Lexicalised Locality: Local Domains and Non-Local Dependencies in a Lexicalised Tree Adjoining Grammar

Contemporary generative grammar assumes that syntactic structure is best described in terms of sets, and that locality conditions, as well as cross-linguistic variation, is determined at the level of designated functional heads. Syntactic operations (merge, MERGE, etc.) build a structure by deriving sets from lexical atoms and recursively (and monotonically) yielding sets of sets. Additional restrictions over the format of structural descriptions limit the number of elements involved in each operation to two at each derivational step, a head and a non-head. In this paper, we will explore an alternative direction for minimalist inquiry based on previous work, e.g., Frank (2002, 2006), albeit under novel assumptions. We propose a view of syntactic structure as a specification of relations in graphs, which correspond to the extended projection of lexical heads; these are elementary trees in Tree Adjoining Grammars. We present empirical motivation for a lexicalised approach to structure building, where the units of the grammar are elementary trees. Our proposal will be based on cross-linguistic evidence; we will consider the structure of elementary trees in Spanish, English and German. We will also explore the consequences of assuming that nodes in elementary trees are addresses for purposes of tree composition operations, substitution and adjunction.

On exotic consistent anomalies in (1+1)$d$: A ghost story

We revisit ’t Hooft anomalies in (1+1)dd non-spin quantum field theory, starting from the consistency and locality conditions, and find that consistent U(1) and gravitational anomalies cannot always be canceled by properly quantized (2+1)dd classical Chern-Simons actions. On the one hand, we prove that certain exotic anomalies can only be realized by non-reflection-positive or non-compact theories; on the other hand, without insisting on reflection-positivity, the exotic anomalies present a caveat to the inflow paradigm. For the mixed U(1) gravitational anomaly, we propose an inflow mechanism involving a mixed U(1)\times×SO(2) classical Chern-Simons action with a boundary condition that matches the SO(2) gauge field with the (1+1)dd spin connection. Furthermore, we show that this mixed anomaly gives rise to an isotopy anomaly of U(1) topological defect lines. The isotopy anomaly can be canceled by an extrinsic curvature improvement term, but at the cost of creating a periodicity anomaly. We survey the holomorphic bcbc ghost system which realizes all the exotic consistent anomalies, and end with comments on a subtlety regarding the anomalies of finite subgroups of U(1).

Default by intervention: Allomorphy and locality in the Modern Greek verb

An often discussed dimension of the locality conditions on allomorphy is visibility: when do the trigger and target of allomorphy ‘see’ each other? An equally important dimension is intervention: when do the trigger and target stop seeing each other? This paper offers two case studies on intervention from Modern Greek verbal morphology. In Greek, Agr is sensitive to the features of Voice, and T is sometimes sensitive to the identity of the root; but in both cases, allomorphy only takes place when all heads intervening between the target and trigger are null. When at least one intervening head is overt, the target retreats to a default realization. I argue that such patterns, whereby intervention leads to the emergence of a default, are readily understandable in theories where adjacency of heads is a necessary condition for allomorphy, and where only null nodes may be transparent.

Complementary Local and Nonlocal Measurements of Conjugate Transformation - Unified Logic Representation of Conjugate 0-1 Vectors

Bohr proposed the complementarity principle in 1927 as the foundation of quantum mechanics, since then relevant debates have been critically discussed for many years. Applying a pair of spin particles, Einstein proposed the EPR paradox in 1935. Using nonlocal potential properties, Aharonov and Bohm proposed the AB effect to test complementary measurement results. Under locality conditions, Bell established a Bell inequality under classical logic. Using a pair of particles and double sets of ZMI devices for complementarity measurements, Hardy proposed the Hardy paradox in 1992. During the past 50 years, locality and nonlocality tests on complementarity were hot-topics among the advanced quantum information, computing and measurement directions with various theoretical extensions and solid experimental results.These complementarity approaches separated local/nonlocal parameters to form different equations without an integrated logic framework to describe these equations including both local and nonlocal features consistently. The main results provide a series of paradoxes that conflict with each other. This paper uses conjugate transformation. Based on the m+1 kernel form of 0-1 states, n pairs of conjugate partitions were established. Under a given configuration in N bits, a set of 2n 0-1 feature vectors are applied to construct conjugate transformation operators in logic levels with intrinsic measurements to be a set of measurement operators.The key results of the paper are listed in Theorem 5. Two special functions of vector logic (CNF or DNF expression) and four equivalent expressions of the elementary equation are examples to show local and nonlocal variables in equations consistently. Applying two pairs of conjugate sets <A, B> and their complementary sets <A', B''>, 4 meta measures are established corresponding to <±aA;±bB> quantitative features under measurement operators. The main results of the paper are represented in Lemma (1-4), Theorem (1-5) and Corollary (1-7). From a vector logic viewpoint, conjugate complementary scheme can organize local and nonlocal variables to satisfy the comprehensive properties of modern logic constructions on completeness, non-conflict and consistence in a united logic framework.

p-Toral Approximations Compute Bredon Homology

We study Bredon homology approximations for spaces with an action of a compact Lie group G. We show that if M is a coMackey functor satisfying mild p-locality conditions, then Bredon homology of a G-space X with coefficients in M is determined by fixed points of p-toral subgroups of G acting on X. As an application we prove a vanishing result for the Bredon homology of the complex ${{\mathcal{L}}}_{n}$ of direct-sum decompositions of ${{\mathbb{C}}}^{n}$.

