Well-Founded Semantics for Extended Datalog and Ontological Reasoning

The Datalog± family of expressive extensions of Datalog has recently been introduced as a new paradigm for query answering over ontologies, which captures and extends several common description logics. It extends plain Datalog by features such as existentially quantified rule heads and, at the same time, restricts the rule syntax so as to achieve decidability and tractability. In this paper, we continue the research on Datalog±. More precisely, we generalize the well-founded semantics (WFS), as the standard semantics for nonmonotonic normal programs in the database context, to Datalog± programs with negation under the unique name assumption (UNA). We prove that for guarded Datalog± with negation under the standard WFS, answering normal Boolean conjunctive queries is decidable, and we provide precise complexity results for this problem, namely, in particular, completeness for PTIME (resp., 2-EXPTIME) in the data (resp., combined) complexity

Equality-friendly well-founded semantics and applications to description logics

We tackle the problem of defining a well-founded semantics (WFS) for Datalog rules with existentially quantified variables in their heads and nega- tions in their bodies. In particular, we provide a WFS for the recent Datalog± family of ontology languages, which covers several important description logics (DLs). To do so, we generalize Datalog± by non-stratified nonmonotonic nega- tion in rule bodies, and we define a WFS for this generalization via guarded fixed point logic. We refer to this approach as equality-friendly WFS, since it has the advantage that it does not make the unique name assumption (UNA); this brings it close to OWL and its profiles as well as typical DLs, which also do not make the UNA. We prove that for guarded Datalog± with negation under the equality- friendly WFS, conjunctive query answering is decidable, and we provide precise complexity results for this problem. From these results, we obtain precise defi- nitions of the standard WFS extensions of EL and of members of the DL-Lite family, as well as corresponding complexity results for query answering

Universal truth of operator statements via ideal membership

We introduce a framework for proving statements about linear operators by verification of ideal membership in a free algebra. More specifically, arbitrary first-order statements about identities of morphisms in preadditive semicategories can be treated. We present a semi-decision procedure for validity of such formulas based on computations with noncommutative polynomials. These algebraic computations automatically incorporate linearity and benefit from efficient ideal membership procedures. In the framework, domains and codomains of operators are modelled using many-sorted first-order logic. To eliminate quantifiers and function symbols from logical formulas, we apply Herbrand's theorem and Ackermann's reduction. The validity of the resulting formulas is shown to be equivalent to finitely many ideal memberships of noncommutative polynomials. We explain all relevant concepts and discuss computational aspects. Furthermore, we illustrate our framework by proving concrete operator statements assisted by our computer algebra software.Comment: 43 pages, plus 8 additional pages appendi

Computing elements of certain form in ideals to prove properties of operators

Proving statements about linear operators expressed in terms of identities often leads to finding elements of certain form in noncommutative polynomial ideals. We illustrate this by examples coming from actual operator statements and discuss relevant algorithmic methods for finding such polynomials based on noncommutative Gr\"obner bases. In particular, we present algorithms for computing the intersection of a two-sided ideal with a one-sided ideal as well as for computing homogeneous polynomials in two-sided ideals and monomials in one-sided ideals. All methods presented in this work are implemented in the Mathematica package OperatorGB.Comment: 26 page

Compatible rewriting of noncommutative polynomials for proving operator identities

The goal of this paper is to prove operator identities using equalities between noncommutative polynomials. In general, a polynomial expression is not valid in terms of operators, since it may not be compatible with domains and codomains of the corresponding operators. Recently, some of the authors introduced a framework based on labelled quivers to rigorously translate polynomial identities to operator identities. In the present paper, we extend and adapt the framework to the context of rewriting and polynomial reduction. We give a sufficient condition on the polynomials used for rewriting to ensure that standard polynomial reduction automatically respects domains and codomains of operators. Finally, we adapt the noncommutative Buchberger procedure to compute additional compatible polynomials for rewriting. In the package OperatorGB, we also provide an implementation of the concepts developed.Comment: 17 page

