Models of Cognition: Neurological possibility does not indicate neurological plausibility

Many activities in Cognitive Science involve complex computer models and simulations of both theoretical and real entities. Artificial Intelligence and the study of artificial neural nets in particular, are seen as major contributors in the quest for understanding the human mind. Computational models serve as objects of experimentation, and results from these virtual experiments are tacitly included in the framework of empirical science. Cognitive functions, like learning to speak, or discovering syntactical structures in language, have been modeled and these models are the basis for many claims about human cognitive capacities. Artificial neural nets (ANNs) have had some successes in the field of Artificial Intelligence, but the results from experiments with simple ANNs may have little value in explaining cognitive functions. The problem seems to be in relating cognitive concepts that belong in the `top-down' approach to models grounded in the `bottom-up' connectionist methodology. Merging the two fundamentally different paradigms within a single model can obfuscate what is really modeled. When the tools (simple artificial neural networks) to solve the problems (explaining aspects of higher cognitive functions) are mismatched, models with little value in terms of explaining functions of the human mind are produced. The ability to learn functions from data-points makes ANNs very attractive analytical tools. These tools can be developed into valuable models, if the data is adequate and a meaningful interpretation of the data is possible. The problem is, that with appropriate data and labels that fit the desired level of description, almost any function can be modeled. It is my argument that small networks offer a universal framework for modeling any conceivable cognitive theory, so that neurological possibility can be demonstrated easily with relatively simple models. However, a model demonstrating the possibility of implementation of a cognitive function using a distributed methodology, does not necessarily add support to any claims or assumptions that the cognitive function in question, is neurologically plausible

On Lattices of Varieties of Restriction Semigroups

The left restriction semigroups have arisen in a number of contexts, one being as the abstract characterization of semigroups of partial maps, another as the ‘weakly left E-ample’ semigroups of the ‘York school’, and, more recently as a variety of unary semigroups defined by a set of simple identities. We initiate a study of the lattice of varieties of such semigroups and, in parallel, of their two-sided versions, the restriction semigroups. Although at the very bottom of the respective lattices the behaviour is akin to that of varieties of inverse semigroups, more interesting features are soon found in the minimal varieties that do not consist of semilattices of monoids, associated with certain ‘forbidden’ semigroups. There are two such in the one-sided case, three in the two-sided case. Also of interest in the one-sided case are the varieties consisting of unions of monoids, far indeed from any analogue for inverse semigroups. In a sequel, the author will show, in the two-sided case, that some rather surprising behavior is observed at the next ‘level’ of the lattice of varieties

On Semigroups with Lower Semimodular Lattice of Subsemigroups

The question of which semigroups have lower semimodular lattice of subsemigroups has been open since the early 1960s, when the corresponding question was answered for modularity and for upper semimodularity. We provide a characterization of such semigroups in the language of principal factors. Since it is easily seen (and has long been known) that semigroups for which Green\u27s relation J is trivial have this property, a description in such terms is natural. In the case of periodic semigroups—a case that turns out to include all eventually regular semigroups—the characterization becomes quite explicit and yields interesting consequences. In the general case, it remains an open question whether there exists a simple, but not completely simple, semigroup with this property. Any such semigroup must at least be idempotent-free and D-trivial

Benchmarking citation measures among the Australian education professoriate

Individual researchers and the organisations for which they work are interested in comparative measures of research performance for a variety of purposes. Such comparisons are facilitated by quantifiable measures that are easily obtained and offer convenience and a sense of objectivity. One popular measure is the Journal Impact Factor based on citation rates but it is a measure intended for journals rather than individuals. Moreover, educational research publications are not well represented in the databases most widely used for calculation of citation measures leading to doubts about the usefulness of such measures in education. Newer measures and data sources offer alternatives that provide wider representation of education research. However, research has shown that citation rates vary according to discipline and valid comparisons depend upon the availability of discipline specific benchmarks. This study sought to provide such benchmarks for Australian educational researchers based on analysis of citation measures obtained for the Australian education professoriate

[Review] Jay M. Smith, ed. (2006) The French nobility in the eighteenth century: reassessments and new approaches

A 6,000 word review article discussing this book and recent approaches to the nobility in eighteenth-century France