The concept of representation has been a key element in the scientific study of mental processes, ever since such studies commenced. However, usage of the term has been all but too liberal—if one were to adhere to common use it remains unclear if there are examples of physical systems which cannot be construed in terms of representation. The problem is considered afresh, taking as the starting point the notion of activity spaces—spaces of spatiotemporal events produced by dynamical systems. (...) It is argued that representation can be analyzed in terms of the geometrical and topological properties of such spaces. Several attributes and processes associated with conceptual domains, such as logical structure, generalization and learning are considered, and given analogues in structural facets of activity spaces, as are misrepresentation and states of arousal. Based on this analysis, representational systems are defined, as is a key concept associated with such systems, the notion of representational capacity. According to the proposed theory, rather than being an all or none phenomenon, representation is in fact a matter of degree—that is can be associated with measurable quantities, as is behooving of a putative naturalistic construct. (shrink)

The introduction of connectionist or parallel distributed processing (PDP) systems to model cognitive functions has raised the question of the possible relations between these models and traditional information processing models which employ rules to manipulate representations. After presenting a brief account of PDP models and two ways in which they are commonly interpreted by those seeking to use them to explain cognitive functions, I present two ways one might relate these models to traditional information processing models and so not (...) totally repudiate the tradition of modelling cognition through systems of rules and representations. The proposal that seems most promising is that PDP-type structures might provide the underlying framework in which a rule and representation model might be implemented. To show how one might pursue such a strategy, I discuss recent research by Barsalou on the instability of concepts and show how that might be accounted for in a system whose microstructure had a PDP architecture. I also outline how adopting a multi-leveled view of the mind, where on one level the mind employed a PDP-type system and at another level constituted a rule processing system, would allow researchers to relocate some problems which seemed difficult to explain at one level, such as the capacity for concept learning, to another level where it could be handled in a straightforward manner. (shrink)

In this paper, it will be argued that each time a procedure in a representational system is functioning adequately and automatically, the child steps up to a metaprocedural level and considers the procedure as a unit in its own right. Data will be drawn from microdevelopment in children's creation of external memory devices (i.e., changes in representation of a spatial task during a one hour's session) as well as from macrodevelopment in language acquisition (i.e., changes occurring over age in (...) a study of nominal determiners, pronouns and gender markers). These two aspects of development of representational systems are examined with respect to the spontaneous passage from concrete reference to abstract systems, from idiosyncratic to conventional notations, from redundant to economic marking, from unifunctional to plurifunctional meaningful units. These micro‐ and manodevelopmental changes take place in a spontaneous fashion despite the fact that the child's earlier system is adequate for successfully conveying the information required. A discussion will be made of the way in which children tend to indicate externally, by unifunctional markers, information which was implicit in their earlier use of an adult‐like system. They appear to be striving for the delicate balance between encoding and decoding efforts, ultimately leading to a felicitous representational system. Metaprocedural behavior is hypothesized to act as a control mechanism in the striving for this delicate balance of information content and information processing effort. It also appears to act as a control mechanism for the interprocedural organizotion of what was previously a plethora of juxtaposed, unconnected procedures yielding superficially analogous behavior. The stepping‐up to a metaprocedural level seems to occur each time the child has a handle on his currently functioning, goal‐oriented system. This enables the child to treat the system, or procedures which are part thereof, as units functioning in their own right. Thus there appears to be a deep‐rooted psychological tendency for a representational tool which functions well procedurally to become subsequently a problem‐space per se. (shrink)

Positing the importance of sensorimotor contingencies for perception is by no means denying the presence and importance of representations. Using the evidence of mirror neurons we will show the intrinsic relationship between action control and representation within the logic of forward models.