Complete homotopy invariants for translation invariant symmetric quantum walks on a chain

We provide a classification of translation invariant one-dimensional quantum walks with respect to continuous deformations preserving unitarity, locality, translation invariance, a gap condition, and some symmetry of the tenfold way. The classification largely matches the one recently obtained (arXiv:1611.04439) for a similar setting leaving out translation invariance. However, the translation invariant case has some finer distinctions, because some walks may be connected only by breaking translation invariance along the way, retaining only invariance by an even number of sites. Similarly, if walks are considered equivalent when they differ only by adding a trivial walk, i.e., one that allows no jumps between cells, then the classification collapses also to the general one. The indices of the general classification can be computed in practice only for walks closely related to some translation invariant ones. We prove a completed collection of simple formulas in terms of winding numbers of band structures covering all symmetry types. Furthermore, we determine the strength of the locality conditions, and show that the continuity of the band structure, which is a minimal requirement for topological classifications in terms of winding numbers to make sense, implies the compactness of the commutator of the walk with a half-space projection, a condition which was also the basis of the general theory. In order to apply the theory to the joining of large but finite bulk pieces, one needs to determine the asymptotic behaviour of a stationary Schrödinger equation. We show exponential behaviour, and give a practical method for computing the decay constants.

Full and Special Colombeau Algebras

We introduce full diffeomorphism-invariant Colombeau algebras with addedε-dependence in the basic space. This unites the full and special settings of the theory into one single framework. Using locality conditions we find the appropriate definition of point values in full Colombeau algebras and show that special generalized points suffice to characterize elements of full Colombeau algebras. Moreover, we specify sufficient conditions for the sheaf property to hold and give a definition of the sharp topology in this framework.

Loophole-Free Bell Tests and the Falsification of Local Realism

Quantum mechanics is strictly incompatible with local realism. It has been shown by Bell and others that it is possible, in principle, to experimentally differentiate between local realism and quantum mechanics. Numerous experiments have attempted to falsify local realism; however, they have consistently failed to close the detection loophole under strict locality conditions, thereby allowing local realistic explanations for their observations. In 2015, three experiments took place that tested local realism without the impediments of these significant loopholes. Between these three experiments, a substantial data set was collected. All of the collected data show a strong violation of local realism and strong support for quantum mechanics. This article reviews the theoretical basis of Bell tests and the affiliated loopholes, as well as the methods employed by these recent experiments and the implications of the results they observed. La mécanique quantique est strictement incompatible avec le réalisme local. Bell et d’autres scientifiques ont montré qu’il est possible, en théorie, de trouver la différence entre le réalisme local et la mécanique quantique expérimentalement. De nombreuses expériences ont tenté de falsifier le réalisme local; cependant, elles ont toujours échoué à combler la faille de détection dans des conditions de localité strictes, permettant ainsi des explications réalistes locales pour leurs observations. En 2015, trois expériences ont testé le réalisme local sans les entraves de ces failles importantes. Entre ces trois expériences, des données substantielles ont été recueillies. Toutes les données recueillies ont montré une forte déviation du réalisme local et un appui solid pour la mécanique quantique. Cet article examine les bases théoriques des tests de Bell et les failles af liées, ainsi que les méthodes employées par ces expériences récentes et les implications de leurs résultats.

Speech production planning affects phonological variability: a case study in French liaison

Connected speech processes have played a major role in shaping theories about phonological organization, and how phonology interacts with other components of the grammar (Selkirk, 1974; Kiparsky, 1982; Kaisse, 1985; Nespor and Vogel, 1986, among others). External sandhi is subject to locality conditions, and it is more variable compared to processes applying word-internally. We suggest that an important part of understanding these two properties of external sandhi is the locality of speech production planning. Presenting evidence from French liaison, we argue that the effect of lexical frequency on variability can be understood as a consequence of the narrow window of phonological encoding during speech production planning. This proposal complements both abstract, symbolic and gestural overlap-based accounts of phonological alternations. By connecting the study of phonological alternations with the study of factors influencing speech production planning, we can derive novel predictions about patterns of variability in external sandhi, and better understand the data that drive the development of phonological theories.