scholarly journals Bidirectional Functional Semantics for Pregroup Grammars

10.29007/2s3s ◽  
2018 ◽  
Author(s):  
Gabriel Gaudreault
Keyword(s):  
Semantic Analysis ◽  
Proper Subset ◽  
Function Composition ◽  
Reduction Strategy ◽  
Categorial Grammars ◽  
Pregroup Grammars ◽  
Functional Types ◽  
Left And Right ◽  
One To One

Pregroup grammars are a recent descendant of the original categorial grammars of Bar-Hillel [1] and Lambek [10] in which types take the form of strings of basic types and left and right adjoints, as opposed to the non-commutative functional types of categorial grammars. Whereas semantic extraction is possible in other categorial grammars through the λ-calculus, this approach will not be feasible for pregroup grammars. In this paper, we show how to build a term calculus that could be used to fill this void. This system is inspired by the λ-calculus but differs in crucial aspects: it uses function composition as its main reduction strategy instead of function application and is bidirectional, i.e. the direction arguments are applied to terms matters. We show how this term calculus is one- to-one with a proper subset of pregroup types and give multiple examples to show how this system could be used to do semantic analysis in parallel to doing grammaticality checks with pregroup grammars.

scholarly journals Mapping Integers and Hensel Codes Onto Farey Fractions

1982 ◽  
Vol 11 (149) ◽  
Author(s):  
Peter Kornerup ◽  
R. T. Gregory
Keyword(s):  
Proper Subset ◽  
Farey Fractions ◽  
Inverse Mapping ◽  
Mapping Problem ◽  
One To One

<p>The order-N Farey fractions, where N is the largest integer satisfying N&lt;= ˆ(p-1)/2, can be mapped onto a proper subset of the integers {0,1,...,p-1} in a one-to-one and onto fashion. However, no completely satisfactory algorithm for affecting the inverse mapping (the mapping of the integers back onto the order-N Farey fractions) appears in the literature.</p><p>A new algorithm for the inverse mapping problem is described which is based on the Euclidian Algorithm. This algorithm solves the inverse mapping problem for both integers and the Hensel codes.</p>

scholarly journals Left and Right Magnifying Elements in Generalized Semigroups of Transformations by Using Partitions of a Set

2018 ◽  
Vol 11 (3) ◽  
pp. 580-588
Author(s):  
Ronnason Chinram ◽  
Pattarawan Petchkaew ◽  
Samruam Baupradist
Keyword(s):  
Linear Transformation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Proper Subset ◽  
Transformation Semigroups ◽  
Left And Right ◽  
Necessary And Sufficient ◽  
Composition Of Functions

An element a of a semigroup S is called left [right] magnifying if there exists a proper subset M of S such that S = aM [S = Ma]. Let X be a nonempty set and T(X) be the semigroup of all transformation from X into itself under the composition of functions. For a partition P = {X_α | α ∈ I} of the set X, let T(X,P) = {f ∈ T(X) | (X_α)f ⊆ X_α for all α ∈ I}. Then T(X,P) is a subsemigroup of T(X) and if P = {X}, T(X,P) = T(X). Our aim in this paper is to give necessary and sufficient conditions for elements in T(X,P) to be left or right magnifying. Moreover, we apply those conditions to give necessary and sufficient conditions for elements in some generalized linear transformation semigroups.

scholarly journals On prime one-sided ideals, bi-ideals and quasi-ideals of a gamma ring

1992 ◽  
Vol 53 (1) ◽  
pp. 55-63 ◽  
Author(s):  
G. L. Booth ◽  
N. J. Groenewald
Keyword(s):  
Left Ideal ◽  
Prime Radical ◽  
Finitely Generated ◽  
Operator Ring ◽  
Left And Right ◽  
One To One

