scholarly journals On Katz-Postal integrated theory of linguistic descriptions

Author(s):  
Snježana Smodlaka

In 1963 J. J. Katz and J. A. Fodor in their »The Structure of a Semantic Theory« encouraged semantic studies and proposed to consider semantics as an integral part of generative grammar. Next year J. J. Katz and P. M. Postal in »An Integrated Theory of Linguistic Description« tried to integrate generative concepts of phonology and syntax proposed by Chomsky with semantics; they also aimed to provide an adequate means of incorporating grammatical and semantic description of a language into one integrated description. Of the three components of any linguistic description syntactic component represents generative source, generates the abstract formal structures that underlie actual sentence; semantic and phonological components operate on the syntactic output, perform independent operations on the syntactic structures and provide respectively semantic interpretation and phonological representation to each of the formal structures generated by the syntactic component. The syntactic component must be a system of rules that enumerates the infinite set of abstract formal structures; the rules assign one or more structural descriptions to each sitring of formatives. The semantic component consists of a dictionary, containing meanings of each lexical item of a language, and a finite set of projection rules. String of formatives is given the meaning from the dictionary; projection rules provide semantic interpretation of each element of the string, combining the meanings according to the syntactic description of the string. This paper explains their theory and proceedings in detail.

2007 ◽  
pp. 169-183
Author(s):  
Irena Szczepankowska

In the article the Author poses a question concerning the understanding of the term "concept" (syn. "notion") in linguistics - its status as a subject of a semantic description ("concept" in relation to "meaning") and as an element of metalanguage. She confronts the earlier structuralist perspective originating from logic with more recent ones used in psychology and cognitive linguistics, in which the meaning of linguistic units is equated directly with a notion as a mental conceptualisation and in fact as a conceptualisation process. The most important novum in the cognitive understanding of a "concept" as a subject of linguistic description is, according to the Author, the renunciation of the classical perspective (a conceptual category as "a set of features reserved for a class of items") and demystification - especially with reference to popular categories - its ostensibly objective static nature. A notion is treated as an area of knowledge organised (profiled) in a special manner at the background of the whole network of cognitive relations, that is embracing also elements of emotions, valuation, perspective and interaction of conceptualisers. Creating notions and encoding them in language thus requires other methods of representing the meaning of linguistic units than those well-grounded in linguistics under the influence of logical semantics - so that the descriptions refer not only to the designatum but also to the cognising entity.


Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3074
Author(s):  
Cristian Preda ◽  
Quentin Grimonprez ◽  
Vincent Vandewalle

Categorical functional data represented by paths of a stochastic jump process with continuous time and a finite set of states are considered. As an extension of the multiple correspondence analysis to an infinite set of variables, optimal encodings of states over time are approximated using an arbitrary finite basis of functions. This allows dimension reduction, optimal representation, and visualisation of data in lower dimensional spaces. The methodology is implemented in the cfda R package and is illustrated using a real data set in the clustering framework.


Author(s):  
Joseph Mazur

This chapter traces the beginnings of mathematical notation. For tens of thousands of years, humans had been leaving signification marks in their surroundings, gouges on trees, footprints in hard mud, scratches in skin, and even pigments on rocks. A simple mark can represent a thought, indicate a plan, or record a historical event. Yet the most significant thing about human language and writing is that speakers and writers can produce a virtually infinite set of sounds, declarations, notions, and ideas from a finite set of marks and characters. The chapter discusses the emergence of the alphabet, counting, and mathematical writing. It also considers the discovery of traces of Sumerian number writing on clay tablets in caves from Europe to Asia, the use of Egyptian hieroglyphics, and algebra problems in the Rhind (or Ahmes) papyrus that presented simple equations without any symbols other than those used to indicate numbers.


2002 ◽  
Vol 67 (3) ◽  
pp. 1078-1082
Author(s):  
Carl G. Jockusch ◽  
Tamara J. Lakins

AbstractFor X ⊆ ω, let [X]n denote the class of all n-element subsets of X. An infinite set A ⊆ ω is called n-r-cohesive if for each computable function f: [ω]n → {0, 1} there is a finite set F such that f is constant on [A − F]n. We show that for each n > 2 there is no Πn0 set A ⊆ ω which is n-r-cohesive. For n = 2 this refutes a result previously claimed by the authors, and for n ≥ 3 it answers a question raised by the authors.


