I propose a semi-eliminative reduction of Fodors concept of module to the concept of attractor basin which is used in Cognitive Dynamic Systems Theory (DST). I show how attractor basins perform the same explanatory function as modules in several DST based research program. Attractor basins in some organic dynamic systems have even been able to perform cognitive functions which are equivalent to the If/Then/Else loop in the computer language LISP. I suggest directions for future research (...) programs which could find similar equivalencies between organic dynamic systems and other cognitive functions. This type of research could help us discover how (and/or if) it is possible to use Dynamic Systems Theory to more accurately model the cognitive functions that are now being modeled by subroutines in Symbolic AI computer models. If such a reduction of subroutines to basins of attraction is possible, it could free AI from the limitations that prompted Fodor to say that it was impossible to model certain higher level cognitive functions. (shrink)

Recent work in the Philosophy of Mind has suggested that alternatives to reduction are required in order to explain the relationship between psychology and biology or physics. Emergence has been proposed as one such alternative. In this paper, I propose a precise definition of emergence, and I argue that chaotic systems provide concrete examples of properties that meet this definition. In particular, I suggest that being in the basin of attraction of a strange attractor is an emergent property of (...) any chaotic nonlinear dynamical system. This shows that non-reductive accounts of inter-theoretic relations are necessary, and that non-reductive accounts of the mental are possible. Moreover, this work provides a foundation for future work investigating the nature of explanation, prediction, and scientific understanding of non-reductive phenomena. (shrink)

Social behavior in most human societies is characterized by the following of moral rules explicitly justified by religious belief systems. These systems constitute the diverse domain of human sacred values. Supernatural entities as founders or warranty of moral principles may be seen as a form of “conversation stoppers,” considerations that can be dropped into a moral decision process in order to prevent endlessly reconsidering and endlessly asking for further justification. In this article we offer a general naturalistic framework toward answering (...) the question of why supernatural entities are so attractive in moral argumentation. We present an explanatory model based on the phenomena of multiple channels of moral reasoning, the suspension of epistemic vigilance, and relevance assumptions through the attractiveness of the sacred, moral dumbfounding, and the expression of social coalitionary commitment. Thus, in light of much of current cognitive theory, sacred values make sense as basins in the evolutionary landscape of human morality. (shrink)

Multi-level institutional designs with distributed power and authority arrangements among federal, state, regional, and local government agencies could lead to the emergence of differential patterns of socioeconomic and infrastructure development pathways in complex social–ecological systems. Both exogenous drivers and endogenous processes in social–ecological systems can lead to changes in the number of “basins of attraction,” changes in the positions of the basins within the state space, and changes in the positions of the thresholds between basins. In an (...) effort to advance the theory and practice of the governance of policy systems, this study addresses a narrower empirical question: how do intergovernmental institutional rules set by federal, state, and regional government agencies generate and sustain basins of attraction in funding infrastructure projects? A pattern-oriented, agent-based model (ABM) of an intergovernmental network has been developed to simulate real-world transportation policy implementation processes across the federal, the state of Vermont, regional, and local governments for prioritizing transportation projects. The ABM simulates baseline and alternative intergovernmental institutional rule structures and assesses their impacts on financial investment flows. The ABM was calibrated with data from multiple focus groups, individual interviews, and analysis of federal, state, and regional scale transportation projects and programs. The results from experimental simulations are presented to test system-wide effects of alternative multi-level institutional designs, in particular different power and authority arrangements between state and regional governments, on the emergence of roadway project prioritization patterns and funding allocations across regions and towns. (shrink)

Most words in English are ambiguous between different interpretations; words can mean different things in different contexts. We investigate the implications of different types of semantic ambiguity for connectionist models of word recognition. We present a model in which there is competition to activate distributed semantic representations. The model performs well on the task of retrieving the different meanings of ambiguous words, and is able to simulate data reported by Rodd, Gaskell, and Marslen‐Wilson [J. Mem. Lang. 46 (2002) 245] on (...) how semantic ambiguity affects lexical decision performance. In particular, the network shows a disadvantage forwords with multiple unrelated meanings (e.g., bark) that coexists with a benefit for words with multiple related word senses (e.g., twist). The ambiguity disadvantage arises because of interference between the different meanings, while the sense benefit arises because of differences in the structure of the attractor basins formed during learning. Words with few senses develop deep, narrow attractor basins, while words with many senses develop shallow, broad basins. We conclude that the mental representations of word meanings can be modelled as stable states within a high‐dimensional semantic space, and that variations in the meanings of words shape the landscape of this space. (shrink)

