Showing papers on "Class (philosophy) published in 1971"

Quantification in query systems

Abstract: Questions which involve 'all', 'every', 'some', or the indefinite article, pose some peculiar problems when presented to a computerized question-answering system where ambiguities cannot be tolerated. These problems vary from the nature of the correct answer in special cases to the very admissibility of the question itself. To deal with these problems it is convenient to divide questions into two classes---extensional questions whose answers are to name things or truth values, intensional questions whose answers are to give meanings. This paper examines extensional questions. For these, the interpretative problems arising with 'all' and 'every' can be solved by introducing a new kind of quantification, extensional universal quantification, that has the meaning of 'all F' together with a secondary meaning that the class F is not empty. Formal rules for this quantification are given, and it is shown that the so-called definite formulas (which explicate permissible queries) are closed under the new operator.

The Content of Form: A Commentary

Abstract: s one could have anticipated, the essays before us vary in their content, if not in their form. Thus, Professor Chatman ("On j Defining 'Form' ") argues that every piece of discourse has a clearly identifiable content and form. The content is the message or reference--"not the language but what the language stands for, its reference"; and the form presumably is the specific way in which the message is expressed. Barthes's recent rejection of the distinction in favor of an identity of form (signifiant) and content (signifie), Chatman counters, establishes only their covariance, not their indistinguishability. Consequently, two literary works or a paraphrase of one literary work may retain the same content yet differ in their form. Form, he says, is a class term, with two subclasses: texture or small-scale form and structure or large-scale form. Shakespeare's first seventeen sonnets illustrate the contention that literary works have a form varying "around a more-or-less constant content .... That is, they share a relatively common message-the 'motive to procreation.' " In particular, it is the structure of the sonnetswhat Chatman calls the interplay of the syntax of English, the functional speech act system, and the metrics-which "keeps the repetition of the message from seeming tedious."

A characterization of k-ary algebraic categories

Abstract: Let k be a regular infinite cardinal number. A primitive (=equationally definable) class of algebras is called k-ary provided the algebras can be described in a specified way by means of operations whose arity is less than k. Such k-ary primitive classes of algebras (resp. k-ary varietal categories) have been characterized categorically by Lawvere [5] in case k = ℵo and by Linton [7], Felscher [1], and others in the general case. In this paper we propose a general definition of k-arity for arbitrary concrete categories, show that this concept is useful at least for algebraic categories, defined below, and coincides with the corresponding concept for varietal categories.

The Problem of Communication in Art Education: The Need for a Theory of Description

Abstract: In his Autobiography, Bertrand Russell relates that at one time he was completely baffled by the contradictory meanings implicit in the following words, written upon each side of a single sheet of paper: "The statement on the other side of this paper is false." Russell pondered the problem until realizing the resolution of apparent contradiction lay in an explanation of how the ambiguities of word structure and syntaxical order affect the meaning of philosophical statements. Thus a "Theory of Description" for verbal and written phenomena was formulated which accounted for seemingly contradictory statements in philosophical analysis. In the area of art education, as well as others, the salient statements of principle, definition, and technique require a modifying commentary so as to explain the distinctive operation of the elements of a sentence for our special purposes. In the sciences this notion of qualification and description of statements has been developed through the conception of theoretical models of behavior, such as those of quantum mechanics, which provide controls and a standard against which propositions in the field may be checked. It is, to sum up, a frame of reference problem and may be resolved to some extent by the creation of either a model of behavior with verbal correlation or a theoretical model of description which itself may be used for the formulation of general hypotheses in the field. Each discipline requires a manner of describing the particular verbal template through which it views the world. In art education, the necessary conditions for proposing a theory of description are evident. First, there is a lack of agreement by writers in the field as to the meaning of commonly used words and phrases. A sentence such as "The creative child expresses his artistic experience" is a complex proposition, the meaning of which is difficult to ascertain precisely because art educators lack a theoretical model for standardizing the verbal phenomena used in description. There is no general basis to appeal to for modifying common-usage words for the special requirements of art education. Terms such as "creative", "perception", "expression", and "artistic" are overlaid with multiple meanings, some more appropriate to art education than others. For example, consider the verb "to perceive". There are numerous acceptable meanings in ordinary usage; "to perceive" runs the definitional gamut from sensory impression to cognitive understanding. But would it not be helpful in art education if such multi-definitional words as "perceive" were categorically narrowed to apply to fewer cases of verbal phenomena? A suggestion proposed here for illustration might be to restrict the location of "perceive" to statements indicating visual scanning only, or to that class of behavior in which a person merely "looks" at objects without scrutinizing, analyzing, or identifying them for information. Thus art educators writing about observation of art works might distinguish the act of physically view-

