Pointwise intersection in neighbourhood modal logic

We study the logic of neighbourhood models with pointwise intersection, as a means to characterize multi-modal logics. Pointwise intersection takes us from a set of neighbourhood sets $\mathcal{N}_i$ (one for each member $i$ of a set $G$, used to interpret the modality $\square_i$) to a new neighbourhood set $\mathcal{N}_G$, which in turn allows us to interpret the operator $\square_G$. Here, $X$ is in the neighbourhood for $G$ if and only if $X$ equals the intersection of some $\mathcal{Y} = \{Y_i \mid i\in G\}$. We show that the notion of pointwise intersection has various applications in epistemic and doxastic logic, deontic logic, coalition logic, and evidence logic. We then establish sound and strongly complete axiomatizations for the weakest logic characterized by pointwise intersection and for a number of variants, using a new and generally applicable technique for canonical model construction.Comment: Submitted to Advances in Modal Logic 201

Analytical expressions and numerical evaluation of the luminosity distance in a flat cosmology

Accurate and efficient methods to evaluate cosmological distances are an important tool in modern precision cosmology. In a flat $\Lambda$CDM cosmology, the luminosity distance can be expressed in terms of elliptic integrals. We derive an alternative and simple expression for the luminosity distance in a flat $\Lambda$CDM based on hypergeometric functions. Using a timing experiment we compare the computation time for the numerical evaluation of the various exact formulae, as well as for two approximate fitting formulae available in the literature. We find that our novel expression is the most efficient exact expression in the redshift range $z\gtrsim1$. Ideally, it can be combined with the expression based on Carlson's elliptic integrals in the range $z\lesssim1$ for high precision cosmology distance calculations over the entire redshift range. On the other hand, for practical work where relative errors of about 0.1% are acceptable, the analytical approximation proposed by Adachi & Kasai (2012) is a suitable alternative.Comment: 4 pages, 1 figure, accepted for publication in MNRA

Adaptive logic characterizations of input/output logic

We translate unconstrained and constrained input/output logics as introduced by Makinson and van der Torre to modal logics, using adaptive logics for the constrained case. The resulting reformulation has some additional benefits. First, we obtain a proof-theoretic (dynamic) characterization of input/output logics. Second, we demonstrate that our framework naturally gives rise to useful variants and allows to express important notions that go beyond the expressive means of input/output logics, such as violations and sanctions

Educational heterogamy and the division of paid labour in the family: a comparison of present-day Belgium and Sweden

Building on the growing importance of partner effects in stratification research, this study adopts a couple perspective on the division of paid labour in the family. It considers the role of educational heterogamy, and takes account of the family life cycle by means of the presence of (young) children. The importance of these two factors for women’s relative labour market participation is compared between Belgium and Sweden – two European countries that share socio-economic features but differ regarding labour market and social policies. Multinomial logistic Diagonal Reference Models are used to analyse the pooled cross-sectional data of the EU-SILC 2004-2008. Our results show that women’s relative labour market participation is less education-driven in Sweden than in Belgium, and it is more related to the couple effect of educational heterogamy and the life cycle effect of the presence of (young) children, confirming more egalitarianism and family friendliness in Scandinavia than in continental Europe

Marrying out of the lower classes in nineteenth-century Belgium

In this article we address one of the most prominent questions in historical sociology: did economic modernization in the nineteenth century lead to societal openness? In an attempt to answer the question we examine the chances for lower-class grooms of marrying upwardly in five Belgian cities (Aalst, Leuven, Ghent, Verviers, and Liège). Our findings show that there is no support for a meritocracy hypothesis. The chances of marrying out of the lower classes did not increase, in either absolute or relative terms. Social closure strategies were efficient in that they apparently prevented upward marital mobility for lower-class grooms. As these findings were measured in a highly advanced economic context, this study casts strong doubts on the relationship between economic modernization, meritocracy, and marital mobility, at least for the nineteenth century