Modeling Belief in Dynamic Systems, Part II: Revision and Update

The study of belief change has been an active area in philosophy and AI. In recent years two special cases of belief change, belief revision and belief update, have been studied in detail. In a companion paper (Friedman & Halpern, 1997), we introduce a new framework to model belief change. This framework combines temporal and epistemic modalities with a notion of plausibility, allowing us to examine the change of beliefs over time. In this paper, we show how belief revision and belief update can be captured in our framework. This allows us to compare the assumptions made by each method, and to better understand the principles underlying them. In particular, it shows that Katsuno and Mendelzon's notion of belief update (Katsuno & Mendelzon, 1991a) depends on several strong assumptions that may limit its applicability in artificial intelligence. Finally, our analysis allow us to identify a notion of minimal change that underlies a broad range of belief change operations including revision and update.Comment: See http://www.jair.org/ for other files accompanying this articl

Probabilistic Algorithmic Knowledge

The framework of algorithmic knowledge assumes that agents use deterministic knowledge algorithms to compute the facts they explicitly know. We extend the framework to allow for randomized knowledge algorithms. We then characterize the information provided by a randomized knowledge algorithm when its answers have some probability of being incorrect. We formalize this information in terms of evidence; a randomized knowledge algorithm returning ``Yes'' to a query about a fact \phi provides evidence for \phi being true. Finally, we discuss the extent to which this evidence can be used as a basis for decisions.Comment: 26 pages. A preliminary version appeared in Proc. 9th Conference on Theoretical Aspects of Rationality and Knowledge (TARK'03

Optical and X-ray Spectroscopy of 1E 0449.4-1823: Demise of the original type 2 QSO

New optical spectra of the original narrow-line quasar 1E 0449.4-1823 show that it now has broad emission lines of considerable strength, eliminating it as a "type 2 QSO" candidate. We suggest that the behavior of 1E 0449.4-1823 is the same as that of some Seyfert 1.8 and 1.9 galaxies, in which Goodrich attributed long-term variations of their broad Balmer lines to dynamical motions of obscuring material located in or around the broad-line region. The optical continuum and broad emission-line regions of 1E 0449.4-1823 may still be partly covered in our line of sight, which would explain its large forbidden-line equivalent widths and flat alpha_ox relative to other low-redshift QSOs. Also present are apparent absorption features in the broad Balmer lines and in Mg II, which may be related to the past obscuration and current emergence of the broad-line region. However, it is difficult to distinguish absorption from broad emission-line peaks that are displaced in velocity; we consider the latter a plausible competing interpretation of these peculiar line profiles. An ASCA X-ray spectrum of 1E 0449.4-1823 can be fitted with a power-law of Gamma = 1.63, intrinsic N_H < 9 x 10^20 cm-2, and no Fe Kalpha line emission. Its 2-10 keV luminosity is 6.7 x 10^44 ergs/s. With regard to the still hypothetical type 2 QSOs, we argue that there is little evidence for the existence of any among X-ray selected samples.Comment: to appear in ApJ July 1, 1998 (vol. 501). 23 pages including figures. Uses LaTeX macro aasms4.st

New X-ray Constraints on Starburst and Seyfert Activity in the Barred Spiral Galaxy NGC 1672

The nearby barred spiral galaxy NGC 1672 shows dramatic starburst activity and may also host a Seyfert 2 nucleus. We present new X-ray observations that set constraints on starburst and Seyfert activity in NGC 1672. Two ROSAT HRI exposures, taken in 1992 and 1997, are used to investigate long-term variability of the known X-ray sources and to search for new sources of X-ray emission. We find large-amplitude (about 69%) variability from X-3, one of the off-nuclear sources located near an end of the galactic bar. X-3 has a peak observed 0.2-2.0 keV luminosity of about 2.5 x 10^{39} erg/s, and it is probably a luminous X-ray binary or young supernova remnant. We do not observe variability of the nuclear source X-1 or the strong off-nuclear source X-2. Our analyses also reveal two new off-nuclear sources, one of which is associated with a bright region along a spiral arm, and we find evidence for large-scale diffuse X-ray emission throughout part of the disk of NGC 1672. Furthermore, we use ASCA data taken in 1995 to constrain the hard X-ray properties of NGC 1672. While the nuclear source X-1 is the dominant soft X-ray source in NGC 1672, we find that the bulk of the 2-10 keV and 5-10 keV emission is spatially coincident with the off-nuclear source X-3, giving it an apparent 0.2-8 keV luminosity of about 6 x 10^{39} erg/s. A power-law plus Raymond-Smith model provides an acceptable fit to the full-band ASCA spectra. We do not find any evidence for a luminous but absorbed nuclear X-ray source. If there is a luminous Seyfert 2 nucleus in NGC 1672, it must be obscured by a `Compton-thick' torus with a column density of > 2 x 10^{24} cm^{-2}.Comment: 19 pages, AJ, accepted, also available from http://www.astro.psu.edu/users/niel/papers/papers.htm

Wigner's little group and Berry's phase for massless particles

The ``little group'' for massless particles (namely, the Lorentz transformations $\Lambda$ that leave a null vector invariant) is isomorphic to the Euclidean group E2: translations and rotations in a plane. We show how to obtain explicitly the rotation angle of E2 as a function of $\Lambda$ and we relate that angle to Berry's topological phase. Some particles admit both signs of helicity, and it is then possible to define a reduced density matrix for their polarization. However, that density matrix is physically meaningless, because it has no transformation law under the Lorentz group, even under ordinary rotations.Comment: 4 pages revte

Search for a Point-Source Counterpart of the Unidentified Gamma-Ray Source TeV J2032+4130 in Cygnus