AbstractLet M be a Γ-ring with right operator ring R. We define one-sided ideals of M and show that there is a one-to-one correspondence between the prime left ideals of M and R and hence that the prime radical of M is the intersection of its prime left ideals. It is shown that if M has left and right unities, then M is left Noetherian if and only if every prime left ideal of M is finitely generated, thus extending a result of Michler for rings to Γ-rings.Bi-ideals and quasi-ideals of M are defined, and their relationships with corresponding structures in R are established. Analogies of various results for rings are obtained for Γ-rings. In particular we show that M is regular if and only if every bi-ideal of M is semi-prime.

scholarly journals The Meaning of Mono and EPI in Some Familiar Categories

1965 ◽  
Vol 8 (6) ◽  
pp. 759-769 ◽  
Author(s):  
W. Burgess
Keyword(s):  
Function Composition ◽  
Cancellation Property ◽  
Set Functions ◽  
One To One ◽  
The University ◽  
Set Function

This expository note was prompted by some questions asked by Professor P. Hilton during his lectures "Catégories non-abétiennes" at the University of Montréal, July 1964.The descriptions of set functions as one to one and as onto can be characterized in terms of set function composition. A set function is one to one iff it has the left cancellation property, that is, f · g = f · h implies g = h.

scholarly journals Left and Right Magnifying Elements in the Semigroup of all Binary Relations

2020 ◽  
Vol 13 (4) ◽  
pp. 987-994
Author(s):  
Watchara Teparos ◽  
Soontorn Boonta ◽  
Thitiya Theparod
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Proper Subset ◽  
Binary Relations ◽  
Left And Right ◽  
Necessary And Sufficient

An element a of a semigroup S is called left [right] magnifying if there exists a proper subset M of S such that S = aM [S = M a]. Let X be a nonempty set and BX the semigroup of binary relations on X. In this paper, we give necessary and sufficient conditions for elements in BX to be left or right magnifying.

scholarly journals SET SIZE AND THE PART–WHOLE PRINCIPLE

2013 ◽  
Vol 6 (4) ◽  
pp. 589-612 ◽  
Author(s):  
MATTHEW W. PARKER
Keyword(s):  
Recent Work ◽  
Cardinal Number ◽  
Proper Subset ◽  
Set Size ◽  
One To One

AbstractGödel argued that Cantor’s notion of cardinal number was uniquely correct. More recent work has defended alternative “Euclidean”' theories of set size, in which Cantor’s Principle (two sets have the same size if and only if there is a one-to-one correspondence between them) is abandoned in favor of the Part–Whole Principle (if A is a proper subset of B then A is smaller than B). Here we see from simple examples, not that Euclidean theories of set size are wrong, nor merely that they are counterintuitive, but that they must be either very weak or in large part arbitrary and misleading. This limits their epistemic usefulness.

The three-dimensional structure of frozen-hydrated left- and right-handed forms of bacterial flagellar filaments from an identical serotype

1986 ◽  
Vol 44 ◽  
pp. 298-299
Author(s):  
S. Trachtenberg ◽  
D. J. DeRosier
Keyword(s):  
Ionic Strength ◽  
Basal Body ◽  
Three Dimensional ◽  
Dimensional Structure ◽  
Protein Species ◽  
Liquid Environment ◽  
Bacterial Flagellum ◽  
Left And Right ◽  
Rotary Motor ◽  
Helical Parameters

The bacterial cell is propelled through the liquid environment by means of one or more rotating flagella. The bacterial flagellum is composed of a basal body (rotary motor), hook (universal coupler), and filament (propellor). The filament is a rigid helical assembly of only one protein species — flagellin. The filament can adopt different morphologies and change, reversibly, its helical parameters (pitch and hand) as a function of mechanical stress and chemical changes (pH, ionic strength) in the environment.