Goodman's Languages of Art

Abstract: It is added that "the most literal portrait and the most prosaic passage are as much symbols, and as 'highly symbolic,' as the most fanciful and figurative" (p. xi). Is every painting and every piece of sculpture, whether representational or abstract or nonobjective, a symbol? Is a toy airplane a symbol? Is a mask? What about a doll, or a chess piece, or a lock of hair? I do not know what the answers to these questions are supposed to be: the author's usage is unclear. Goodman is concerned with "symbol systems." (He mentions that the word "languages" in the title of the book "should, strictly, be replaced by 'symbol systems' " [p. xii].) A symbol system "consists of a symbol scheme correlated with a field of reference" (p. I43). What then is a symbol scheme? "Any symbol scheme consists of characters" (p. I3I). And what are characters? "Characters are certain classes of utterances or inscriptions or marks" (p. I3i). The term "inscription" is used "to include utterances, and 'mark' to include inscriptions; an inscription is any mark-visual, auditory, etc.-that belongs to a character" (p. I31). So a symbol scheme consists of characters, where characters are certain classes of marks. If characters are "certain classes of marks," which classes are they? Goodman does not seem to say. If someone's boots make marks on a newly waxed floor, do those marks belong to a character? They do belong to the class of marks made by that person and the presence of such marks could be of significance. Does such a class constitute a character? Or suppose a house decorator is instructed to decorate a wall with three

Convex Iteration Procedures and a Related Class of Summability Methods.

Abstract: In this paper certain convex averaging procedures are investigated with the purpose of: (a) approximating fixed points of nonlinear nonexpansive mappings in uniformly convex spaces, (b) approximating solutions of certain linear operator equations in reflexive Banach spaces, and (c) summing divergent sequences and series in Banach spaces. Chapter I consists of preliminary material concern­ ing mappings in Banach spaces, abstract ergodic theory, summability theory and miscellaneous results. In Chapter II the iterative process

Dynamic Optimization of a Certain Class of Nonlinear Systems.

Abstract: In the dynamic optimization of linear systems, it is often easier to represent the system by its transfer function and proceed in the minimization scheme after taking full advantage of the fact that the partial fraction expansion yields a diagonalized system. The elements of the system matrix then represent the poles and the output is expressed as a linear combination of all the state variables. The poles are assummed to be distinct, thus allowing the system to be synthesised and only equality constraints are considered. This method of solution for the linear problem is important in both the formu­ lation of the nonlinear problem and in attempting to minimize a cost function for nonlinear feedback control systems with a nonlinearity in the feedback branch. Although present numerical techniques are available to obtain an open loop control for nonlinear systems, an exact solution for a closed loop control law is practically impossible. Even for the more simple cases, the Hamilton Jacobi Equation is extremely complex and only approximate solutions have been obtained for the control and the trajectories. In this study, a certain class of nonlinear systems is considered; one that yields an exact solution for the closed loop control u*(xjt) and limited studies for the open loop control and trajectories. A number of example problems are solved using the methods outlined. These examples show definitely that an exact solution may be obtained for the class of nonlinear systems in vi V consideration. Finally, the application of these methods of solution to nonlinear feedback systems provides an interesting study, particularly in the case of the nonlinear servomechanism problem. LIST OF FIGURES Page Figure 1. Diagram Illustrating Variable End Point 4 Problem * r \ Figure 2. Optimal Control Law u (x) for Example I 79 Figure 3Family of Optimal Trajectories for Example I 80 Figure Optimal Control Law u (x) for Example II 8l Figure 5« Family of Optimal Trajectories for Example II 82 Figure 6. Block Diagram of the Nonlinear System 85 Figure J. Block Diagram for the Nonlinear System 103 Figure 8. Block Diagram for the Nonlinear System 112 Figure 9» Block Diagram Representing the System 119