Boolean Dependence Logic and Partially-Ordered Connectives

We introduce a new variant of dependence logic called Boolean dependence logic. In Boolean dependence logic dependence atoms are of the type =(x_1,...,x_n,\alpha), where \alpha is a Boolean variable. Intuitively, with Boolean dependence atoms one can express quantification of relations, while standard dependence atoms express quantification over functions. We compare the expressive power of Boolean dependence logic to dependence logic and first-order logic enriched by partially-ordered connectives. We show that the expressive power of Boolean dependence logic and dependence logic coincide. We define natural syntactic fragments of Boolean dependence logic and show that they coincide with the corresponding fragments of first-order logic enriched by partially-ordered connectives with respect to expressive power. We then show that the fragments form a strict hierarchy.Comment: 41 page

A Fragment of Dependence Logic Capturing Polynomial Time

In this paper we study the expressive power of Horn-formulae in dependence logic and show that they can express NP-complete problems. Therefore we define an even smaller fragment D-Horn* and show that over finite successor structures it captures the complexity class P of all sets decidable in polynomial time. Furthermore we study the question which of our results can ge generalized to the case of open formulae of D-Horn* and so-called downwards monotone polynomial time properties of teams

Earth tectonics as seen by GOCE - Enhanced satellite gravity gradient imaging

Curvature components derived from satellite gravity gradients provide new global views of Earth’s structure. The satellite gravity gradients are based on the GOCE satellite mission and we illustrate by curvature images how the Earth is seen differently compared to seismic imaging. Tectonic domains with similar seismic characteristic can exhibit distinct differences in satellite gravity gradients maps, which points to differences in the lithospheric build-up. This is particularly apparent for the cratonic regions of the Earth. The comparisons demonstrate that the combination of seismological, and satellite gravity gradient imaging has significant potential to enhance our knowledge of Earth’s structure. In remote frontiers like the Antarctic continent, where even basic knowledge of lithospheric scale features remains incomplete, the curvature images help unveil the heterogeneity in lithospheric structure, e.g. between the composite East Antarctic Craton and the West Antarctic Rift System

Dependence logic with a majority quantifier ∗

We study the extension of dependence logic D by a majority quantifier M over finite structures. We show that the resulting logic is equi-expressive with the extension of second-order logic by second-order majority quantifiers of all arities. Our results imply that, from the point of view of descriptive complexity theory, D(M) captures the complexity class counting hierarchy