Author(s):  
J. M. Hammersley

Let G be an infinite partially directed graph of finite outgoing degree. Thus G consists of an infinite set of vertices, together with a set of edges between certain prescribed pairs of vertices. Each edge may be directed or undirected, and the number of edges from (but not necessarily to) any given vertex is always finite (though possibly unbounded). A path on G from a vertex V1 to a vertex Vn (if such a path exists) is a finite sequence of alternate edges and vertices of the form E12, V2, E23, V3, …, En − 1, n, Vn such that Ei, i + 1 is an edge connecting Vi and Vi + 1 (and in the direction from Vi to Vi + 1 if that edge happens to be directed). In mixed Bernoulli percolation, each vertex Vi carries a random variable di, and each edge Eij carries a random variable dij. All these random variables di and dij are mutually independent, and take only the values 0 or 1; the di take the value 1 with probability p, while the dij take the value 1 with probability p. A path is said to be open if and only if all the random variables carried by all its edges and all its vertices assume the value 1. Let S be a given finite set of vertices, called the source set; and let T be the set of all vertices such that there exists at least one open path from some vertex of S to each vertex of T. (We imagine that fluid, supplied to all the source vertices, can flow along any open path; and thus T is the random set of vertices eventually wetted by the fluid). The percolation probabilityis defined to be the probability that T is an infinite set.


1985 ◽  
Vol 31 (3) ◽  
pp. 325-328
Author(s):  
Choo-Whan Kim

On a set X, let μ* be an outer measure and μ the measure induced by μ*. We show that if X is a finite set, then the measure μ is saturated. We give two examples of non-regular outer measures on an infinite set X which induce non-saturated and saturated measures, respectively. These answer a query posed by Wilansky.


2009 ◽  
pp. 2915-2942
Author(s):  
Yingxu Wang

Deductive semantics is a novel software semantic theory that deduces the semantics of a program in a given programming language from a unique abstract semantic function to the concrete semantics embodied by the changes of status of a finite set of variables constituting the semantic environment of the program. There is a lack of a generic semantic function and its unified mathematical model in conventional semantics, which may be used to explain a comprehensive set of programming statements and computing behaviors. This article presents a complete paradigm of formal semantics that explains how deductive semantics is applied to specify the semantics of real-time process algebra (RTPA) and how RTPA challenges conventional formal semantic theories. Deductive semantics can be applied to define abstract and concrete semantics of programming languages, formal notation systems, and large-scale software systems, to facilitate software comprehension and recognition, to support tool development, to enable semantics-based software testing and verification, and to explore the semantic complexity of software systems. Deductive semantics may greatly simplify the description and analysis of the semantics of complicated software systems specified in formal notations and implemented in programming languages.


2008 ◽  
Vol 18 (02) ◽  
pp. 209-226 ◽  
Author(s):  
VITALY ROMAN'KOV

Let K be a field of any characteristic. We prove that a free metabelian Lie algebra M3 of rank 3 over K admits wild automorphisms. Moreover, the subgroup I Aut M3 of all automorphisms identical modulo the derived subalgebra [Formula: see text] cannot be generated by any finite set of IA-automorphisms together with the sets of all inner and all tame IA-automorphisms. In the case if K is finite the group Aut M3 cannot be generated by any finite set of automorphisms together with the sets of all tame, all inner automorphisms and all one-row automorphisms. We present an infinite set of wild IA-automorphisms of M3 which generates a free subgroup F∞ modulo normal subgroup generated by all tame, all inner and all one-row automorphisms of M3.


