Leibniz's laws of consistency and the philosophical foundations of connexive logic

As an extension of the traditional theory of the syllogism, Leibniz’s algebra of concepts is built up from the term-logical operators of conjunction, negation, and the relation of containment.Leibniz’s laws of consistency state that no concept contains its own negation, and that if concept A contains concept B, then A cannot also contain Not-B. Leibniz believed that these principles would be universally valid, but he eventually discovered that they have to be restricted to self-consistent concepts.This result is of utmost importance for the philosophical foundations of connexive logic, i.e. for the question how far either “Aristotle’s Thesis”, ¬(α → ¬α), or “Boethius’s Thesis”, (α → β) → ¬(α → ¬β), should be accepted as reasonable principles of a logic of conditionals.

Kilwardby's 55th Lesson

In “Lectio 55” of his Notule libri Priorum, Robert Kilwardby discussed various objections that had been raised against Aristotle’s Theses. The first thesis, AT1, says that no proposition q is implied both by a proposition p and by its negation, ∼p. AT2 says that no proposition p is implied by its own negation. In Prior Analytics, Aristotle had shown that AT2 entails AT1, and he argued that the assumption of a proposition p such that (∼p → p) would be “absurd”.The unrestricted validity of AT1, AT2, however, is at odds with other principles which were widely accepted by medieval logicians, namely the law Ex Impossibili Quodlibet, EIQ, and the rules of disjunction introduction. Since, according to EIQ, the impossible proposition (p ∧ ∼p) implies every proposition, it also implies ∼(p∧∼p), in contradiction to AT2. Furthermore, by way of disjunction introduction, the proposition (p∨∼p) is implied both by p and by ∼p, in contradiction to AT1.Kilwardby tried to defend AT1, AT2 against these objections by claiming that EIQ holds only for accidental but not for natural implications. The second argument, however, cannot be refuted in this way because Kilwardby had to admit that every disjunction (p ∨ q) is naturally implied by its disjuncts. He therefore introduced the further requirement that, in order to constitute a genuine counterexample to AT1, (p → q) and (∼p → q) have to hold “by virtue of the same thing”.In a recently published paper, Spencer Johnston accepted this futile defence of AT1 and developed a formal semantics that would fit Kilwardby’s presumably connexive implication. This procedure, however, is misguided because the remaining considerations of Lesson 55 which were entirely ignored by Johnston show that Kilwardby eventually recognized that AT2 is bound to fail. After all he concluded: “So it should be granted that from the impossible its opposite follows, and that the necessary follows from its opposite”

A comprehensive examination of the Eps Eri system -- Verification of a 4 micron narrow-band high-contrast imaging approach for planet searches

Due to its proximity, youth, and solar-like characteristics with a spectral type of K2V, Eps Eri is one of the most extensively studied systems in an extrasolar planet context. Based on radial velocity, astrometry, and studies of the structure of its circumstellar debris disk, at least two planetary companion candidates to Eps Eri have been inferred in the literature (Eps Eri b, Eps Eri c). Some of these methods also hint at additional companions residing in the system. Here we present a new adaptive optics assisted high-contrast imaging approach that takes advantage of the favourable planet spectral energy distribution at 4 microns, using narrow-band angular differential imaging to provide an improved contrast at small and intermediate separations from the star. We use this method to search for planets at orbits intermediate between Eps Eri b (3.4 AU) and Eps Eri c (40 AU). The method is described in detail, and important issues related to the detectability of planets such as the age of Eps Eri and constraints from indirect measurements are discussed. The non-detection of companion candidates provides stringent upper limits for the masses of additional planets. Using a combination of the existing dynamic and imaging data, we exclude the presence of any planetary companion more massive than 3 Mjup anywhere in the Eps Eri system. Specifically, with regards to the possible residual linear radial velocity trend, we find that it is unlikely to correspond to a real physical companion if the system is as young as 200 Myr, whereas if it is as old as 800 Myr, there is an allowed semi-major axis range between about 8.5 and 25 AU.Comment: 11 pages, 8 figures, A&A accepte

Graph machine learning for assembly modeling

Assembly modeling refers to the design engineering process of composing assemblies (e.g., machines or machine components) from a common catalog of existing parts. There is a natural correspondence of assemblies to graphs which can be exploited for services based on graph machine learning such as part recommendation, clustering/taxonomy creation, or anomaly detection. However, this domain imposes particular challenges such as the treatment of unknown or new parts, ambiguously extracted edges, incomplete information about the design sequence, interaction with design engineers as users, to name a few. Along with open research questions, we present a novel data set