Six characteristics of effective representational systems for conceptual learning in complex domains have been identified. Such representations should: (1) integrate levels of abstraction; (2) combine globally homogeneous with locally heterogeneous representation of concepts; (3) integrate alternative perspectives of the domain; (4) support malleable manipulation of expressions; (5) possess compact procedures; and (6) have uniform procedures. The characteristics were discovered by analysing and evaluating a novel diagrammatic representation that has been invented to support students' comprehension of electricity—AVOW diagrams (Amps, (...) Volts, Ohms, Watts). A task analysis is presented that demonstrates that problem solving using a conventional algebraic approach demands more effort than AVOW diagrams. In an experiment comparing two groups of learners using the alternative approaches, the group using AVOW diagrams learned more than the group using equations and were better able to solve complex transfer problems and questions involving multiple constraints. Analysis of verbal protocols and work scratchings showed that the AVOW diagram group, in contrast to the equations group, acquired a coherently organised network of concepts, learnt effective problem solving procedures, and experienced more positive learning events. The six principles of effective representations were proposed on the basis of these findings. AVOW diagrams are Law Encoding Diagrams, a general class of representations that have been shown to support learning in other scientific domains. (shrink)

In this paper, it will be argued that each time a procedure in a representational system is functioning adequately and automatically, the child steps up to a metaprocedural level and considers the procedure as a unit in its own right. Data will be drawn from microdevelopment in children's creation of external memory devices (i.e., changes in representation of a spatial task during a one hour's session) as well as from macrodevelopment in language acquisition (i.e., changes occurring over age in (...) a study of nominal determiners, pronouns and gender markers). These two aspects of development of representational systems are examined with respect to the spontaneous passage from concrete reference to abstract systems, from idiosyncratic to conventional notations, from redundant to economic marking, from unifunctional to plurifunctional meaningful units. These micro‐ and manodevelopmental changes take place in a spontaneous fashion despite the fact that the child's earlier system is adequate for successfully conveying the information required. A discussion will be made of the way in which children tend to indicate externally, by unifunctional markers, information which was implicit in their earlier use of an adult‐like system. They appear to be striving for the delicate balance between encoding and decoding efforts, ultimately leading to a felicitous representational system. Metaprocedural behavior is hypothesized to act as a control mechanism in the striving for this delicate balance of information content and information processing effort. It also appears to act as a control mechanism for the interprocedural organizotion of what was previously a plethora of juxtaposed, unconnected procedures yielding superficially analogous behavior. The stepping‐up to a metaprocedural level seems to occur each time the child has a handle on his currently functioning, goal‐oriented system. This enables the child to treat the system, or procedures which are part thereof, as units functioning in their own right. Thus there appears to be a deep‐rooted psychological tendency for a representational tool which functions well procedurally to become subsequently a problem‐space per se. (shrink)

Six characteristics of effective representational systems for conceptual learning in complex domains have been identified. Such representations should: (1) integrate levels of abstraction; (2) combine globally homogeneous with locally heterogeneous representation of concepts; (3) integrate alternative perspectives of the domain; (4) support malleable manipulation of expressions; (5) possess compact procedures; and (6) have uniform procedures. The characteristics were discovered by analysing and evaluating a novel diagrammatic representation that has been invented to support students' comprehension of electricity—AVOW diagrams (Amps, (...) Volts, Ohms, Watts). A task analysis is presented that demonstrates that problem solving using a conventional algebraic approach demands more effort than AVOW diagrams. In an experiment comparing two groups of learners using the alternative approaches, the group using AVOW diagrams learned more than the group using equations and were better able to solve complex transfer problems and questions involving multiple constraints. Analysis of verbal protocols and work scratchings showed that the AVOW diagram group, in contrast to the equations group, acquired a coherently organised network of concepts, learnt effective problem solving procedures, and experienced more positive learning events. The six principles of effective representations were proposed on the basis of these findings. AVOW diagrams are Law Encoding Diagrams, a general class of representations that have been shown to support learning in other scientific domains. (shrink)

In this paper, we develop primitive recursive analogues of regular cardinals by using ordinal representation systems for KPi and KPM. We also define primitive recursive analogues of inaccessible and hyperinaccessible cardinals. Moreover, we characterize the primitive recursive analogue of the least (uncountable) regular cardinal.