We have made a multiwavelength study of the overlapping error boxes of the unidentified gamma-ray sources TeV J2032+4130 and 3EG J2033+4118 in the direction of the Cygnus OB2 association (d = 1.7 kpc) in order to search for a point-source counterpart of the first unidentified TeV source. Optical identifications and spectroscopic classifications for the brighter X-ray sources in ROSAT PSPC and Chandra ACIS images are obtained, without finding a compelling counterpart. The classified X-ray sources are a mix of early and late-type stars, with one exception. The brightest source in the Chandra observation is a new, hard absorbed source that is both transient and rapidly variable. It lies 7' from the centroid of the TeV emission, which places it outside of the claimed 2 sigma location (r = 4.8'). A possible eclipse or "dip" transition is seen in its light curve. With a peak 1-10 keV luminosity of 7 x 10^(32) (d/1.7 kpc})^2 ergs s^(-1), this source could be a quiescent low-mass X-ray binary that lies beyond the Cyg OB2 association. A coincident, reddened optical object of R = 20.4, J = 15.4, H = 14.2, and K = 13.4 is observed, but not yet classified due to the lack of obvious emission or absorption features in its spectrum. Alternatively, this Chandra} and optical source might be a considered a candidate for a proton blazar, a long hypothesized type of radio-weak gamma-ray source. More detailed observations will be needed to determine the nature of this variable X-ray source, and to assess the possibility of its connection with TeV J2032+4130.Comment: 24 pages, 8 figures, accepted by Ap

The Optical Design and Characterization of the Microwave Anisotropy Probe

The primary goal of the MAP satellite, now in orbit, is to make high fidelity polarization sensitive maps of the full sky in five frequency bands between 20 and 100 GHz. From these maps we will characterize the properties of the cosmic microwave background (CMB) anisotropy and Galactic and extragalactic emission on angular scales ranging from the effective beam size, <0.23 degree, to the full sky. MAP is a differential microwave radiometer. Two back-to-back shaped offset Gregorian telescopes feed two mirror symmetric arrays of ten corrugated feeds. We describe the prelaunch design and characterization of the optical system, compare the optical models to the measurements, and consider multiple possible sources of systematic error.Comment: ApJ in press; 22 pages with 11 low resolution figures; paper is available with higher quality figures at http://map.gsfc.nasa.gov/m_mm/tp_links.htm

Model Checking CTL is Almost Always Inherently Sequential

The model checking problem for CTL is known to be P-complete (Clarke, Emerson, and Sistla (1986), see Schnoebelen (2002)). We consider fragments of CTL obtained by restricting the use of temporal modalities or the use of negations---restrictions already studied for LTL by Sistla and Clarke (1985) and Markey (2004). For all these fragments, except for the trivial case without any temporal operator, we systematically prove model checking to be either inherently sequential (P-complete) or very efficiently parallelizable (LOGCFL-complete). For most fragments, however, model checking for CTL is already P-complete. Hence our results indicate that, in cases where the combined complexity is of relevance, approaching CTL model checking by parallelism cannot be expected to result in any significant speedup. We also completely determine the complexity of the model checking problem for all fragments of the extensions ECTL, CTL+, and ECTL+

Multifrequency Strategies for the Identification of Gamma-Ray Sources

More than half the sources in the Third EGRET (3EG) catalog have no firmly established counterparts at other wavelengths and are unidentified. Some of these unidentified sources have remained a mystery since the first surveys of the gamma-ray sky with the COS-B satellite. The unidentified sources generally have large error circles, and finding counterparts has often been a challenging job. A multiwavelength approach, using X-ray, optical, and radio data, is often needed to understand the nature of these sources. This chapter reviews the technique of identification of EGRET sources using multiwavelength studies of the gamma-ray fields.Comment: 35 pages, 22 figures. Chapter prepared for the book "Cosmic Gamma-ray Sources", edited by K.S. Cheng and G.E. Romero, to be published by Kluwer Academic Press, 2004. For complete article and higher resolution figures, go to: http://www.astro.columbia.edu/~muk/mukherjee_multiwave.pd

The ASCA X-Ray Spectrum Of The Broad-Line Radio Galaxy Pictor A: A Simple Power Law With No Fe K-alpha Line

We present the X-ray spectrum of the broad-line radio galaxy Pictor A as observed by ASCA in 1996. The main objective of the observation was to detect and study the profiles of the Fe~K$\alpha$ lines. The motivation was the fact that the Balmer lines of this object show well-separated displaced peaks, suggesting an origin in an accretion disk. The 0.5-10 keV X-ray spectrum is described very well by a model consisting of a power law of photon index 1.77 modified by interstellar photoelectric absorption. We find evidence for neither a soft nor a hard (Compton reflection) excess. More importantly, we do not detect an Fe K-alpha line, in marked contrast with the spectra of typical Seyfert galaxies and other broad-line radio galaxies observed by ASCA. The 99%-confidence upper limit on the equivalent width of an unresolved line at a rest energy of 6.4 keV is 100 eV, while for a broad line (FWHM of approximately 60,000 km/s) the corresponding upper limit is 135 eV. We discuss several possible explanations for the weakness of the Fe K-alpha line in Pictor~A paying attention to the currently available data on the properties of Fe K-alpha lines in other broad-line radio galaxies observed by ASCA. We speculate that the absence of a hard excess (Compton reflection) or an Fe K-alpha line is an indication of an accretion disk structure that is different from that of typical Seyfert galaxies, e.g., the inner disk may be an ion torus.Comment: To appear in the Astrophysical Journal (18 pages, including 8 postscript figures; uses psfig.tex