A speculation about what linguistic structures might be

2021 ◽  
pp. 9-21
Author(s):  
Avery Andrews
Keyword(s):  
Proof Theory ◽  
Equivalence Classes ◽  
Intermediate Level ◽  
Functional Structure ◽  
Linguistic Structures ◽  
Insight Into

Linguistics is heavily invested in the idea that linguistic utterances have ‘structures’, but there seems to be relatively little insight into what these structures actually are. In this chapter, Andrews suggests that they can be regarded as ‘aspirational equivalence classes’ of computations whereby the utterances are produced or understood. ‘Aspirational’ refers to the fact that unlike the case of Proof Theory, where the idea of equivalence classes of proofs a.k.a. computations originated, in linguistics we do not know what the computations are, but can nevertheless motivate some ideas about how they are organized. A classic example from LFG is the proposal that constituent-structures are found by a different set of processes than those that find functional-structures; a suggested new example is a proposal that functional-structures for ‘words’ are computed prior to their integration into the functional-structure for the utterance. Andrews suggests that this might be an intermediate level ‘1.6’ in Marr’s system of levels.

Mass Problems and Randomness

2005 ◽  
Vol 11 (1) ◽  
pp. 1-27 ◽  
Author(s):  
Stephen G. Simpson
Keyword(s):  
Computational Complexity ◽  
Positive Measure ◽  
Proof Theory ◽  
Reverse Mathematics ◽  
Equivalence Classes ◽  
Distributive Lattices ◽  
Intermediate Degree ◽  
Associated Mass ◽  
Weakly Reducible ◽  
Mass Problems

AbstractA mass problem is a set of Turing oracles. If P and Q are mass problems, we say that P is weakly reducible to Q if every member of Q Turing computes a member of P. We say that P is strongly reducible to Q if every member of Q Turing computes a member of P via a fixed Turing functional. The weak degrees and strong degrees are the equivalence classes of mass problems under weak and strong reducibility, respectively. We focus on the countable distributive lattices ω and s of weak and strong degrees of mass problems given by nonempty subsets of 2ω. Using an abstract Gödel/Rosser incompleteness property, we characterize the subsets of 2ω whose associated mass problems are of top degree in ω and s, respectively Let R be the set of Turing oracles which are random in the sense of Martin-Löf, and let r be the weak degree of R. We show that r is a natural intermediate degree within ω. Namely, we characterize r as the unique largest weak degree of a subset of 2ω of positive measure. Within ω we show that r is meet irreducible, does not join to 1, and is incomparable with all weak degrees of nonempty thin perfect subsets of 2ω. In addition, we present other natural examples of intermediate degrees in ω. We relate these examples to reverse mathematics, computational complexity, and Gentzen-style proof theory.

A geometrical derivation of the shape density

1991 ◽  
Vol 23 (03) ◽  
pp. 496-514 ◽  
Author(s):  
Colin R. Goodall ◽  
Kanti V. Mardia
Keyword(s):  
Rotation Group ◽  
Shape Space ◽  
Canonical System ◽  
Single Step ◽  
Equivalence Classes ◽  
Polar Coordinates ◽  
Dimension 2 ◽  
Original Derivation ◽  
Insight Into ◽  
Original Configuration

The density for the shapes of random configurations of N independent Gaussian-distributed landmarks in the plane with unequal means was first derived by Mardia and Dryden (1989a). Kendall (1984), (1989) describes a hierarchy of spaces for landmarks, including Euclidean figure space containing the original configuration, preform space (with location removed), preshape space (with location and scale removed), and shape space. We derive the joint density of the landmark points in each of these intermediate spaces, culminating in confirmation of the Mardia–Dryden result in shape space. This three-step derivation is an appealing alternative to the single-step original derivation, and also provides strong geometrical motivation and insight into Kendall's hierarchy. Preform space and preshape space are respectively Euclidean space with dimension 2(N–1) and the sphere in that space, and thus the first two steps are reasonably familiar. The third step, from preshape space to shape space, is more interesting. The quotient by the rotation group partitions the preshape sphere into equivalence classes of preshapes with the same shape. We introduce a canonical system of preshape coordinates that include 2(N–2) polar coordinates for shape and one coordinate for rotation. Integration over the rotation coordinate gives the Mardia–Dryden result. However, the usual geometrical intuition fails because the set of preshapes keeping the rotation coordinate (however chosen) fixed is not an integrable manifold. We characterize the geometry of the quotient operation through the relationships between distances in preshape space and distances among the corresponding shapes.

