Admissibility in Finitely Generated Quasivarieties

Checking the admissibility of quasiequations in a finitely generated (i.e., generated by a finite set of finite algebras) quasivariety Q amounts to checking validity in a suitable finite free algebra of the quasivariety, and is therefore decidable. However, since free algebras may be large even for small sets of small algebras and very few generators, this naive method for checking admissibility in \Q is not computationally feasible. In this paper, algorithms are introduced that generate a minimal (with respect to a multiset well-ordering on their cardinalities) finite set of algebras such that the validity of a quasiequation in this set corresponds to admissibility of the quasiequation in Q. In particular, structural completeness (validity and admissibility coincide) and almost structural completeness (validity and admissibility coincide for quasiequations with unifiable premises) can be checked. The algorithms are illustrated with a selection of well-known finitely generated quasivarieties, and adapted to handle also admissibility of rules in finite-valued logics

Admissibility in De Morgan algebras

Characterizations of admissible quasi-identities, which may be understood as quasi-identities holding in free algebras on countably infinitely many generators, are provided for classes of De Morgan algebras and lattice

Holocene dynamics of the Southern Hemisphere westerly winds and possible links to CO2 outgassing

The Southern Hemisphere westerly winds (SHW) play an important role in regulating the capacity of the Southern Ocean carbon sink. They modulate upwelling of carbon-rich deep water and, with sea ice, determine the ocean surface area available for air–sea gas exchange. Some models indicate that the current strengthening and poleward shift of these winds will weaken the carbon sink. If correct, centennial- to millennial-scale reconstructions of the SHW intensity should be linked with past changes in atmospheric CO2, temperature and sea ice. Here we present a 12,300-year reconstruction of wind strength based on three independent proxies that track inputs of sea-salt aerosols and minerogenic particles accumulating in lake sediments on sub-Antarctic Macquarie Island. Between about 12.1 thousand years ago (ka) and 11.2 ka, and since about 7 ka, the wind intensities were above their long-term mean and corresponded with increasing atmospheric CO2. Conversely, from about 11.2 to 7.2 ka, the wind intensities were below their long-term mean and corresponded with decreasing atmospheric CO2. These observations are consistent with model inferences of enhanced SHW contributing to the long-term outgassing of CO2 from the Southern Ocean

Matthew effect in vocabulary and reading: A comparison of good and average readers in Grade 1 to Grade 3

There is quite a large body of research about the influence that vocabulary plays in poor comprehenders reading. Yet, little is known about the role of vocabulary in good comprehenders’ reading skills. In the present study, third graders with a one-year advantage in reading comprehension (N = 105) were compared to average comprehenders (N = 177) in terms of vocabulary knowledge at three timepoints (Grade 1 to 3). Vocabulary was operationalized as vocabulary breadth (receptive and expressive) and vocabulary depth in form of semantic word knowledge. Latent growth models showed a superiority of good over average comprehenders both cross-sectionally and longitudinally in all assessed vocabulary skills. Moreover, the impact of vocabulary skills on sentence and text reading increased significantly from Grade 1 to Grade 3 in both groups. These results substantiate the increasing importance of vocabulary skills on reading comprehension yielding a Matthew effect