2020 ◽  
Vol 14 (1) ◽  
pp. 94-119
Author(s):  
Bartosz Stopel

AbstractThe article traces the relationship between what is called surface, aesthetic interpretation and deep, semantic, theory-driven interpretation of literature. The former is identified with how interpretation is typically understood in analytic philosophy of art, whereas the latter as belonging to continental literary theory, thus framing the discussion within the relevant debates that the two eminent philosophical schools engage in. Specifically, the article argues in favor of a number of claims. It discusses the notion of surface interpretation, understood as the informed practice involved in general attention to a literary work with an aim of attaining an aesthetically rewarding experience (appreciation). Surface interpretation locates a literary work in a specific art-historical context and at minimum acknowledges the author’s categorial intentions pertinent to genre, general aims and representational content of the work. The article also argues against the notion that appreciation, which is supposed to be the main aim of surface interpretation, is purely perceptual (Carroll, Lamarque) and that consequently aesthetic experience does not involve affective experiences. Grounding appreciation in affective experiences (Levinson) leads me to acknowledge an important continuity between fully formed aesthetic experience and more instinctive or »effortless« ways of attending to a work, such as when one »just enjoys« the emotions afforded by, say, a horror story rather than with full aesthetic attention to the work, where the affective component dominates, but which are less structured to be properly called aesthetic within the conceptual framework I offer here. As a result, I divide the pleasures of attending to an artwork into the instinctive, hedonic ones and the properly aesthetic ones, which both constitute two basic modes of reading. The aesthetic mode is not fully separate from the hedonic one, but on the contrary, by tapping directly into the hardwired human cognitive-affective architecture, it provides a general framework and parameters for the emergence of the higher-order aesthetic mode where more prominence is given to art-historical knowledge and more attention to the design and form/content interrelation. Importantly, aesthetic mode does not operate with the absence of the hedonic one, though they can simultaneously produce different evaluations (e. g. hedonically positive, aesthetically/artistically negative). The two modes could be said to have distinct model readers with corresponding levels of competence. The hedonic reader, as opposed to the aesthetic one, would be largely oblivious to art-historical contexts and would be more selective in terms of attention to the work, relying on direct affect-triggering textual cues. Interpretive effort would be reduced, too. I also discuss my model with reference to the psycho-historical framework for the study of art appreciation as developed by Bullot and Reber which attempts to explain how art responders acquire more complex types of attention to the work, or stances, from mere exposure to the work’s perceptual content to tracing causal history and integrating historical contexts into a more rounded approach to art appreciation. An important part of my argument is the indication that non-habitual pattern isolation responsible for identifying structures, interrelations between a work’s elements and forming predictions about its development in the process of reading is a crucial component of aesthetic experience. Next, I move on to discuss deep interpretation, which typically is seen as miles apart from aesthetic interpretation. It is sometimes assumed that deep, semantic interpretation disregards surface interpretation, including authorial intentions and art-historical contexts and emphasizes reader’s active, playful role in generating an unconstrained swirl of connotations. Such a practice is seen either as being a source of bliss (Barthes) or as a purely intellectual pursuit attempting at enhancing the understanding of the work (Sontag). I argue against all three views and integrate deep interpretation into the model sketched so far. Seeing deep interpretation as unconstrained and purposeless (Lamarque) is an uncharitable straw man. Such a vision would render semantic interpretation unintelligible and random, but this is not the case. By looking into some examples taken from Roland Barthes’ own work which is one of the foundations of modern theory-driven interpretation, I argue that despite his bombastic claims, he is unable to start his deep interpretation project without acknowledging categorial intentions and art-historical context of the work’s creation. Consequently, and comparing his views to contemporary debates on work, authorship, intentions and aesthetics, his work is an attack on a rather dated understanding of these concepts. Theory-driven interpretation can be flawed or stretched, if it does not pay its dues to surface interpretation. Next, I argue that both surface and deep interpretation operate according to the principles of value-maximization (Davies) which can override author’s intentions about the details of her work’s meaning. Using a specific theoretical framework in deep interpretation is an extension of the non-habitual patterns isolation principle and serves to enhance the experience of the work by trying to recognize more pattern that add up to the work’s complexity while remaining faithful to the work’s basic contents. Taking up the semantic reading stance already entails taking up the underlying aesthetic and, more distantly, hedonic stances. In the end, theory-driven interpretation forms the third reading mode which emerges with a correspondingly more competent model reader from the partly-constraining aesthetic mode.


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