There are various approaches to ontology metamodelling, and the notion of biologically inspired modular knowledge representation systems can provide insight in the workings of such phenomena as emergent properties of network structures. What is more relevant from knowledge engineering standpoint, such approach could provide innovation and enhancement of the level of expression as well as overall functionality of modular ontologies. To do so, one needs to find biological structures that would be the basis for modularity on different levels of (...) hierarchy within the artificial system. Network analysis tools as well as systems biology and biocomputing provide a framework for research in this field. (shrink)

The possibility of ideography is an empirical question. Prior examples of graphic codes do not provide compelling evidence for the infeasibility of ideography, because they fail to satisfy essential cognitive requirements that have only recently been revealed by studies of representational systems in cognitive science. Design criteria derived from cognitive principles suggest how effective graphic codes may be engineered.

o formalization of intensional functions was made for the purpose of many-valued interpretation of the belief-operators within the scope of the classical logic system. The first aim of the paper is to present and discuss this rather unknown many-valued construction and its properties. The fact that the manyvaluedness of o systems is purely formal - their characteristic matrices are Boolean - calls for further consideration. Departing from intristic similarities of the tables for the epistemic operators to the information functions (...) we show that o structures may be rewritten as special knowledge representation systems. These systems use 0 and 1 as the only values and are called “epistemic”. Their role for the theory of knowledge information systems may be compared to that of the functionally complete matrices in the class of all logical matrices for a given propositional language. (shrink)

A duality between Pawlak's knowledge representation systems and certain information systems of logical type, called bi-consequence systems is established. As an application a first-order characterization of some informational relations is given and a completeness theorem for the corresponding modal logic INF is proved. It is shown that INF possesses finite model property and hence is decidable.

En este trabajo se define formamente el concepto de representacion en química utilizando homomorfismos desde estructuras algebraicas, que llamamos sistemas de tipo C, en otras estructuras especiales de símbolos muy relacionados con los que son habituales en la qímica experimental. Para la definicion de los sistemas de tipo C se ha seleccionado un conjunto minimo de relaciones y funciones, que son necesarias para expresar proposiciones significativas en química. Tambien se define un lenguaje formal de primer orden adecuado a los sistemas (...) de tipo C, que llamamos L(C). EI resultado principal que se demuestra es que toda representación que verifica las mismas sentencias de L(C) que un sistema de tipo C, es necesariamente isomorfo a él. Se concluye por lo tanto que puede existir un problema linguístico subyacente en la aplicacion que de la mecaníca cuántica se hace en la química teórica.The concept of representation in chemistry bas been formallv defined by means of homomorphisms from algebraical structures, which we call type-C systems, to some special sets of symbols which can be related to the symbols ordinarily used in experimental chemistry. A minimum number of relations and functions, which would suffice to express significant propositions in chemistry, have been chosen to define type-C systems. A first order formal language L(C) adequate to type-C systems has been defined. It has been shown that each representation that verifies the same sentences of L(C) as a type-C system is necessarily isomorphic to it. It is concluded that a systematic study of the representation problem in chemistry is in order because a deep language problem underlies the application of quantum mechanies to chemical problems. (shrink)

Though capturing powerful analytical principles, this excellent article misses ways in which psychology and neuroscience bear on reciprocity and decision-making. I suggest more explicit consideration of scale. We may go further beyond gene-culture dualism by articulating how varieties of living systems, while ultimately drawing from both genetic and cultural streams, evolve sufficiently as unitary targets of selection to mediate higher-level complex systems. (Published Online April 27 2007).

In this article, network science is discussed from a methodological perspective, and two central theses are defended. The first is that network science exploits the very properties that make a system complex. Rather than using idealization techniques to strip those properties away, as is standard practice in other areas of science, network science brings them to the fore, and uses them to furnish new forms of explanation. The second thesis is that network representations are particularly helpful in explaining the properties (...) of non-decomposable systems. Where part-whole decomposition is not possible, network science provides a much-needed alternative method of compressing information about the behavior of complex systems, and does so without succumbing to problems associated with combinatorial explosion. The article concludes with a comparison between the uses of network representation analyzed in the main discussion, and an entirely distinct use of network representation that has recently been discussed in connection with mechanistic modeling. (shrink)

