Decidability of the Clark's Completion Semantics for Monadic Programs and Queries

There are many different semantics for general logic programs (i.e. programs that use negation in the bodies of clauses). Most of these semantics are Turing complete (in a sense that can be made precise), implying that they are undecidable. To obtain decidability one needs to put additional restrictions on programs and queries. In logic programming it is natural to put restrictions on the underlying first-order language. In this note we show the decidability of the Clark's completion semantics for monadic general programs and queries. To appear in Theory and Practice of Logic Programming (TPLP

Searching for primordial magnetism with multi-frequency CMB experiments

Bounds on the amplitude of a scale-invariant stochastic primordial magnetic field (PMF) can be significantly improved by measurements of the Faraday Rotation (FR) of CMB polarization. The mode-coupling correlations induced by FR make it possible to extract it from cross-correlations of the B-mode polarization with the E-mode and the temperature anisotropy. In this paper, we construct an estimator of the rotation measure that appropriately combines measurements of the FR from multiple frequency channels. We study the dependence of the signal-to-noise in the PMF detection on the resolution and the noise of the detectors, as well as the removal of the weak lensing contribution and the galactic FR. We show that a recently proposed space-based experiment PRISM can detect magnetic fields of 0.1 nano-Gauss strength at a 2 sigma level. Higher detection levels can be achieved by reducing the detector noise and improving the resolution or increasing the number of channels in the 30-70 GHz frequency range.Comment: 6 pages, 1 figure, 1 table; references added, Figure and the caption improved; matches the version accepted to MNRA

Categoricity in Quasiminimal Pregeometry Classes

Quasiminimal pregeometry classes were introduces by Zilber [2005a] to isolate the model theoretical core of several interesting examples. He proves that a quasiminimal pregeometry class satisfying an additional axiom, called excellence, is categorical in all uncountable cardinalities. Recently Bays et al. [2014] showed that excellence follows from the rest of axioms. In this paper we present a direct proof of the categoricity result without using excellence