set of possibilistic knowledge bases and a formula representing the integrity constraints to a classical knowledge base by using lexicographic ordering. We show that it satisfies nine postulates that generalize basic postulates for propositional merging given in [11]. These postulates capture the principle of minimal change in some sense. We then provide an algorithm for generating the resulting knowledge base of our merging operator. Finally, we discuss the compatibility of our merging operator with propositional merging and establish the advantage of our merging operator over existing semantic merging operators in the propositional case.

Early Medieval Ireland, AD 400-1100: The evidence from archaeological excavations

Overview and synthesis of early medieval Irish excavations between 1930 and the present.

Mapping Medieval Geographies: Geographical Encounters in the Latin West and Beyond, 300–1600

'Mapping Medieval Geographies' explores the ways in which geographical knowledge, ideas and traditions were formed in Europe during the Middle Ages. Leading scholars reveal the connections between Islamic, Christian, Biblical, and Classical geographical traditions from Antiquity to the later Middle Ages and Renaissance. The book is divided into two parts: Part I focuses on the notion of geographical tradition and charts the evolution of celestial and earthly geography in terms of its intellectual, visual and textual representations; whilst Part II explores geographical imaginations; that is to say, those 'imagined geographies' that came into being as a result of everyday spatial and spiritual experience. Bringing together approaches from art, literary studies, intellectual history and historical geography, this pioneering volume will be essential reading for scholars concerned with visual and textual modes of geographical representation and transmission, as well as the spaces and places of knowledge creation and consumption.