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We characterize well-founded algebraic lattices by means of forbidden subsemilattices of the join-semilattice made of their compact elements. More specifically, we show that an algebraic lattice $L$ is well-founded if and only if $K(L)$, the join-semilattice of compact elements of $L$, is well-founded and contains neither $[ω]^{<ω}$, nor $\underlineΩ(ω^*)$ as a join-subsemilattice. As an immediate corollary, we get that an algebraic modular lattice $L$ is well-founded if and only if $K(L)$ is well-founded and contains no infinite independent set. If $K(L)$ is a join-subsemilattice of $I_{<ω}(Q)$, the set of finitely generated initial segments of a well-founded poset $Q$, then $L$ is well-founded if and only if $K(L)$ is well-quasi-ordered.

This paper studies fundamental questions concerning category-theoretic models of induction and recursion. We are concerned with the relationship between well-founded and recursive coalgebras for an endofunctor. For monomorphism preserving endofunctors on complete and well-powered categories every coalgebra has a well-founded part, and we provide a new, shorter proof that this is the coreflection in the category of all well-founded coalgebras. We present a new more general proof of Taylor's General Recursion Theorem that every well-founded coalgebra is recursive, and we study under which hypothesis the converse holds. In addition, we present a new equivalent characterization of well-foundedness: a coalgebra is well-founded iff it admits a coalgebra-to-algebra morphism to the initial algebra.

Many native ASP solvers exploit unfounded sets to compute consequences of a logic program via some form of well-founded negation, but disregard its contrapositive, well-founded justification (WFJ), due to computational cost. However, we demonstrate that this can hinder propagation of many relevant conditions such as reachability. In order to perform WFJ with low computational cost, we devise a method that approximates its consequences by computing dominators in a flowgraph, a problem for which linear-time algorithms exist. Furthermore, our method allows for additional unfounded set inference, called well-founded domination (WFD). We show that the effect of WFJ and WFD can be simulated for a important classes of logic programs that include reachability. This paper is a corrected and extended version of a paper published at the 12th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR 2013). It has been adapted to exclude Theorem 10 and its consequences, but provides all missing proofs.

In this note, we use Kunen's notion of a signing to establish two theorems about the well-founded semantics of logic programs, in the case where we are interested in only (say) the positive literals of a predicate $p$ that are consequences of the program. The first theorem identifies a class of programs for which the well-founded and Fitting semantics coincide for the positive part of $p$. The second theorem shows that if a program has a signing then computing the positive part of $p$ under the well-founded semantics requires the computation of only one part of each predicate. This theorem suggests an analysis for query-answering under the well-founded semantics. In the process of proving these results, we use an alternative formulation of the well-founded semantics of logic programs, which might be of independent interest. Under consideration in Theory and Practice of Logic Programming (TPLP)

Aim of this paper is to confute two views, the first about Schröder's presumptive foundationalism, according to he founded mathematics on the calculus of relatives; the second one mantaining that Schröder only in his last years (from 1890 onwards) focused on an universal and symbolic language (by him called pasigraphy). We will argue that, on the one hand Schröder considered the problem of founding mathematics already solved by Dedekind, limiting himself in a mere translation of the Chain Theory in the language of the relatives. On the other hand, we will show that Schröder's pasigraphy was connaturate to himself and that it roots in his very childhood and in his love for foreign languages.

Despite much recent interest in compiler randomized testing (fuzzing), the practical impact of fuzzer-found compiler bugs on real-world applications has barely been assessed. We present the first quantitative and qualitative study of the tangible impact of miscompilation bugs in a mature compiler. We follow a rigorous methodology where the bug impact over the compiled application is evaluated based on (1) whether the bug appears to trigger during compilation; (2) the extent to which generated assembly code changes syntactically due to triggering of the bug; and (3) how much such changes do cause regression test suite failures and could be used to manually trigger divergences during execution. The study is conducted with respect to the compilation of more than 10 million lines of C/C++ code from 309 Debian packages, using 12% of the historical and now fixed miscompilation bugs found by four state-of-the-art fuzzers in the Clang/LLVM compiler, as well as 18 bugs found by human users compiling real code or by formal verification. The results show that almost half of the fuzzer-found bugs propagate to the generated binaries for some packages, but rarely affect their syntax and cause tw

We investigate tree-automatic well-founded trees. Using Delhomme's decomposition technique for tree-automatic structures, we show that the (ordinal) rank of a tree-automatic well-founded tree is strictly below omega^omega. Moreover, we make a step towards proving that the ranks of tree-automatic well-founded partial orders are bounded by omega^omega^omega: we prove this bound for what we call upwards linear partial orders. As an application of our result, we show that the isomorphism problem for tree-automatic well-founded trees is complete for level Delta^0_{omega^omega} of the hyperarithmetical hierarchy with respect to Turing-reductions.