A geometrical derivation of the shape density

1991 ◽  
Vol 23 (3) ◽  
pp. 496-514 ◽  
Author(s):  
Colin R. Goodall ◽  
Kanti V. Mardia
Keyword(s):  
Rotation Group ◽  
Shape Space ◽  
Canonical System ◽  
Single Step ◽  
Equivalence Classes ◽  
Polar Coordinates ◽  
Dimension 2 ◽  
Original Derivation ◽  
Insight Into ◽  
Original Configuration

The density for the shapes of random configurations of N independent Gaussian-distributed landmarks in the plane with unequal means was first derived by Mardia and Dryden (1989a). Kendall (1984), (1989) describes a hierarchy of spaces for landmarks, including Euclidean figure space containing the original configuration, preform space (with location removed), preshape space (with location and scale removed), and shape space. We derive the joint density of the landmark points in each of these intermediate spaces, culminating in confirmation of the Mardia–Dryden result in shape space. This three-step derivation is an appealing alternative to the single-step original derivation, and also provides strong geometrical motivation and insight into Kendall's hierarchy. Preform space and preshape space are respectively Euclidean space with dimension 2(N–1) and the sphere in that space, and thus the first two steps are reasonably familiar. The third step, from preshape space to shape space, is more interesting. The quotient by the rotation group partitions the preshape sphere into equivalence classes of preshapes with the same shape. We introduce a canonical system of preshape coordinates that include 2(N–2) polar coordinates for shape and one coordinate for rotation. Integration over the rotation coordinate gives the Mardia–Dryden result. However, the usual geometrical intuition fails because the set of preshapes keeping the rotation coordinate (however chosen) fixed is not an integrable manifold. We characterize the geometry of the quotient operation through the relationships between distances in preshape space and distances among the corresponding shapes.

scholarly journals Lola ReRuns in the Classroom: Dramatic Improvisations on the Film Run Lola Run for Intermediate German Instruction

2011 ◽  
Vol V (2) ◽  
pp. 90-103
Author(s):  
Erika M. Nelson
Keyword(s):  
Language Instruction ◽  
Intermediate Level ◽  
German Language ◽  
Successful Implementation ◽  
Student Centered ◽  
German Film ◽  
Suitable Material ◽  
Tom Tykwer ◽  
Linguistic Structures

This paper presents an approach of how student-created dramatic reenactments and improvisational renditions of the German film Run Lola Run (Lola rennt, Tom Tykwer 1998) can serve as important vehicles to foster transcultural and communicative, student-centered competence in intermediate German language instruction, based on successful implementation in two intermediate college German courses. By performing improvised scenes, inspired by key scenes of the film, students learn to closely interpret and engage with the film’s themes and motifs beyond the meta-textual level, while sharpening their mastery of situational vocabulary, cultural nuance, and linguistic structures of the German language. This film in particular, with its focus on repetition and variation, offers especially suitable material for facilitating students’ awareness of language as a tool with which to access imaginative and interpretative potentials, as well as to express integral aspects of culture itself. The approach presented here also includes suggested materials, methods, and ideas to enhance understanding on the textual and performative levels and incorporate at the intermediate level of the curriculum, particularly for the Independent User level (B1 and B2)2 who has a basic grasp of the German language yet desires to develop greater linguistic flexibility and aptitude.

On the proof theory of the modal logic for arithmetic provability

1981 ◽  
Vol 46 (3) ◽  
pp. 531-538 ◽  
Author(s):  
Daniel Leivant
Keyword(s):  
Modal Logic ◽  
Proof Theory ◽  
Additional Insight ◽  
Semantical Analysis ◽  
Constructive Proofs ◽  
Definite Improvement ◽  
Original Presentation ◽  
Sequential Calculus ◽  
Insight Into

The modal logic GL has been found by Solovay [13] to formalize the provable propositional properties of the provability-predicate for Peano's Arithmetic PA (cf. §1 below). We give several sequential calculi for GL, compare their merits, and use one calculus to syntactically derive several metamathematical results about GL.Some of our results have been proved model theoretically, and similar proofs are fairly straightforward for several of the remaining ones (G. Boolos and the referee have provided such proofs for 4.1, 4.3 and 5.1 below). However, our syntactic techniques often yield more concise and obviously constructive proofs, they offer additional insight into the nature of the systems considered, and are easily adaptable to systems for which semantical analysis is problematic.I am indebted to G. Boolos and to the referee for their valuable advice. The referee has suggested the rule GL of §3 below as an axiomatization of GL; the resulting sequential calculus has allowed a definite improvement of our original presentation.

