Zero morphemes in paradigms

2020 ◽  
Vol 44 (1) ◽  
pp. 1-26
Author(s):  
Matthias Gerner ◽  
Zhang Ling
Keyword(s):  
Language Acquisition ◽  
Ordered Set ◽  
Neutral Element ◽  
Formal Definition ◽  
Minimal Elements ◽  
Totally Ordered Set ◽  
Lexical Relations ◽  
Inflectional Paradigms ◽  
The Way

Abstract This paper sheds a new light on the notion of zero morphemes in inflectional paradigms: on their formal definition (§ 1), on the way of counting them (§ 2–3) and on the way of conceptualizing them at a deeper, mathematical level (§ 4). We define (zero) morphemes in the language of cartesian set products and propose a method of counting them that applies the lexical relations of homophony, polysemy, allomorphy and synonymy to inflectional paradigms (§ 2). In this line, two homophonic or synonymous morphemes are different morphemes, while two polysemous and allomorphic morphemes count as one morpheme (§ 3). In analogy to the number zero in mathematics, zero morphemes can be thought of either as minimal elements in a totally ordered set or as neutral element in a set of opposites (§ 4). Implications for language acquisition are discussed in the conclusion (§ 5).

scholarly journals Language Acquisition in the Light of Rationalist Philosophy of Mind and Philosophy of Language

2016 ◽  
Vol 48 (1) ◽  
pp. 303-315
Author(s):  
Halina Święczkowska ◽  
Beata Piecychna
Keyword(s):  
Language Acquisition ◽  
Philosophy Of Mind ◽  
Cognitive Abilities ◽  
Philosophy Of Language ◽  
17Th Century ◽  
Human Beings ◽  
Speech Acquisition ◽  
The Way

Abstract The present study deals with the problem of the acquisition of language in children in the light of rationalist philosophy of mind and philosophy of language. The main objective of the paper is to present the way Gerauld de Cordemoy’s views on the nature of language, including its socio-linguistic aspects, and on the process of speech acquisition in children are reflected in contemporary writings on how people communicate with each other. Reflections on 17th-century rationalist philosophy of mind and the latest research conducted within the field of cognitive abilities of human beings indicate that between those two spheres many similarities could be discerned in terms of particular stages of the development of speech and its physical aspects.

ON RIBBON PRESENTATIONS OF RIBBON KNOTS

1994 ◽  
Vol 03 (02) ◽  
pp. 223-231
Author(s):  
TOMOYUKI YASUDA
Keyword(s):  
Partially Ordered Set ◽  
Ordered Set ◽  
Partially Ordered ◽  
Totally Ordered Set

A ribbon n-knot Kn is constructed by attaching m bands to m + 1n-spheres in the Euclidean (n + 2)-space. There are many way of attaching them; as a result, Kn has many presentations which are called ribbon presentations. In this note, we will induce a notion to classify ribbon presentations for ribbon n-knots of m-fusions (m ≥ 1, n ≥ 2), and show that such classes form a totally ordered set in the case of m = 2 and a partially ordered set in the case of m ≥ 1.

scholarly journals On the structure of the totally ordered set of unimodal cycles

2001 ◽  
Vol 25 (5) ◽  
pp. 323-329 ◽  
Author(s):  
Irene Mulvey
Keyword(s):  
Ordered Set ◽  
Totally Ordered Set

We continue the study of a class of unimodal cycles where each cycle in the class is forced by every unimodal cycle not in the class. For every order, we identify the cycle in the class of that order, which is maximal with respect to the forcing relation.

The π-Full Tight Riesz Orders on A(Ω)

1981 ◽  
Vol 24 (2) ◽  
pp. 137-151
Author(s):  
Gary Davis ◽  
Stephen H. McCleary
Keyword(s):  
Permutation Group ◽  
Ordered Set ◽  
Lattice Ordered Group ◽  
Ordered Group ◽  
Totally Ordered Set

Let G be a lattice-ordered group (l-group), and let t, u∈ G+. We write tπu if t ∧ g = 1 is equivalent to u ∧ g = 1, and say that a tight Riesz order T on G is π-full if t ∈ T and t π U imply u∈T. We study the set of π-full tight Riesz orders on an l-permutation group (G, Ω), Ω a totally ordered set.