An FOL-program consists of a background theory in a decidable fragment of first-order logic and a collection of rules possibly containing first-order formulas. The formalism stems from recent approaches to tight integrations of ASP with description logics. In this paper, we define a well-founded semantics for FOL-programs based on a new notion of unfounded sets on consistent as well as inconsistent sets of literals, and study some of its properties. The semantics is defined for all FOL-programs, including those where it is necessary to represent inconsistencies explicitly. The semantics supports a form of combined reasoning by rules under closed world as well as open world assumptions, and it is a generalization of the standard well-founded semantics for normal logic programs. We also show that the well-founded semantics defined here approximates the well-supported answer set semantics for normal DL programs.

This note describes an integrated recognition system for identifying missing and found objects as well as missing, dead, and found people during Hajj and Umrah seasons in the two Holy cities of Makkah and Madina in the Kingdom of Saudi Arabia. It is assumed that the total estimated number of pilgrims will reach 20 millions during the next decade. The ultimate goal of this system is to integrate facial recognition and object identification solutions into the Hajj and Umrah rituals. The missing and found computerized system is part of the CrowdSensing system for Hajj and Umrah crowd estimation, management and safety.

Global SLS-resolution and SLG-resolution are two representative mechanisms for top-down evaluation of the well-founded semantics of general logic programs. Global SLS-resolution is linear for query evaluation but suffers from infinite loops and redundant computations. In contrast, SLG-resolution resolves infinite loops and redundant computations by means of tabling, but it is not linear. The principal disadvantage of a non-linear approach is that it cannot be implemented using a simple, efficient stack-based memory structure nor can it be easily extended to handle some strictly sequential operators such as cuts in Prolog. In this paper, we present a linear tabling method, called SLT-resolution, for top-down evaluation of the well-founded semantics. SLT-resolution is a substantial extension of SLDNF-resolution with tabling. Its main features include: (1) It resolves infinite loops and redundant computations while preserving the linearity. (2) It is terminating, and sound and complete w.r.t. the well-founded semantics for programs with the bounded-term-size property with non-floundering queries. Its time complexity is comparable with SLG-resolution and polynomial for function-free lo

Low dispersion optical spectra have been obtained with the Hobby-Eberly Telescope of 22 very red objects found in early imaging data from the Sloan Digital Sky Survey. The objects are assigned spectral types on the 2MASS system (Kirkpatrick et al. 1999) and are found to range from late M to late L. The red- and near-infrared colors from SDSS and 2MASS correlate closely with each other, and most of the colors are closely related to spectral type in this range; the exception is the (i^* - z^*) color, which appears to be independent of spectral type between about M7 and L4. The spectra suggest that this independence is due to the disappearance of the TiO and VO absorption in the i-band for later spectral types; to the presence of strong Na I and K I absorption in the i-band; and to the gradual disappearance of the 8400 Angstrom absorption of TiO and FeH in the z-band.

The ON stars are a rare subtype of O stars, of uncertain origin. We report two new, rapidly-rotating ON stars found in data acquired with the Large Sky Area Multi-Object Fiber Spectroscopic Telescope, LAMOST. LS I +61 28 is an ON8.5 Vn dwarf with a projected equatorial rotational velocity of $v_{\textrm e}\sin{i} \simeq 298$ km$\;$s$^{-1}$, while HDE 236672 is an ON9 IVn subgiant with $v_{\textrm e}\sin{i} \simeq 253$ km$\;$s$^{-1}$ The former is the first rapidly-rotating ON dwarf to be found, and the latter is only the third ON subgiant. The luminosity classes of non-supergiant ON stars appear to be influenced by the axial inclination angle $i$: the rapidly-rotating giants are close to equator-on, while ON dwarfs with lower $v_{\textrm e}\sin{i}$ values are viewed more nearly pole-on. Combining parallaxes and proper motions from Gaia DR2 with radial-velocity measurements, we investigate the kinematics of non-supergiant ON stars, and infer that the dynamics, rapid rotation, and surface-nitrogen characteristics may all be consequences of binary interaction.

In this letter we communicate the identification of a new Galactic O2If* star (MTT 68) isolated at a projected linear distance of 3 pc from the centre of the star-burst cluster NGC 3603. From its optical photometry I computed a bolometric luminosity M_Bol = -10.7, which corresponds to a total stellar luminosity of 1.5 x 10^{6} L_Sun. It was found an interesting similarity between MTT 68 and the well known multiple system HD 93129. From Hubble Space Telescope F656N images of the NGC 3603 field, it was found that MTT 68 is actually a visual binary system with an angular separation of 0.38 arcsec, which corresponds to a projected (minimum) linear distance of r_(A-B) = 1.4 x 10^{-2} pc. This value is similar to that for the HD 93129A (O2If*) and HD 93129B (O3.5) pair, r_(A-B) = 3.0 x 10^{-2} pc. On the other hand, HD93129A has a third closer companion named HD 93129Ab (O3.5) at only 0.053 arcsec, and taking into account that the X-ray to total stellar luminosity ratio for the MTT 68 system (L_X/L_Bol 10^{-5}) is about two orders of magnitude above the canonical value expected for single stars, I suspect that the MTT 68 system probably hosts another massive companion not resolved by the

