RUNNING HEAD : Levels of representation

This article describes a class of theories, the distinguishing characteristic of which is that elements of each of a series of representational systems (levels) are constructed from those of an immediately subordinate, qualitatively distinct, system. Each of these ascending levels of representation (LOR) succeeds in modeling attributes of the environment that are not captured by lower levels (emergent properties); and each ascending level provides correspondingly novel mechanisms for the control of behavior. The class of LOR theories has instantiations as diverse as Aristotle's multilevel conception of the soul, Pavlov's two signal systems, and Piaget's genetic epistemology. This article describes applications to human cognition and behavior of a 5-level LOR theory that is based on recent cognitive research. Address correspondence to: Anthony G. Greenwald Department of Psychology, NI-25 University of Washington Seattle, WA 98195 Draft initially submitted to Psychological Review, April 27, 1987 Revision submitted to Psychological Review, May 16, 1988 Note: This draft contains several figures that will need copyright holders' permissions for reproduction if they are used in a published version. Some of these may be replaced by new, original figures. For comments on an earlier draft, the author is grateful to David A. Balota, Leonard Berkowitz, Jerome S. Bruner, Fergus I. M. Craik, Russell H. Fazio, L. Rowell Huesmann, Earl B. Hunt, Ulric Neisser, Thomas O. Nelson, John R. Palmer, Michael I. Posner, Anthony R. Pratkanis, David L. Ronis, Shelley E. Taylor, Endel Tulving, Gifford Weary, Delos D. Wickens, and several anonymous reviewers. Date of draft: May 13, 1988 (This copy includes minor corrections to submitted version) RUNNING HEAD: Levels of representation Greenwald: Levels of representation (Draft of May 13, 1988) -2LEVELS OF REPRESENTATION Section I of this article describes a general framework for theories of mental representation. Some of the many theoretical precursors of this levels-of-representation (LOR) approach are reviewed in Section II. Section III presents a 5-level LOR theory that is proposed as a model of human representational abilities, and Section IV describes several applications of this theory. Section V contrasts the class of LOR theories with alternative paradigmatic frameworks for representation theory and notes further possibilities for application of this class of theories. I. Representations and Levels In simplest terms, representation is a relationship of reference between two entities, which can be designated representation and referent. Often, but not necessarily, the representation is produced from the referent, as an audio recording is from an orchestral performance, or a library catalog card from a book. The representation is typically more accessible than the referent, and therefore can serve as a proxy for the referent. (Considering a card in a library's catalog and the corresponding book on its shelves, the card generally serves as proxy for the book, even though the reversal of these roles is conceivable.) The sense in which a representation serves as proxy for its referent varies considerably, as is suggested by the following examples: Referent Representation phoneme letter person name of person tables, chairs, etc. word: "furniture" scene photograph research observations theoretical statements Representational systems. Isolated referent-representation pairs are theoretically less interesting than are collections that involve similar reference relations. Some examples are the collection of cards that represent library books (a catalog), the collection of letters that represent phonemes (an alphabet), and the collection of words that represent objects, actions, attributes, etc. (a lexicon). In such systems of representations, each component representation has a relation not only to its referent, but also to other representation elements in the system. Because the relations among representations depend on characteristics of the medium in which they reside, a system of representations can have properties that its collection of referents lacks. Representational media. A system of representations occupies some substrate, or medium. Properties of the medium afford operations that can be performed on its resident representations. Two representational systems that share the same name can be functionally very different because they reside in different media, and therefore afford very different operations. For the example of a library's catalog, the operations that can be performed on catalog elements residing in a digital electronic medium are very different from those that can be performed on cards in file drawers. Similarly, a digitally-recorded symphony can be manipulated in ways that are quite impossible for the same symphony in printed score form. Operations. An operation can be described either as a process that converts one representation into another, or as an n-ary relationship that is specified as a set of n-tuples of elements, which can be understood as the operation's input(s) and output(s) (see Roberts, 1979). For example, the operation of adding 1 to a binary coded 4-bit integer can be described either (a) as a process, by starting at the rightmost (least significant) bit and changing ones to zeros until the first zero is encountered, which is changed to one, or (b) as the set of pairs {(0000,0001), (0001,0010), . , (0111,1000), . , (1110,1111)}. Between-medium operations transform a representation in one medium into a representation in another -such as the Greenwald: Levels of representation (Draft of May 13, 1988) -3The average telephone number in an office building is equally an emergent property of a numerical representation scheme, but it does not appear to be a useful one. There is a considerable body of theory, including some controversy, concerning the conditions under which statements about numerical representations are meaningful (see Michell, 1986). operation of printing xa photographic negative from film to paper. Within-medium operations produce output in the same medium as the input resides -for example, the adding-1 operation just described. Emergent properties. Medium-afforded operations endow representations with functional properties. For example, frames of cinematic film can be subjected to the operation of projection onto a screen in sequence, producing for the viewer the property of an illusion of movement. Properties that result from operations on representations are emergent in one or both of two senses: (a) they are not apparent in the latent (non-operated-upon) state of the representational unit, and (b) there may be no corresponding property in the referent domain. For the film example, motion of the image in ordinary playback is emergent in the first sense. The use of numbers to represent dimensional attributes -such as temperatures, lengths, or weights -permits emergence in the second sense, of properties that are associated with arithmetic operations on numbers. For example, the average age of a group of persons is a property that emerges only by virtue of a system for numerically representing a sequence of days. Levels of Representation The functions of a system of representations have been described as depending on two types of operations on the system's representational units: between-medium and within-medium operations. It is a third, and less familiar, type of operation with which this article is primarily concerned -combinatorial operations on representations, functioning to construct relations between systems of representations. This third type of relation/operation affords the possibility of an interrelated hierarchy of representational systems -in other words, the possibility of a system of levels of representation (an LOR system). The units of the lowest level of an LOR system derive from a between-medium operation that links the representational system to its referent domain. Units of each higher level are produced by composition operations for which units of the immediately lower level serve as input. Composition operations are asymmetric, resulting in a hierarchical ordering of the levels. Elements of each composed (higher) level are mapped onto multiple elements of the composing (lower) level, and are thus more complex than those of the lower level. Operations that apply to units of one level of an LOR system are (by definition of levels) different from those that apply to units of any other. (Units that are subject to the same operations are considered to be at the same level.) Accordingly, the composition operations that construct units of level n+1 from multiple units of level n are different from those that construct units of level n from multiple units of level n-1. As a consequence, units of level n+1 are qualitatively different from those of level n and have novel emergent properties. Three interrelated identifying characteristics of an LOR system are, then: (a) composition operations that combine multiple units of one level to form single units of the next higher level, (b) qualitatively distinct representational units at each level, and (c) novel emergent properties at each ascending level. A suitable format for describing an LOR system is one in which these three characteristics are indicated, as in Figure 1. Figure 1. A generalized levels-of-representation system having 3 levels. Greenwald: Levels of representation (Draft of May 13, 1988) -4Computer Processor/Memory Example Perhaps the best known example of an LOR system is one for which the medium is a computer. Figure 2 summarizes the major characteristics of such a system, designated LORc4 ("c" is for computer, and "4" for the system's four levels). The units at the four levels of LORc4 are bits, constants, variables, and functions. The operations that define units at each ascending level combine multiple units of the immediately lower level, in a fashion affo