Logics for approximate and strong entailments

We consider two kinds of similarity-based reasoning and formalise them in a logical setting. In one case, we are led by the principle that conclusions can be drawn even if they are only approximately correct. This leads to a graded approximate entailment, which is weaker than classical entailment. In the other case, we follow the principle that conclusions must remain correct even if the assumptions are slightly changed. This leads to a notion of a graded strong entailment, which is stronger than classical entailment. We develop two logical calculi based on the notions of approximate and of strong entailment, respectively. © 2011 Elsevier B.V.The authors acknowledge partial support of the bilateral Austrian-Spanish project HA2008-0017 and the Eurocores-LogICCC ESF project LoMoReVI. Esteva and Godo also acknowledge partial support of the Spanish project FFI2008-03126-E/FILO and Rodrıguez acknowledges the projects CyT-UBA X484 and the research CONICET program PIP 12-200801-02543 2009-2011. Finally, Esteva, Godo and Rodrıguez also acknowledge partial support of the MaToMUVI project (PIRSES-GA-2009- 247584).Peer Reviewe

Towards a Proof Theory of G\"odel Modal Logics

Analytic proof calculi are introduced for box and diamond fragments of basic modal fuzzy logics that combine the Kripke semantics of modal logic K with the many-valued semantics of G\"odel logic. The calculi are used to establish completeness and complexity results for these fragments

Bathypelagic Fish Association with the Mid-Atlantic Ridge

The bathypelagic zone, Earth’s largest living space, is essentially boundless in three dimensions for most of its extent, structured only by fluid features (e.g., salinity, temperature) of the seawater itself. However, near certain topographic features this zone intersects the seafloor. The mid-ocean ridge system is by far the largest of these features. Unlike the ecosystems of the continental margins, the mid-ocean ridge systems do not receive terrigenous nutrient inputs. Thus, the deep-water fauna associated with mid-ocean ridges ultimately depend on the generally limited local surface production. Despite this limited surface production, there is evidence that near-ridge demersal fish biomass is increased above the mid-Atlantic Ridge (MAR). Two processes by which organic matter can be transferred to the benthic boundary layer include: 1) sinking of aggregates and the carcasses of larger animals, and 2) vertical migration of living animals. To understand the dynamics of the latter process, deep-pelagic and demersal fishes were studied during the 2004 G.O. Sars Expedition, a field campaign of MAR-ECO. MAR-ECO, a Census of Marine Life project, is an international study of the animals inhabiting the northern Mid-Atlantic. Utilizing multiple technologies the water column (to 3500 m) and benthic realms were sampled. Taxonomic analysis to date has revealed over 300 fish species, with ongoing analysis expected to reveal more species, some new to science. Pelagic sampling collected 207 species, with typical orders dominating. Bottom trawling collected ca. 175 species, with typical demersal families, but also pelagic families occurring in numbers higher than would be expected by contamination alone. Discrete, near-bottom pelagic trawls confirmed this observation. In all, 84 species were caught in both pelagic and bottom trawls, with some species showing enhanced abundances in the near-bottom boundary layer, suggesting that overlap of deep-pelagic and demersal faunas is likely a key process regulating mid-ocean ridge community structure

H.E.S.S. observations of gamma-ray bursts in 2003-2007

Very-high-energy (VHE; >~100 GeV) gamma-rays are expected from gamma-ray bursts (GRBs) in some scenarios. Exploring this photon energy regime is necessary for understanding the energetics and properties of GRBs. GRBs have been one of the prime targets for the H.E.S.S. experiment, which makes use of four Imaging Atmospheric Cherenkov Telescopes (IACTs) to detect VHE gamma-rays. Dedicated observations of 32 GRB positions were made in the years 2003-2007 and a search for VHE gamma-ray counterparts of these GRBs was made. Depending on the visibility and observing conditions, the observations mostly start minutes to hours after the burst and typically last two hours. Results from observations of 22 GRB positions are presented and evidence of a VHE signal was found neither in observations of any individual GRBs, nor from stacking data from subsets of GRBs with higher expected VHE flux according to a model-independent ranking scheme. Upper limits for the VHE gamma-ray flux from the GRB positions were derived. For those GRBs with measured redshifts, differential upper limits at the energy threshold after correcting for absorption due to extra-galactic background light are also presented.Comment: 9 pages, 4 tables, 3 figure

Fermi-LAT Study of Gamma-ray Emission in the Direction of Supernova Remnant W49B

We present an analysis of the gamma-ray data obtained with the Large Area Telescope (LAT) onboard the Fermi Gamma-ray Space Telescope in the direction of SNR W49B (G43.3-0.2). A bright unresolved gamma-ray source detected at a significance of 38 sigma is found to coincide with SNR W49B. The energy spectrum in the 0.2-200 GeV range gradually steepens toward high energies. The luminosity is estimated to be 1.5x10^{36} (D/8 kpc)^2 erg s^-1 in this energy range. There is no indication that the gamma-ray emission comes from a pulsar. Assuming that the SNR shell is the site of gamma-ray production, the observed spectrum can be explained either by the decay of neutral pi mesons produced through the proton-proton collisions or by electron bremsstrahlung. The calculated energy density of relativistic particles responsible for the LAT flux is estimated to be remarkably large, U_{e,p}>10^4 eV cm^-3, for either gamma-ray production mechanism.Comment: 9 pages, 10 figure