The satellite Hinode has recently revealed penumbral structures with a magnetic polarity opposite to the main sunspot polarity. They may be a direct confirmation of magnetic field lines and mass flows returning to the solar interior throughout the penumbra, a configuration previously inferred from interpretation of observed Stokes profile asymmetries. The paper points out the relationship between the reverse polarity features found by Hinode, and the model Micro-Structured Magnetic Atmospheres (MISMAs) proposed for sunspots. We show how the existing model MISMAs produce strongly redshifted reverse polarity structures as found by Hinode. Ad hoc model MISMAs also explain the asymmetric Stokes profiles observed by Hinode. The same modeling may be consistent with magnetograms of dark cored penumbral filaments if the dark cores are associated with the reverse polarity. Such hypothetical relationship will show up only in the far red wings of the spectral lines.

Calibration is one of the long-standing problems in optical interferometric measurements, particularly with long baselines which demand stars with angular sizes on the milliarcsecond scale and no detectable companions. While systems of calibrators have been generally established for the near-infrared in the bright source regime (K$\la 3$\,mag), modern large interferometers are sensitive to significantly fainter magnitudes. We aim at providing a list of sources found unresolved from direct observations with high angular resolution and dynamic range, which can be used to choose interferometric calibrators. To this purpose, we have used a large number of lunar occultations recorded with the ISAAC instrument at the VLT to select sources found to be unresolved and without close companions. An algorithm has been used to determine the limiting angular resolution achieved for each source, taking into account a noise model built from occulted and unocculted portions of the light curves. We have obtained upper limits on the angular sizes of 556 sources, with magnitudes ranging from K$_{\rm s} \approx$4 to 10, with a median of 7.2\,mag. The upper limits on possible undetected companions (with

Non-well-founded trees are used in mathematics and computer science, for modelling non-well-founded sets, as well as non-terminating processes or infinite data-structures. Categorically, they arise as final coalgebras for polynomial endofunctors, which we call M-types. In order to reason about trees, we need the notion of path, which can be formalised in the internal logic of any locally cartesian closed pretopos with a natural number object. In such categories, we derive existence results about M-types, leading to stability of locally cartesian closed pretoposes with a natural number object and M-types under slicing, formation of coalgebras (for a cartesian comonad), and sheaves for an internal site.

The gravity model is a mathematical model that applies Newton's universal law of gravitation to socio-economic transport phenomena and has been widely used to describe world trade, intercity traffic flows, and business transactions for more than several decades. However, its strong nonlinearity and diverse network topology make a theoretical analysis difficult, and only a short history of studies on its stability exist. In this study, the stability of gravity models defined on networks with few nodes is analyzed in detail using numerical simulations. It was found that, other than the previously known transition of stationary solutions from a unique diffusion solution to multiple localized solutions, parameter regions exist where periodic solutions with the same repeated motions and chaotic solutions with no periods are realized. The smallest network with chaotic solutions was found to be a ring with seven nodes, which produced a new type of chaotic solution in the form of a mixture of right and left periodic solutions.

Fundamental errors in the Chubykalo et al paper [Found. of Phys. Lett, 19, 37-46 (2006)] are highlighted. Contrary to their claim that "... the irrotational component of the electric field has a physical meaning and can propagate exclusively instantaneously," it is shown that this instantaneous component is physically irrelevant because it is always canceled by a term contained into the solenoidal component. This result follows directly from the solution of the wave equation that satisfies the solenoidal component. Therefore the subsequent inference of these authors that there are two mechanisms of transmission of energy and momentum in classical electrodynamics, one retarded and the other one instantaneous, has no basis. The example given by these authors in which the full electric field of an oscillating charge equals its instantaneous irrotational component on the axis of oscillations is proved to be false.

In the present work, quantum theory is founded on the framework of consciousness, in contrast to earlier suggestions that consciousness might be understood starting from quantum theory. The notion of streams of consciousness, usually restricted to conscious beings, is extended to the notion of a Universal/Global stream of conscious flow of ordered events. The streams of conscious events which we experience constitute sub-streams of the Universal stream. Our postulated ontological character of consciousness also consists of an operator which acts on a state of potential consciousness to create or modify the likelihoods for later events to occur and become part of the Universal conscious flow. A generalized process of measurement-perception is introduced, where the operation of consciousness brings into existence, from a state of potentiality, the event in consciousness. This is mathematically represented by (a) an operator acting on the state of potential-consciousness before an actual event arises in consciousness and (b) the reflecting of the result of this operation back onto the state of potential-consciousness for comparison in order for the event to arise in consciousness. Beg

The lightest scalar glueball and ground state hybrids may have been found. I compare signals reported at this conference with theoretical expectations and highlight the questions that need to be addressed in forthcoming experiments.