Classical cognitive science assumes that intelligentlybehaving systems must be symbol processors that are implemented in physical systems such as brains or digital computers. By contrast, connectionists suppose that symbol manipulating systems could be approximations of neural networks dynamics. Both classicists and connectionists argue that symbolic computation and subsymbolic dynamics are incompatible, though on different grounds. While classicists saythat connectionist architectures and symbol processors are either incompatible or the former are mere implementations of the latter, connectionists replythat neural networks might be incompatible with symbol processors because the latter cannot be implementations of the former. In this contribution, the notions of “incompatibility ” and “implementation ” will be criticized to show that they must be revised in the context of the dynamical system approach to cognitive science. Examples for implementations of symbol processors that are incompatible with respect to contextual topologies will be discussed. 1.

Dual Dynamics (DD) is a mathematical model of a behavior control system for mobile autonomous robots. Behaviors are specified through di#erential equations, forming a global dynamical system made of behavior subsystems which interact in a number of ways. DD models can be directly compiled into executable code. The article (i) explains the model, (ii) sketches the Dual Dynamics Designer (DDD) environment that we use for the design, simulation, implementation and documentation, and (iii) illustrates our approach with the example of kicking a moving ball into a goal. 1 Introduction In the RoboCup mid-size league, robots have to kick a ball into the right direction. For many reasons, this is a hard task, which calls for robotic methods from many fields: 1. The situation on the field changes rapidly and drastically. This suggests a reactive, behavior-based approach to robot control [ Brooks, 1991 ] . 2. Kicking a moving ball is a continuous and dynamic task. Methods from con...

Advocates of dynamic systems have suggested that higher mental processes are based on continuous representations. In order to evaluate this claim, we first define the concept of representation, and rigorously distinguish between discrete representations and continuous representations. We also explore two important bases of representational content. Then, we present seven arguments that discrete representations are necessary for any system that must discriminate between two or more states. It follows that higher mental processes require discrete representations. We also argue that discrete representations are more influenced by conceptual role than continuous representations. We end by

Abstract We present a new definition of the concept of representation for cognitive science that is based on a study of the origin of structures that are used to store memory in evolving systems. This study consists of novel computer experiments in the evolution of cellular automata to perform nontrivial tasks as well as evidence from biology concerning genetic memory. Our key observation is that representations require inert structures to encode information used to construct appropriate dynamic configurations for the evolving system. We propose criteria to decide if a given structure is a representation by unpacking the idea of inert structures that can be used as memory for arbitrary dynamic configurations. Using a genetic algorithm, we evolved cellular automata rules that can perform nontrivial tasks related to the density task (or majority classification problem) commonly used in the literature. We present the particle catalogs of the new rules following the computational mechanics framework. We discuss if the evolved cellular automata particles may be seen as representations according to our criteria. We show that while they capture some of the essential characteristics of representations, they lack an essential one. Our goal is to show that artificial life can be used to shed new light on the computation-versus-dynamics debate in cognitive science, and indeed function as a constructive bridge between the two camps. Our definitions of representation and cellular automata experiments are proposed as a complementary approach, with both dynamics and informational modes of explanation.

With the advent of computers in the experimental labs, dynamic systems have become a new tool for research on problem solving and decision making. A short review of this research is given and the main features of these systems (connectivity and dynamics) are illustrated. To allow systematic approaches to the influential variables in this area, two formal frameworks (linear structural equations and finite state automata) are presented. Besides the formal background, the article sets out how the task demands of system identification and system control can be realised in these environments, and how psychometrically acceptable dependent variables can be derived. The use of computer-simulated scenarios in problem-solving research has become increasingly popular during the last 25 years (for a representative collection of papers see, e.g., the two editions from Sternberg & Frensch, 1991, and Frensch & Funke, 1995). This new approach to problem solving seems attractive for several reasons. In contrast to static problems, computer-simulated scenarios provide a unique opportunity to study human problem-solving and decision-making behaviour when the task environment and subjects ’ actions change concurrently. Subjects can manipulate a specific scenario via a number of input variables (typically ranging from 2 to 20, and in some exceptional instances even up to 2000), and they observe the system’s state changes in a number of output variables. In exploring and/or controlling a system, subjects have to continuously acquire and use knowledge about the internal structure of the system.