A recommendation system for CAD assembly modeling based on graph neural networks

In computer-aided design (CAD), software tools support design engineers during the modeling of assemblies, i.e., products that consist of multiple components. Selecting the right components is a cumbersome task for design engineers as they have to pick from a large number of possibilities. Therefore, we propose to analyze a data set of past assemblies composed of components from the same component catalog, represented as connected, undirected graphs of components, in order to suggest the next needed component. In terms of graph machine learning, we formulate this as graph classification problem where each class corresponds to a component ID from a catalog and the models are trained to predict the next required component. In addition to pretraining of component embeddings, we recursively decompose the graphs to obtain data instances in a self-supervised fashion without imposing any node insertion order. Our results indicate that models based on graph convolution networks and graph attention networks achieve high predictive performance, reducing the cognitive load of choosing among 2,000 and 3,000 components by recommending the ten most likely components with 82-92% accuracy, depending on the chosen catalog

The Arches Cluster - Evidence for a Truncated Mass Function?

We have analyzed high-resolution, adaptive optics (AO) HK observations of the Arches cluster obtained with NAOS/CONICA. With a spatial resolution of 84 mas, the cluster center is uniquely resolved. From these data the present-day mass function (MF) of Arches is derived down to about 4 Msun. The integrated MF as well as the core and 2nd annulus MFs are consistent with a turn-over at 6-7 Msun. This turn-over indicates severe depletion of intermediate and low-mass stars in the Arches cluster, possibly caused by its evolution in the Galactic Center environment. The Arches MF represents the first resolved observation of a starburst cluster exhibiting a low-mass truncated MF. This finding has severe implications for stellar population synthesis modelling of extragalactic starbursts, the derivation of integrated properties such as the total mass of star clusters in dense environments, the survival of low-mass remnants from starburst populations, and chemical enrichment during starburst phases.Comment: aastex preprint, 14 pages, 4 figures, accepted by ApJ Letter

Near-infrared wavefront sensing for the VLT interferometer

The very large telescope (VLT) interferometer (VLTI) in its current operating state is equipped with high-order adaptive optics (MACAO) working in the visible spectrum. A low-order near-infrared wavefront sensor (IRIS) is available to measure non-common path tilt aberrations downstream the high-order deformable mirror. For the next generation of VLTI instrumentation, in particular for the designated GRAVITY instrument, we have examined various designs of a four channel high-order near-infrared wavefront sensor. Particular objectives of our study were the specification of the near-infrared detector in combination with a standard wavefront sensing system. In this paper we present the preliminary design of a Shack-Hartmann wavefront sensor operating in the near-infrared wavelength range, which is capable of measuring the wavefronts of four telescopes simultaneously. We further present results of our design study, which aimed at providing a first instrumental concept for GRAVITY.Comment: 10 pages, 7 figures, to appear in "Ground-based and Airborne Instrumentation for Astronomy II" SPIE conference, Marseille, 23-28 June 200

The GRAVITY Coud\'e Infrared Adaptive Optics (CIAO) system for the VLT Interferometer

GRAVITY is a second generation instrument for the VLT Interferometer, designed to enhance the near-infrared astrometric and spectro-imaging capabilities of VLTI. Combining beams from four telescopes, GRAVITY will provide an astrometric precision of order 10 micro-arcseconds, imaging resolution of 4 milli-arcseconds, and low and medium resolution spectro-interferometry, pushing its performance far beyond current infrared interfero- metric capabilities. To maximise the performance of GRAVITY, adaptive optics correction will be implemented at each of the VLT Unit Telescopes to correct for the effects of atmospheric turbulence. To achieve this, the GRAVITY project includes a development programme for four new wavefront sensors (WFS) and NIR-optimized real time control system. These devices will enable closed-loop adaptive correction at the four Unit Telescopes in the range 1.4-2.4 {\mu}m. This is crucially important for an efficient adaptive optics implementation in regions where optically bright references sources are scarce, such as the Galactic Centre. We present here the design of the GRAVITY wavefront sensors and give an overview of the expected adaptive optics performance under typical observing conditions. Benefiting from newly developed SELEX/ESO SAPHIRA electron avalanche photodiode (eAPD) detectors providing fast readout with low noise in the near-infrared, the AO systems are expected to achieve residual wavefront errors of \leq400 nm at an operating frequency of 500 Hz.Comment: to be published in Proc. SPIE vol. 8446 (2012