There is disagreement over the notion of representation in cognitive science. Many investigators equate representations with symbols, that is, with syntactically defined elements in an internal symbol system. In recent years there have been two challenges to this orthodoxy. First, a number of philosophers, including many outside the symbolist orthodoxy, have argued that "representation" should be understood in its classical sense, as denoting a "stands for" relation between representation and represented. Second, there has been a growing challenge to orthodoxy under (...) the banner of connectionism. Although this connectionist challenge has evoked emotionally-charged rebukes from the symbolist camp, connectionists as a group have not articulated a conception of representation to replace the symbolist view. Nonetheless, most agree on the need for a nonsymbolic notion of representation. This paper advances a "stands for" sense of representation as primary by incorporating it into a general approach to cognitive science consonant with the connectionism. The idea is to marry connectionism to a particular version of functionalism, viz., one that builds its notion of "function" on the similarity between functional analysis in biology and in psychology. It builds on my earlier work adapting and revising Marr's tri-level approach to cognition. My proposal frees Marr's analysis from its moorings in the orthodox symbolic view of representation and allies it with a notion of functional analysis akin to that proposed by Cummins, developed further by Haugeland, and invoked by Millikan and Dretske. Unlike these authors, however, I do not wed representation to a general belief-desire analysis of behavior. Rather, I follow what I take to be the lesson of psychological practice, according to which the investigator does not seek to explain behavior in general but seeks to analyze the cognitive capacities that underlie behavior, such as vision, memory, learning, and linguistic capacities. Accordingly, ascriptions of representational content are made not by working back from belief-desire ascriptions, but in the context of forming psychological models to account for specific cognitive capacities. Because conceptions of representation in cognitive science typically are embedded in a general approach to the study of cognition, arguments for the comparative plausibility of a particular conception of representation must scout these larger frameworks. I therefore begin by characterizing the interlocking set of assumptions that gave life to the orthodox symbolist approach, paying special attention to the complementarity between representation and process that naturally arises from those assumptions. I then consider two versions of an alternative approach to representation: Dretske's and my own. Finally, I urge the merits of the "cognitive capacities" over the "belief-desire" approach to the subject-matter of cognitive science. (shrink)

The concept of representation has become almost inextricably bound to the concept of symbol systems. the concepts is nowhere more prevalent than in descriptions of "internal representations." These representations are thought to occur in an internal symbol system that allows the brain to store and use information. In this paper we explore a different approach to understanding psychological processes, one that retains a commitment to representations and computations but that is not based on the idea that information must be (...) stored and manipulated in symbol systems. In particular, we suggest that the notion of a symbol system as currently understood construes psychological processes in terms of a specific type of computational system, in which a control function "reads," "interprets," and manipulates discrete entities called "symbols." We argue that other types of computational systems may provide a more appropriate characterization of psychological processes. One implication of our argument is the need to consider the constraints placed on computational theories in psychology by the nature of the computing device itself, the human brain. Perhaps surprisingly, this implication leads us to the conclusion that a "functionalist" conception of psychological processes (discussed below) does not entail that physiology is irrelevant to psychology, as has been maintained by prominent adherents of the symbol-systems approach. (shrink)

"The Natural System" is the abstract notion of the order in living diversity. The richness and complexity of this notion is revealed by the diversity of representations of the Natural System drawn by ornithologists in the Nineteenth Century. These representations varied in overall form from stars, to circles, to maps, to evolutionary trees and cross-sections through trees. They differed in their depiction of affinity, analogy, continuity, directionality, symmetry, reticulation and branching, evolution, and morphological convergence and divergence. Some representations were two-dimensional, (...) and some were three-dimensional; n-dimensional representations were discussed but never illustrated. The study of diagrammatic representations of the Natural System is made difficult by the frequent failure of authors to discuss them in their texts, and by the consequent problem of distinguishing features which carried meaning from arbitrary features and printing conventions which did not. Many of the systematics controversies of the last thirty years have their roots in the conceptual problems which surrounded the Natural System in the late 1800s, problems which were left unresolved when interest in higher-level systematics declined at the turn of this century. (shrink)