Advantages of Complementary Stereo Images as Viewed with the Low-Temperature Field-Emission SEM

1992 ◽  
Vol 50 (2) ◽  
pp. 1314-1315
Author(s):  
William P. Wergin ◽  
Eric F. Erbe
Keyword(s):  
Fold Increase ◽  
Horizontal Displacement ◽  
Three Dimensions ◽  
Stereo Image ◽  
Stereo Pair ◽  
Sem Micrograph ◽  
Left And Right ◽  
The Common ◽  
The Brain ◽  
Pair Analysis

The eye-brain complex allows those of us with normal vision to perceive and evaluate our surroundings in three-dimensions (3-D). The principle factor that makes this possible is parallax - the horizontal displacement of objects that results from the independent views that the left and right eyes detect and simultaneously transmit to the brain for superimposition. The common SEM micrograph is a 2-D representation of a 3-D specimen. Depriving the brain of the 3-D view can lead to erroneous conclusions about the relative sizes, positions and convergence of structures within a specimen. In addition, Walter has suggested that the stereo image contains information equivalent to a two-fold increase in magnification over that found in a 2-D image. Because of these factors, stereo pair analysis should be routinely employed when studying specimens.Imaging complementary faces of a fractured specimen is a second method by which the topography of a specimen can be more accurately evaluated.

Histological evaluation of cochlear hair cell damage from noise-induced hearing loss in chinchillas

1990 ◽  
Vol 48 (3) ◽  
pp. 332-333
Author(s):  
R.V. Harrison ◽  
R.J. Mount ◽  
P. White ◽  
N. Fukushima
Keyword(s):  
Hair Cell ◽  
Evoked Potential ◽  
Cell Damage ◽  
Acoustic Trauma ◽  
Histological Evaluation ◽  
Cell Integrity ◽  
Functional Changes ◽  
Cochlear Hair Cell ◽  
Left And Right ◽  
Contralateral Ear

In studies which attempt to define the influence of various factors on recovery of hair cell integrity after acoustic trauma, an experimental and a control ear which initially have equal degrees of damage are required. With in a group of animals receiving an identical level of acoustic trauma there is more symmetry between the ears of each individual, in respect to function, than between animals. Figure 1 illustrates this, left and right cochlear evoked potential (CAP) audiograms are shown for two chinchillas receiving identical trauma. For this reason the contralateral ear is used as control.To compliment such functional evaluations we have devised a scoring system, based on the condition of hair cell stereocilia as revealed by scanning electron microscopy, which permits total stereociliar damage to be expressed numerically. This quantification permits correlation of the degree of structural pathology with functional changes. In this paper wereport experiments to verify the symmetry of stereociliar integrity between two ears, both for normal (non-exposed) animals and chinchillas in which each ear has received identical noise trauma.

The crystallography characteristic of (Mn,Fe)S single crystal

1990 ◽  
Vol 48 (4) ◽  
pp. 898-899
Author(s):  
Jiang Xishan
Keyword(s):  
Single Crystal ◽  
Cast Steel ◽  
Point Group ◽  
Central Area ◽  
Hexagonal Crystal ◽  
Growth Step ◽  
Left And Right ◽  
Relationship Of ◽  
Fcc Structure ◽  
New Discovery

This paper reports the growth step pattern and morphology at equilibrium and growth states of (Mn,Fe)S single crystal on the wall of micro-voids in ZG25 cast steel by using scanning electron microscope. Seldom report was presented on the growth morphology and steppattern of (Mn,Fe)S single crystal.Fig.1 shows the front half of the polyhedron of(Mn,Fe)S single crystal,its central area being the square crystal plane,the two pairs of hexagons symmetrically located in the high and low, the left and right with a certain, angle to the square crystal plane.According to the symmetrical relationship of crystal, it was defined that the (Mn,Fe)S single crystal at equilibrium state is tetrakaidecahedron consisted of eight hexagonal crystal planes and six square crystal planes. The macroscopic symmetry elements of the tetrakaidecahedron correpond to Oh—n3m symmetry class of fcc structure,in which the hexagonal crystal planes are the { 111 } crystal planes group,square crystal plaits are the { 100 } crystal planes group. This new discovery of the (Mn,Fe)S single crystal provides a typical example of the point group of Oh—n3m.

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