Accent in Japanese Phonology

2017 ◽  
Author(s):  
Haruo Kubozono
Keyword(s):  
Careful Analysis ◽  
Syllable Structure ◽  
Syllable Boundary ◽  
Compound Nouns ◽  
Pitch Pattern ◽  
Tokyo Japanese ◽  
New Evidence ◽  
Japanese Pitch Accent ◽  
Linguistic Structures ◽  
Insight Into

The word accent system of Tokyo Japanese might look quite complex with a number of accent patterns and rules. However, recent research has shown that it is not as complex as has been assumed if one incorporates the notion of markedness into the analysis: nouns have only two productive accent patterns, the antepenultimate and the unaccented pattern, and different accent rules can be generalized if one focuses on these two productive accent patterns. The word accent system raises some new interesting issues. One of them concerns the fact that a majority of nouns are ‘unaccented,’ that is, they are pronounced with a rather flat pitch pattern, apparently violating the principle of obligatoriness. A careful analysis of noun accentuation reveals that this strange accent pattern occurs in some linguistically predictable structures. In morphologically simplex nouns, it typically tends to emerge in four-mora nouns ending in a sequence of light syllables. In compound nouns, on the other hand, it emerges due to multiple factors, such as compound-final deaccenting morphemes, deaccenting pseudo-morphemes, and some types of prosodic configurations. Japanese pitch accent exhibits an interesting aspect in its interactions with other phonological and linguistic structures. For example, the accent of compound nouns is closely related with rendaku, or sequential voicing; the choice between the accented and unaccented patterns in certain types of compound nouns correlates with the presence or absence of the sequential voicing. Moreover, whether the compound accent rule applies to a certain compound depends on its internal morphosyntactic configuration as well as its meaning; alternatively, the compound accent rule is blocked in certain types of morphosyntactic and semantic structures. Finally, careful analysis of word accent sheds new light on the syllable structure of the language, notably on two interrelated questions about diphthong-hood and super-heavy syllables. It provides crucial insight into ‘diphthongs,’ or the question of which vowel sequence constitutes a diphthong, against a vowel sequence across a syllable boundary. It also presents new evidence against trimoraic syllables in the language.

Insight into the mechanism of persulfate activated by bone char: Unraveling the role of functional structure of biochar

2020 ◽  
Vol 401 ◽  
pp. 126127 ◽  
Author(s):  
Xuerong Zhou ◽  
Zhuotong Zeng ◽  
Guangming Zeng ◽  
Cui Lai ◽  
Rong Xiao ◽  
...  
Keyword(s):  
Functional Structure ◽  
Bone Char ◽  
Insight Into

Calibration problems in hydrogen luminosities

1966 ◽  
Vol 24 ◽  
pp. 322-330
Author(s):  
A. Beer
Keyword(s):  
Galactic Structure ◽  
B Stars ◽  
Insight Into

The investigations which I should like to summarize in this paper concern recent photo-electric luminosity determinations of O and B stars. Their final aim has been the derivation of new stellar distances, and some insight into certain patterns of galactic structure.

Stochasting modeling of planetary ring systems

1984 ◽  
Vol 75 ◽  
pp. 461-469 ◽  
Author(s):  
Robert W. Hart
Keyword(s):  
Maximum Entropy ◽  
Ring System ◽  
The Sun ◽  
Ultimate State ◽  
Interparticle Interactions ◽  
Ring Systems ◽  
First Order ◽  
Planetary Ring ◽  
Insight Into

ABSTRACTThis paper models maximum entropy configurations of idealized gravitational ring systems. Such configurations are of interest because systems generally evolve toward an ultimate state of maximum randomness. For simplicity, attention is confined to ultimate states for which interparticle interactions are no longer of first order importance. The planets, in their orbits about the sun, are one example of such a ring system. The extent to which the present approximation yields insight into ring systems such as Saturn's is explored briefly.

Skeletal elements of crinoid echinoderms: High-resolution structural and microanalytical results

1983 ◽  
Vol 41 ◽  
pp. 194-195
Author(s):  
D. F. Blake ◽  
L. F. Allard ◽  
D. R. Peacor
Keyword(s):  
High Resolution ◽  
Marine Invertebrates ◽  
Sea Urchins ◽  
Structural Features ◽  
Sea Stars ◽  
High Resolution Tem ◽  
Relationship Of ◽  
The Relationship ◽  
Insight Into

Echinodermata is a phylum of marine invertebrates which has been extant since Cambrian time (c.a. 500 m.y. before the present). Modern examples of echinoderms include sea urchins, sea stars, and sea lilies (crinoids). The endoskeletons of echinoderms are composed of plates or ossicles (Fig. 1) which are with few exceptions, porous, single crystals of high-magnesian calcite. Despite their single crystal nature, fracture surfaces do not exhibit the near-perfect {10.4} cleavage characteristic of inorganic calcite. This paradoxical mix of biogenic and inorganic features has prompted much recent work on echinoderm skeletal crystallography. Furthermore, fossil echinoderm hard parts comprise a volumetrically significant portion of some marine limestones sequences. The ultrastructural and microchemical characterization of modern skeletal material should lend insight into: 1). The nature of the biogenic processes involved, for example, the relationship of Mg heterogeneity to morphological and structural features in modern echinoderm material, and 2). The nature of the diagenetic changes undergone by their ancient, fossilized counterparts. In this study, high resolution TEM (HRTEM), high voltage TEM (HVTEM), and STEM microanalysis are used to characterize tha ultrastructural and microchemical composition of skeletal elements of the modern crinoid Neocrinus blakei.

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