Improved comprehensibility and reliability of explanations via restricted halfspace discretization

Abstract. A number of two-class classification methods first discretize each attribute of two given training sets and then construct a propositional DNF formula that evaluates to True for one of the two discretized training sets and to False for the other one. The formula is not just a classification tool but constitutes a useful explanation for the differences between the two underlying populations if it can be comprehended by humans and is reliable. This paper shows that comprehensibility as well as reliability of the formulas can sometimes be improved using a discretization scheme where linear combinations of a small number of attributes are discretized

Using a cognitive architecture to examine what develops

Different theories of development propose alternative mechanisms by which development occurs. Cognitive architectures can be used to examine the influence of each proposed mechanism of development while keeping all other mechanisms constant. An ACT-R computational model that matched adult behavior in solving a 21-block pyramid puzzle was created. The model was modified in three ways that corresponded to mechanisms of development proposed by developmental theories. The results showed that all the modifications (two of capacity and one of strategy choice) could approximate the behavior of 7-year-old children on the task. The strategy-choice modification provided the closest match on the two central measures of task behavior (time taken per layer, r = .99, and construction attempts per layer, r = .73). Modifying cognitive architectures is a fruitful way to compare and test potential developmental mechanisms, and can therefore help in specifying “what develops.

The usability of description logics: understanding the cognitive difficulties presented by description logics

Description Logics have been extensively studied from the viewpoint of decidability and computational tractability. Less attention has been given to their usability and the cognitive difficulties they present, in particular for those who are not specialists in logic. This paper reports on a study into the difficulties associated with the most commonly used Description Logic features. Psychological theories are used to take account of these. Whilst most of the features presented no difficulty to participants, the comprehension of some was affected by commonly occurring misconceptions. The paper proposes explanations and remedies for some of these difficulties. In addition, the time to confirm stated inferences was found to depend both on the maximum complexity of the relations involved and the number of steps in the argument

From music to mathematics and backwards: introducing algebra, topology and category theory into computational musicology

International audienceDespite a long historical relationship between mathematics and music, the interest of mathematicians is a recent phenomenon. In contrast to statistical methods and signal-based approaches currently employed in MIR (Music Information Research), the research project described in this paper stresses the necessity of introducing a structural multidisciplinary approach into computational musicology making use of advanced mathematics. It is based on the interplay between three main mathematical disciplines: algebra, topology and category theory. It therefore opens promising perspectives on important prevailing challenges, such as the automatic classification of musical styles or the solution of open mathematical conjectures, asking for new collaborations between mathematicians, computer scientists, musicologists, and composers. Music can in fact occupy a strategic place in the development of mathematics since music-theoretical constructions can be used to solve open mathematical problems. The SMIR project also differs from traditional applications of mathematics to music in aiming to build bridges between different musical genres, ranging from contemporary art music to popular music, including rock, pop, jazz and chanson. Beyond its academic ambition, the project carries an important societal dimension stressing the cultural component of 'mathemusical' research, that naturally resonates with the underlying philosophy of the “Imagine Maths”conference series. The article describes for a general public some of the most promising interdisciplinary research lines of this project

A learning set approach to multiple classification: Evidence for a theory of cognitive levels

Eighty children aged 3 to 6 years were given learning set training in classification under one of two conditions: a one attribute condition in which the cells of the matrix could be filled by taking account of only one dimension, or a two attribute condition in which the cells of the same matrix had to be filled by considering both dimensions. All age groups learned the one attribute task, but the majority of 3-year-olds failed the two attribute condition and there was a significant interaction between age and experimental condition. The results are discussed in terms of cognitive developmental stage theory, and while it is concluded that unmodified Piagetian theory is inconsistent with the results, they can be accommodated by a reformulated theory

Can young children integrate premises in transitivity and serial order tasks?

An analysis is presented of the relational information needed for premise integration in transitivity and simple serial order tasks. The tasks are divided into those where an ordering decision can be made by considering a single binary relation, and those where two binary relations must be considered. Four experiments are reported, the principal purpose of which is to manipulate the number of relations which must be considered in making decisions about the order of a small set of elements. In every test it was found that preschool children succeeded if decisions could be made by considering one relation, but failed if two relations had to be considered. Children over 5 almost always succeeded in both cases. It is concluded that preschool children cannot integrate relational premise information, and therefore cannot understand transitivity or serial order. This would impose limitations on their understanding of quantification and a number of other concepts. It is also suggested that the amount of information required to make a single decision may be an important factor determining cognitive complexity generally

Reflections on 25 years of piagetian cognitive developmental psychology, 1963-1988

In this article some of the issues are examined that have arisen in one quarter of a century of intensive research on cognitive development from a Piagetian perspective. It is suggested that there is no evidence clearly confirming the existence of Piaget’s cognitive structures in explicit form. Consequently, neo-Piagetian theories have proliferated, in an attempt to conceptualize the increasingly powerful cognitive systems that have been observed to develop with age. Research on the object concept indicates that children have knowledge and skills that would not have been predicted by the Piagetian position, but that children progressively develop an integrated conception of space that is consistent with some of Piaget’s basic tenets. Some of the major studies purportedly demonstrating understanding of concrete operational concepts by 3- and 4-year-olds are shown to be based on false positives. There is rigorous evidence of hypothesis testing in middle childhood, but this performance does not necessarily entail formal operations as defined by Inhelder and Piaget. It is concluded that Piaget’s empirical work has held up better than is often thought but that his conceptualization of cognitive development is inadequate. Consequently, it is suggested, empirical researchers should devote more attention to testing alternative theories