A Representation Theorem for Distributive l-Monoids

1984 ◽  
Vol 27 (2) ◽  
pp. 238-240 ◽  
Author(s):  
Marlow Anderson ◽  
C. C. Edwards
Keyword(s):  
Group Theory ◽  
Representation Theorem ◽  
Ordered Set ◽  
Totally Ordered Set

AbstractIn this note the Holland representation theorem for l-groups is extended to l-monoids by the following theorem: an l-monoid is distributive if and only if it may be embedded into the l-monoid of order-preserving functions on some totally ordered set. A corollary of this representation theorem is that a monoid is right orderable if and only if it is a subsemigroup of a distributive l-monoid; this result is analogous to the group theory case.

scholarly journals Boundaries in digital planes

1990 ◽  
Vol 3 (1) ◽  
pp. 27-55 ◽  
Author(s):  
Efim Khalimsky ◽  
Ralph Kopperman ◽  
Paul R. Meyer
Keyword(s):  
Jordan Curve ◽  
Ordered Set ◽  
Continuous Functions ◽  
Jordan Curve Theorem ◽  
Connected Sets ◽  
Digital Plane ◽  
Parameter Interval ◽  
Totally Ordered Set ◽  
Definition Of ◽  
Natural Way

The importance of topological connectedness properties in processing digital pictures is well known. A natural way to begin a theory for this is to give a definition of connectedness for subsets of a digital plane which allows one to prove a Jordan curve theorem. The generally accepted approach to this has been a non-topological Jordan curve theorem which requires two different definitions, 4-connectedness, and 8-connectedness, one for the curve and the other for its complement.In [KKM] we introduced a purely topological context for a digital plane and proved a Jordan curve theorem. The present paper gives a topological proof of the non-topological Jordan curve theorem mentioned above and extends our previous work by considering some questions associated with image processing:How do more complicated curves separate the digital plane into connected sets? Conversely given a partition of the digital plane into connected sets, what are the boundaries like and how can we recover them? Our construction gives a unified answer to these questions.The crucial step in making our approach topological is to utilize a natural connected topology on a finite, totally ordered set; the topologies on the digital spaces are then just the associated product topologies. Furthermore, this permits us to define path, arc, and curve as certain continuous functions on such a parameter interval.

The adaptation of French liquids in Haitian

2018 ◽  
Vol 33 (2) ◽  
pp. 386-410
Author(s):  
Benjamin Storme
Keyword(s):  
Second Language ◽  
Second Language Acquisition ◽  
Language Acquisition ◽  
Sound Change ◽  
Loanword Adaptation ◽  
Perceptual Asymmetry ◽  
The Way

Abstract Haitian, a French-lexifier creole with a Gbe substrate, shows an asymmetry in the way it has adapted French liquids: the French lateral was maintained in postvocalic coda position in Haitian, but the French rhotic was systematically deleted in this position. This paper presents the results of a perception study showing that the lateral is generally more perceptible than the rhotic in coda position in Modern French. The hypothesis that perception played a role in the phonological asymmetry in Haitian is compatible with these results. The paper sketches an analysis of how the perceptual asymmetry between French coda laterals and rhotics resulted in the emergence of a new phonological grammar, distinct from both the grammar of the substrate and superstrate languages. This analysis is in line with previous works on the role of perception in second language acquisition, loanword adaptation, creolization, and sound change more generally.

scholarly journals Rigidity in order-types

1977 ◽  
Vol 24 (2) ◽  
pp. 203-215 ◽  
Author(s):  
J. L. Hickman
Keyword(s):  
Ordered Set ◽  
Characterization Theorem ◽  
Decomposition Theorem ◽  
Order Type ◽  
Partial Ordering ◽  
Limit Laws ◽  
Order Types ◽  
Totally Ordered Set ◽  
The Axiom Of Choice ◽  
Increasing Sequences

AbstractA totally ordered set (and corresponding order-type) is said to be rigid if it is not similar to any proper initial segment of itself. The class of rigid ordertypes is closed under addition and multiplication, satisfies both cancellation laws from the left, and admits a partial ordering that is an extension of the ordering of the ordinals. Under this ordering, limits of increasing sequences of rigid order-types are well defined, rigid and satisfy the usual limit laws concerning addition and multiplication. A decomposition theorem is obtained, and is used to prove a characterization theorem on rigid order-types that are additively prime. Wherever possible, use of the Axiom of Choice is eschewed, and theorems whose proofs depend upon Choice are marked.

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