There is ongoing controversy as to whether the genome is a representing system. Although it is widely recognised that DNA carries information, both correlating with and coding for various outcomes, neither of these implies that the genome has semantic properties like correctness or satisfaction conditions, In the Scope of Logic, Methodology, and the Philosophy of Sciences, Vol. II. Kluwer, Dordrecht, pp. 387–400). Here a modified version of teleosemantics is applied to the genome to show that it does indeed have semantic (...) properties – there is representation in the genome. The account differs in three respects from previous attempts to apply teleosemantics to genes. It emphasises the role of the consumer of representations. It rejects the standard assumption that genetic representation can be used to explain the course of an organism’s development. And it identifies the explanatory role played by representational properties of the genome. A striking consequence of this account is that other inheritance systems could also be representational. Thus, a version of the parity thesis is accepted. However, the criteria for being an inheritance system are demanding, so semantic properties are not ubiquitous. (shrink)

Developmental Systems Theory (DST) emphasises the importance of non-genetic factors in development and their relevance to evolution. A common, deflationary reaction is that it has long been appreciated that non-genetic factors are causally indispensable. This paper argues that DST can be reformulated to make a more substantive claim: that the special role played by genes is also played by some (but not all) non-genetic resources. That special role is to transmit inherited representations, in the sense of Shea (2007: Biology (...) and Philosophy, 22, 313-331). Formulating DST as the claim that there are non-genetic inherited representations turns it into a striking, empirically-testable hypothesis, driving the sort of investigations that are only now beginning to appear in the scientific literature. DST’s characteristic rejection of a gene vs. environment dichotomy is preserved, but without dissolving all potentially explanatory distinctions into an interactionist causal soup, as some have alleged. (shrink)

The present study evaluates the cognitive representation of a kicking movement performed by a human and a humanoid robot, and how they are represented in experts and novices of soccer and robotics, respectively. To learn about the expertise-dependent development of memory structures, we compared the representation structures of soccer experts and robot experts concerning a human and humanoid robot kicking movement. We found different cognitive representation structures for both expertise groups under two different motor performance conditions . In general, the (...) expertise relies on the perceptual-motor knowledge of the human motor system. Thus, the soccer experts’ cognitive representation of the humanoid robot movement is dominated by their representation of the corresponding human movement. Additionally, our results suggest that robot experts, in contrast to soccer experts, access functional features of the technical system of the humanoid robot in addition to their perceptual-motor knowledge about the human motor system. Thus, their perceptual-motor and neuro-functional machine representation are integrated into a cognitive representation of the humanoid robot movement. (shrink)

The Approximate Number System (ANS) is a system that allows us to distinguish between collections based on the number of items, though only if the ratio between numbers is high enough. One of the questions that has been raised is what the representations involved in this system represent. I point to two important constraints for any account: (a) it doesn’t involve numbers, and (b) it can account for the approximate nature of the ANS. Furthermore, I argue that representations of pure (...) magnitude with vehicles that have an imprecision in the value of the unit of measurement (further clarified through a formal model from measurement theory) fit both these requirements. (shrink)

Cognition is commonly taken to be computational manipulation of representations. These representations are assumed to be digital, but it is not usually specified what that means and what relevance it has for the theory. I propose a specification for being a digital state in a digital system, especially a digital computational system. The specification shows that identification of digital states requires functional directedness, either for someone or for the system of which it is a part. In the case or digital (...) representations, to be a token of a representational type, where the function of the type is to represent. [An earlier version of this paper was discussed in the web-conference "Interdisciplines" https://web.archive.org/web/20100221125700/http://www.interdisciplines.org/adaptation/papers/7 ]. (shrink)

There are simple mechanical systems that elude causal representation. We describe one that cannot be represented in a single directed acyclic graph. Our case suggests limitations on the use of causal graphs for causal inference and makes salient the point that causal relations among variables depend upon details of causal setups, including values of variables.