Goldstone for useful chats about learning, abstraction and surrogate situations. What do linguistic symbols do for minds like ours, and how (if at all) can basic embodied, dynamical and situated approaches do justice to high-level human thought and reason? These two questions are best addressed together, since our answers to the first may inform the second. The key move in ‘scaling-up ’ simple embodied cognitive science is, I argue, to take very seriously the potent role of human-built structures in transforming the spaces of human learning and reason. In particular, in this paper I look at a range of cases involving what I dub ‘surrogate situations’. Here, we actively create restricted artificial environments that allow us to deploy basic perception-actionreason routines in the absence of their proper objects. Examples include the use of real-world models, diagrams and other concrete external symbols to support dense looping interactions with a variety of stable external structures that stand in for the absent states of affairs. 1 Language itself, I shall finally suggest, is the most potent and fundamental form of such surrogacy. Words are both cheap stand-ins for gross behavioral outcomes, and the concrete objects that structure new spaces for basic forms of learning and reason. A good hard look at surrogate situatedness thus turns the standard skeptical challenge on its head. But it raises important questions concerning what really matters about these new approaches, and it helps focus what I see as the major challenge for the future: how, in detail, to conceptualize the role of symbols (both internal and external) in dynamical cognitive processes.

We introduce symbolic dynamics to cognitive scientists with the aim of furthering constructive debate on representation. Symbolic dynamics is a mathematical framework in which both continuous and discrete states of a system can be considered jointly. We discuss a number of theoretical implications this framework has for cognitive science, and offer some consideration of the way in which it might be employed for comparing or conciliating discrete and continuous representational theories. Symbolic dynamics may thus serve as a common, level playing field for debate in theories of cognitive representation.

The mechanisms supporting robot behaviors are increasingly often designed as dynamical systems. Such mechanisms are inherently multifunctional. This means that they can exhibit different qualitative behavior in different circumstances. Multifunctionality makes system design difficult. On the other hand, it may be beneficial for adaptiveness, since it allows qualitative changes in a robot's behaviors without changing the supporting mechanisms.

We applied spectral analysis on series of time intervals produced in a synchronizationcontinuation experiment. In the first condition intervals were produced by finger tapping, and in the second by an oscillatory motion of the hand. Results obtained in tapping were consistent with a discrete, event-based timing model. In the oscillatory condition, the spectra suggested a continuous, dynamic timing mechanism, based on the regulation of effector stiffness. It is concluded that the oscillatory character of movement can offer an important resource for timing control. The use of an event-based timing control such as postulated in the Wing-Kristoffersson model could be restricted to a quite limited class of rhythmic tasks, characterized by the concatenation of discrete events. Key-words: Tapping, oscillations, event-based timers, dynamic timers, 1/f fluctuation PsycINFO Classification: 2330 The production of rhythmical movements is a central theme of research for the psychology of motor control. Among a number of complementary lines of research, tapping performance has received a persistent attention over more than a century (Nicholson, 1925; Stevens, 1886; Woodrow, 1932). In tapping experiments, participants attempt to tap continuously at a specified tempo. The simplest experimental tapping design is the synchronization-continuation paradigm: in this kind of experiment, subjects have in a first phase to synchronize their taps with the periodic signals given by a metronome, then the metronome is removed and subjects try to continue to tap regularly following the prescribed tempo. The variable of interest is the series of inter-tap intervals (I) produced during the continuation phase of the experiment. Wing and Kristofferson (1973) proposed a very simple model for accounting for I variability in synchronization-continuation experiments. This model includes two components: an internal clock, which provides a series of temporal intervals Ci, and a motor component, responsible for the execution of the tap i at the expiration of the interval Ci. This motor component does not operate instantaneously, and all taps have an assigned motor delay Mi. In terms of these two components, the observed Ii interval is written as

This article deals with mathematical models of discrete, identifiable, "symbolic" events in neural and cognitive dynamics. These dynamical symbols are the supposed correlates of identifiable motor action patterns, from phoneme utterances to restaurant visits. In the first main part of the article, models of dynamical symbols offered by dynamical systems theory are reviewed: attractors, bifurcations, spatial segregation and boundary formation, and several others. In the second main part, transient attractors (TA's) are offered as yet another mathematical model of dynamical symbols. TAs share with ordinary attractors a basic property, namely, local phase space contraction. However, a TA can disappear almost as soon as it is created, which could (not very rigorously) be interpreted as a bifurcation induced by quickly changing control parameters. Such "fast bifurcation sequences" standardly occur in neural and cognitive dynamics. 1 Introduction This paper is about symbols, viewed as ide...