A compliance-centric view of grasping

We advocate the central importance of compliance for grasp performance and demonstrate that grasp algorithms can achieve robust performance by explicitly considering and exploiting mechanical compliance of the grasping hand. Specifically, we consider the problem of robust grasping in the absence of a priori object models, focusing on object capture and grasp stability under variations of object shape for a given robotic hand. We present a simple characterization of the relationship between hand compliance, object shape, and grasp success. Based on this hypothesis, we devise a compliance-centric grasping algorithm. Real-world experiments show that this algorithm outperforms compliance-agnostic grasping, eliminates the need for explicit contact state planning, and simplifies the perceptual requirements when no a priori information about the environment is available.EC/FP7/248258/EU/Flexible Skill Acquisition and Intuitive Robot Tasking for Mobile Manipulation in the Real World/FIRST-M

Observation of directly interacting coherent two-level systems in a solid

Parasitic two-level tunneling systems originating from structural material defects affect the functionality of various microfabricated devices by acting as a source of noise. In particular, superconducting quantum bits may be sensitive to even single defects when these reside in the tunnel barrier of the qubit's Josephson junctions, and this can be exploited to observe and manipulate the quantum states of individual tunneling systems. Here, we detect and fully characterize a system of two strongly interacting defects using a novel technique for high-resolution spectroscopy. Mutual defect coupling has been conjectured to explain various anomalies of glasses, and was recently suggested as the origin of low frequency noise in superconducting devices. Our study provides conclusive evidence of defect interactions with full access to the individual constituents, demonstrating the potential of superconducting qubits for studying material defects. All our observations are consistent with the assumption that defects are generated by atomic tunneling.Comment: 13 pages, 7 figures. Includes supplementary materia

Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.Comment: 22 page

Hagenbeck's anthropologisch-zoologische Kalmücken Ausstellung

Die Völkerschau der KalmückInnen von 1883 wird untersucht und analysiert. Die Anwerbung, Anreise, der Aufenthalt und die Durchführung der Völkerschau sowie deren Rezeption bei dem Publikum, den Medien und WissenschafterInnen werden thematisiert

Simulation of vapour-liquid condensation in dipolar fluids and uniform sampling Monte Carlo algorithms

This works examines the question whether a vapour-liquid phase transition exists in systems of particles with purely dipolar interactions, a topic which has been the subject of a longstanding debate. Monte Carlo simulation results for two modi operandi to tackle this issue are presented. One approach examines the phase behaviour of fluids of charged hard dumbbells (CHD), each made up of two oppositely charged hard spheres with diameters σ and separation d. In the limit d/σ → 0, and with the temperature scaled accordingly, the system corresponds to dipolar hard spheres (DHS) while for larger values of d ionic interactions are dominant. The crossover between ionic and dipolar regimes is examined and a linear variation of the critical temperature T*c in dipolar reduced units as a function of d is observed, giving rise to an extrapolated T*cDHS ≈ 0:15. The second approach focuses on the dipolar Yukawa hard sphere (DYHS)fluid, which is given by a dipolar hard sphere and an attractive isotropic interaction Y of the Yukawa tail form. In this case, the DHS limit is obtained for Y → 0. It is found that T*c depends linearly on the isotropic interaction strength Y over a wide range, coinciding with the results for the CHD model and extrapolating to a similar value of T*c;DHS. However, with the use of specially adapted biased Monte Carlo techniques which are highly efficient, it is shown that the linear variation of T*c is violated for very small values of the Yukawa interaction strength, almost two orders of magnitude smaller than the characteristic dipolar interaction energy. It is found that phase separation is not observable beyond a critical value of the Yukawa energy parameter, even though in thermodynamic and structural terms, the DYHS and DHS systems are very similar. It is suggested that either some very subtle physics distinguishes the DYHS and DHS systems, or the observation of a phase transition in DHSs is precluded by finite-size effects. In the context of phase separation in highly correlated fluids, new flat-histogram Monte Carlo simulation techniques based on the Wang-Landau algorithm are evaluated and shown to be useful tools. This work presents a general and unifying framework for deriving Monte Carlo acceptance rules which facilitate flat histogram sampling. The framework yields uniform sampling rules for thermodynamic states given either by the mechanically extensive variables appearing in the Hamiltonian or, equivalently, uniformly sample the thermodynamic fields which are conjugate to these mechanical variables