‘The Natural System’ is the abstract notion of the order in living diversity. The richness and complexity of this notion is revealed by the diversity of representations of the Natural System drawn by ornithologists in the Nineteenth Century. These representations varied in overall form from stars, to circles, to maps, to evolutionary trees and cross-sections through trees. They differed in their depiction of affinity, analogy, continuity, directionality, symmetry, reticulation and branching, evolution, and morphological convergence and divergence. Some representations were two-dimensional, (...) and some were three-dimensional; n-dimensional representations were discussed but never illustrated. The study of diagrammatic representations of the Natural System is made difficult by the frequent failure of authors to discuss them in their texts, and by the consequent problem of distinguishing features which carried meaning from arbitrary features and printing conventions which did not. Many of the systematics controversies of the last thirty years have their roots in the conceptual problems which surrounded the Natural System in the late 1800s, problems which were left unresolved when interest in higher-level systematics declined at the turn of this century. (shrink)

Society is becoming increasingly reliant upon the dependability of computerbased systems. Achieving and demonstrating the dependability of systems requires the construction and review of valid and coherent arguments. This paper discusses the need for a variety of classes of arguments in dependable systems and reviews existing approaches to the representation of arguments in each of these classes. The issues surrounding the certification of safety critical systems demonstrate the current need for richer representations of dependability arguments which (...) support tools for their construction and review. The paper discusses how a meta-logical framework, informed by aspects of both formal and informal logic, offers a rich and unified means of representing dependability arguments and of thus addressing this need. (shrink)

Biologists often study particular biological systems as models of a phenomenon of interest even if they already know that the phenomenon is produced by diverse mechanisms and hence none of those systems alone can sufficiently represent it. To understand this modeling practice, the present paper provides an account of how multiple model systems can be used to study a phenomenon that is produced by diverse mechanisms. Even if generalizability of results from a single model system is significantly (...) limited, generalizations concerning specific aspects of mechanisms often hold across certain ranges of biological systems, which enables multiple model systems to jointly represent such a phenomenon. Comparing mechanisms that operate in different biological systems as examples of the same phenomenon also facilitates characterization and investigation of individual mechanisms. I also compare my account with two existing accounts of the use of multiple model systems and argue that my account is distinct from and complementary to them. (shrink)

In the last decade, the notion of triad was reintroduced by Eric Scerri, who suggested it as a possible categorical criterion to represent chemical periodicity. In particular, he reformulated the notion of triad in terms of atomic number instead of atomic weights; in this way, the value of the intermediate term of the triad became the exact average of the values of the two extremes. Following the inspiration of Scerri’s work, the main purpose of this article is to obtain a (...) representation where all the relations among the chemical elements that form the groups of the periodic system can be reconstructed on the basis of triads, without using electronic configurations. (shrink)

The approximate number system (ANS) enables organisms to represent the approximate number of items in an observed collection, quickly and independently of natural language. Recently, it has been proposed that the ANS goes beyond representing natural numbers by extracting and representing rational numbers (Clarke & Beck, 2021a). Prior work demonstrates that adults and children discriminate ratios in an approximate and ratio-dependent manner, consistent with the hallmarks of the ANS. Here, we use a well-known “connectedness illusion” to provide evidence that these (...) ratio-dependent ratio discriminations are (a) based on the perceived number of items in seen displays (and not just non-numerical confounds), (b) are not dependent on verbal working memory, or explicit counting routines, and (c) involve representations with a part-whole (or subset-superset) format, like a fraction, rather than a part-part format, like a ratio. These results vindicate key predictions of the hypothesis that the ANS represents rational numbers. (shrink)

In this article we present an advanced version of Dual-PECCS, a cognitively-inspired knowledge representation and reasoning system aimed at extending the capabilities of artificial systems in conceptual categorization tasks. It combines different sorts of common-sense categorization (prototypical and exemplars-based categorization) with standard monotonic categorization procedures. These different types of inferential procedures are reconciled according to the tenets coming from the dual process theory of reasoning. On the other hand, from a representational perspective, the system relies on the hypothesis (...) of conceptual structures represented as heterogeneous proxytypes. Dual-PECCS has been experimentally assessed in a task of conceptual categorization where a target concept illustrated by a simple common-sense linguistic description had to be identified by resorting to a mix of categorization strategies, and its output has been compared to human responses. The obtained results suggest that our approach can be beneficial to improve the representational and reasoning conceptual capabilities of standard cognitive artificial systems, and –in addition– that it may be plausibly applied to different general computational models of cognition. The current version of the system, in fact, extends our previous work, in that Dual-PECCS is now integrated and tested into two cognitive architectures, ACT-R and CLARION, implementing different assumptions on the underlying invariant structures governing human cognition. Such integration allowed us to extend our previous evaluation. (shrink)