GeV Gamma-ray Flux Upper Limits from Clusters of Galaxies

The detection of diffuse radio emission associated with clusters of galaxies indicates populations of relativistic leptons infusing the intracluster medium. Those electrons and positrons are either injected into and accelerated directly in the intracluster medium, or produced as secondary pairs by cosmic-ray ions scattering on ambient protons. Radiation mechanisms involving the energetic leptons together with decay of neutral pions produced by hadronic interactions have the potential to produce abundant GeV photons. Here, we report on the search for GeV emission from clusters of galaxies using data collected by the Large Area Telescope (LAT) on the Fermi Gamma-ray Space Telescope (Fermi) from August 2008 to February 2010. Thirty-three galaxy clusters have been selected according to their proximity and high mass, X-ray flux and temperature, and indications of non-thermal activity for this study. We report upper limits on the photon flux in the range 0.2-100 GeV towards a sample of observed clusters (typical values 1-5 x 10^-9 ph cm^-2 s^-1) considering both point-like and spatially resolved models for the high-energy emission, and discuss how these results constrain the characteristics of energetic leptons and hadrons, and magnetic fields in the intracluster medium. The volume-averaged relativistic-hadron-to-thermal energy density ratio is found to be < 5-10% in several clusters.Comment: 9 pages, 3 tables, 1 figure, accepted for publication in ApJ Letter

Constraints on dark matter models from a Fermi LAT search for high-energy cosmic-ray electrons from the Sun

During its first year of data taking, the Large Area Telescope (LAT) onboard the Fermi Gamma-Ray Space Telescope has collected a large sample of high-energy cosmic-ray electrons and positrons (CREs). We present the results of a directional analysis of the CRE events, in which we searched for a flux excess correlated with the direction of the Sun. Two different and complementary analysis approaches were implemented, and neither yielded evidence of a significant CRE flux excess from the Sun. We derive upper limits on the CRE flux from the Sun's direction, and use these bounds to constrain two classes of dark matter models which predict a solar CRE flux: (1) models in which dark matter annihilates to CREs via a light intermediate state, and (2) inelastic dark matter models in which dark matter annihilates to CREs.Comment: 18 pages, 8 figures, accepted for publication in Physical Review D - contact authors: Francesco Loparco ([email protected]), M. Nicola Mazziotta ([email protected]) and Jennifer Siegal-Gaskins ([email protected]

Gamma-ray flares from the Crab Nebula

A young and energetic pulsar powers the well-known Crab Nebula. Here we describe two separate gamma-ray (photon energy >100 MeV) flares from this source detected by the Large Area Telescope on board the Fermi Gamma-ray Space Telescope. The first flare occurred in February 2009 and lasted approximately 16 days. The second flare was detected in September 2010 and lasted approximately 4 days. During these outbursts the gamma-ray flux from the nebula increased by factors of four and six, respectively. The brevity of the flares implies that the gamma rays were emitted via synchrotron radiation from PeV (10^15 eV) electrons in a region smaller than 1.4 10^-2 pc. These are the highest energy particles that can be associated with a discrete astronomical source, and they pose challenges to particle acceleration theory.Comment: Contact authors: Rolf Buehler,[email protected]; Stefan Funk,[email protected]; Roger Blandford,rdb3@stanford ; 16 pages,2 figure

Fermi observations of high-energy gamma-ray emission from GRB 090217A

The Fermi observatory is advancing our knowledge of Gamma-Ray Bursts (GRBs) through pioneering observations at high energies, covering more than 7 decades in energy with the two on-board detectors, the Large Area Telescope (LAT) and the Gamma-ray Burst Monitor (GBM). Here we report on the observation of the long GRB 090217A which triggered the GBM and has been detected by the LAT with a significance greater than 9 sigma. We present the GBM and LAT observations and on-ground analyses, including the time-resolved spectra and the study of the temporal profile from 8 keV up to 1 GeV. All spectra are well reproduced by a Band model. We compare these observations to the first two LAT-detected, long bursts GRB 080825C and GRB 080916C. These bursts were found to have time-dependent spectra and exhibited a delayed onset of the high-energy emission, which are not observed in the case of GRB 090217A. We discuss some theoretical implications for the high-energy emission of GRBs.Comment: 17 pages, 4 figures. Contact Authors: Fred, Piron; Sara, Cutini; Andreas, von Kienli

Constraints on the Cosmic-Ray Density Gradient beyond the Solar Circle from Fermi gamma-ray Observations of the Third Galactic Quadrant

We report an analysis of the interstellar $\gamma$-ray emission in the third Galactic quadrant measured by the {Fermi} Large Area Telescope. The window encompassing the Galactic plane from longitude 210\arcdeg to 250\arcdeg has kinematically well-defined segments of the Local and the Perseus arms, suitable to study the cosmic-ray densities across the outer Galaxy. We measure no large gradient with Galactocentric distance of the $\gamma$-ray emissivities per interstellar H atom over the regions sampled in this study. The gradient depends, however, on the optical depth correction applied to derive the \HI\ column densities. No significant variations are found in the interstellar spectra in the outer Galaxy, indicating similar shapes of the cosmic-ray spectrum up to the Perseus arm for particles with GeV to tens of GeV energies. The emissivity as a function of Galactocentric radius does not show a large enhancement in the spiral arms with respect to the interarm region. The measured emissivity gradient is flatter than expectations based on a cosmic-ray propagation model using the radial distribution of supernova remnants and uniform diffusion properties. In this context, observations require a larger halo size and/or a flatter CR source distribution than usually assumed. The molecular mass calibrating ratio, $X_{\rm CO} = N({\rm H_{2}})/W_{\rm CO}$, is found to be $(2.08 \pm 0.11) \times 10^{20} {\rm cm^{-2} (K km s^{-1})^{-1}}$ in the Local-arm clouds and is not significantly sensitive to the choice of \HI\ spin temperature. No significant variations are found for clouds in the interarm region.Comment: Corresponding authors: I. A. Grenier ([email protected]); T. Mizuno ([email protected]); L. Tibaldo ([email protected]) accepted for publication in Ap