Hybrid Rules with Well-Founded Semantics

A general framework is proposed for integration of rules and external first order theories. It is based on the well-founded semantics of normal logic programs and inspired by ideas of Constraint Logic Programming (CLP) and constructive negation for logic programs. Hybrid rules are normal clauses extended with constraints in the bodies; constraints are certain formulae in the language of the external theory. A hybrid program is a pair of a set of hybrid rules and an external theory. Instances of the framework are obtained by specifying the class of external theories, and the class of constraints. An example instance is integration of (non-disjunctive) Datalog with ontologies formalized as description logics. The paper defines a declarative semantics of hybrid programs and a goal-driven formal operational semantics. The latter can be seen as a generalization of SLS-resolution. It provides a basis for hybrid implementations combining Prolog with constraint solvers. Soundness of the operational semantics is proven. Sufficient conditions for decidability of the declarative semantics, and for completeness of the operational semantics are given

Using global analysis, partial specifications, and an extensible assertion language for program validation and debugging

We discuss a framework for the application of abstract interpretation as an aid during program development, rather than in the more traditional application of program optimization. Program validation and detection of errors is first performed statically by comparing (partial) specifications written in terms of assertions against information obtained from (global) static analysis of the program. The results of this process are expressed in the user assertion language. Assertions (or parts of assertions) which cannot be checked statically are translated into run-time tests. The framework allows the use of assertions to be optional. It also allows using very general properties in assertions, beyond the predefined set understandable by the static analyzer and including properties defined by user programs. We also report briefly on an implementation of the framework. The resulting tool generates and checks assertions for Prolog, CLP(R), and CHIP/CLP(fd) programs, and integrates compile-time and run-time checking in a uniform way. The tool allows using properties such as types, modes, non-failure, determinacy, and computational cost, and can treat modules separately, performing incremental analysis

Low frequency radio properties of the z > 5 quasar population

Optically luminous quasars at $z > 5$ are important probes of super-massive black hole (SMBH) formation. With new and future radio facilities, the discovery of the brightest low-frequency radio sources in this epoch would be an important new probe of cosmic reionization through 21-cm absorption experiments. In this work, we systematically study the low-frequency radio properties of a sample of 115 known spectroscopically confirmed $z>5$ quasars using the second data release of the Low Frequency Array (LOFAR) Two Metre Sky survey (LoTSS-DR2), reaching noise levels of $\sim$80 $\mu$Jy beam$^{-1}$ (at 144 MHz) over an area of $\sim5720$ deg$^2$. We find that 41 sources (36%) are detected in LoTSS-DR2 at $>2 \sigma$ significance and we explore the evolution of their radio properties (power, spectral index, and radio loudness) as a function of redshift and rest-frame ultra-violet properties. We obtain a median spectral index of $-0.29^{+0.10}_{-0.09}$ by stacking 93 quasars using LoTSS-DR2 and Faint Images of the Radio Sky at Twenty Centimetres (FIRST) data at 1.4 GHz, in line with observations of quasars at $z<3$. We compare the radio loudness of the high-$z$ quasar sample to a lower-$z$ quasar sample at $z\sim2$ and find that the two radio loudness distributions are consistent with no evolution, although the low number of high-z quasars means that we cannot rule out weak evolution. Furthermore, we make a first order empirical estimate of the $z=6$ quasar radio luminosity function, which is used to derive the expected number of high-$z$ sources that will be detected in the completed LoTSS survey. This work highlights the fact that new deep radio observations can be a valuable tool in selecting high-$z$ quasar candidates for follow-up spectroscopic observations by decreasing contamination of stellar dwarfs and reducing possible selection biases introduced by strict colour cuts.Comment: 11 pages, 10 figures, accepted for publication in A&

The Faraday Rotation Measure Grid of the LOFAR Two-metre Sky Survey: Data Release 2

© 2022 The Author(s) Published by Oxford University Press on behalf of Royal Astronomical Society. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1093/mnras/stac3820A Faraday rotation measure (RM) catalogue, or RM Grid, is a valuable resource for the study of cosmic magnetism. Using the second data release (DR2) from the LOFAR Two-metre Sky Survey (LoTSS), we have produced a catalogue of 2461 extragalactic high-precision RM values across 5720 deg$^{2}$ of sky (corresponding to a polarized source areal number density of $\sim$0.43 deg$^{-2}$). The linear polarization and RM properties were derived using RM synthesis from the Stokes $Q$ and $U$ channel images at an angular resolution of 20'' across a frequency range of 120 to 168 MHz with a channel bandwidth of 97.6 kHz. The fraction of total intensity sources ($>1$ mJy beam$^{-1}$) found to be polarized was $\sim$0.2%. The median detection threshold was 0.6 mJy beam$^{-1}$ ($8\sigma_{QU}$), with a median RM uncertainty of 0.06 rad m$^{-2}$ (although a systematic uncertainty of up to 0.3 rad m$^{-2}$ is possible, after the ionosphere RM correction). The median degree of polarization of the detected sources is 1.8%, with a range of 0.05% to 31%. Comparisons with cm-wavelength RMs indicate minimal amounts of Faraday complexity in the LoTSS detections, making them ideal sources for RM Grid studies. Host galaxy identifications were obtained for 88% of the sources, along with redshifts for 79% (both photometric and spectroscopic), with the median redshift being 0.6. The focus of the current catalogue was on reliability rather than completeness, and we expect future versions of the LoTSS RM Grid to have a higher areal number density. In addition, 25 pulsars were identified, mainly through their high degrees of linear polarization.Peer reviewe

The Beautiful Mess in Abell 2255

We present LOFAR observations of one of the most spectacular objects in the radio sky: Abell 2255. This is a nearby (z = 0.0806) merging galaxy cluster hosting one of the first radio halos ever detected in the intracluster medium (ICM). The deep LOFAR images at 144 MHz of the central ∼10 Mpc2 region show a plethora of emission on different scales, from tens of kiloparsecs to above megaparsec sizes. In this work, we focus on the innermost region of the cluster. Among the numerous interesting features observed, we discover remarkable bright and filamentary structures embedded in the radio halo. We incorporate archival WSRT 1.2 GHz data to study the spectral properties of the diffuse synchrotron emission and find a very complex spectral index distribution in the halo spanning a wide range of values. We combine the radio data with Chandra observations to investigate the connection between the thermal and nonthermal components by quantitatively comparing the radio and X-ray surface brightness and the spectral index of the radio emission with the thermodynamical quantities of the ICM. Despite the multitude of structures observed in the radio halo, we find that the X-ray and radio emission are overall well correlated. The fact that the steepest spectrum emission is located in the cluster center and traces regions with high entropy possibly suggests the presence of seed particles injected by radio galaxies that are spread in the ICM by the turbulence generating the extended radio halo