This article reports on a study that took a Dynamic Systems Theory perspective to second language motivational self system. More specifically, it investigated the influence of an Intensive English Reading course based on the Production-Oriented Approach upon the L2MSS of Chinese university English majorsfrom the DST perspective. To this end, two intact classes composed of 50 students were assigned into experimental group and control group, who responded to an L2MSS scale before and after the one-semester intervention. Eight and five students (...) were respectively selected using the purposive sampling method from the experimental and control groups for follow-up semi-structured interviews. The quantitative results revealed that the overall and dimensional levels of L2MSS were significantly strengthened over time in the EG while kept stable in the CG. The qualitative results suggested that the enhanced Ideal L2 Self of the participants stemmed from an attractor basin that was deepened by a number of attractors encompassing Output Tasks and Peer Performance. The interview results also showed that the increased L2 Learning Experience of the participants pertained to an attractor basin that was consolidated by an array of attractors containing Output Tasks, Teacher Guidance, Group Discussion, and Peer Assessment. The findings indicated that the attractors at the subjective and social dimensions in the POA-based course collectively worked together to cause changes in L2MSS among the participants. The implications for intervening L2 motivation from a POA approach in English as a Foreign Language classrooms were discussed. (shrink)

This paper argues in favor of the ambiguity in the interpretive process and mechanisms that can lead to stop the so-called unlimited semiosis. As we shall see, our way of approaching the problem can be used in other contexts, and the resulting conclusions can be applied to text, artwork, spoken messages, and to any sign to be interpreted.

In this paper, chaotic dynamics of a mixed Rayleigh–Liénard oscillator driven by parametric periodic damping and external excitations is investigated analytically and numerically. The equilibrium points and their stability evolutions are analytically analyzed, and the transitions of dynamical behaviors are explored in detail. Furthermore, from the Melnikov method, the analytical criterion for the appearance of the homoclinic chaos is derived. Analytical prediction is tested against numerical simulations based on the basin of attraction of initial conditions. As a result, it is (...) found that for ω = ν, the chaotic region decreases and disappears when the amplitude of the parametric periodic damping excitation increases. Moreover, increasing of F 1 and F 0 provokes an erosion of the basin of attraction and a modification of the geometrical shape of the chaotic attractors. For ω ≠ ν and η = 0.8, the fractality of the basin of attraction increases as the amplitude of the external periodic excitation and constant term increase. Bifurcation structures of our system are performed through the fourth-order Runge–Kutta ode 45 algorithm. It is found that the system displays a remarkable route to chaos. It is also found that the system exhibits monostable and bistable oscillations as well as the phenomenon of coexistence of attractors. (shrink)

This work introduces a three-dimensional, highly nonlinear quadratic oscillator with no linear terms in its equations. Most of the quadratic ordinary differential equations such as Chen, Rossler, and Lorenz have at least one linear term in their equations. Very few quadratic systems have been introduced and all of their terms are nonlinear. Considering this point, a new quadratic system with no linear term is introduced. This oscillator is analyzed by mathematical tools such as bifurcation and Lyapunov exponent diagrams. It is (...) revealed that this system can generate different behaviors such as limit cycle, torus, and chaos for its different parameters’ sets. Besides, the basins of attractions for this system are investigated. As a result, it is revealed that this system’s attractor is self-excited. In addition, the analog circuit of this oscillator is designed and analyzed to assess the feasibility of the system’s chaotic solution. The PSpice simulations confirm the theoretical analysis. The oscillator’s time series complexity is also investigated using sample entropy. It is revealed that this system can generate dynamics with different sample entropies by changing parameters. Finally, impulsive control is applied to the system to represent a possible solution for stabilizing the system. (shrink)

In this paper, a 4D fractional-order centrifugal flywheel governor system is proposed. Dynamics including the multistability of the system with the variation of system parameters and the derivative order are investigated by Lyapunov exponents, bifurcation diagram, phase portrait, entropy measure, and basins of attraction, numerically. It shows that the minimum order for chaos of the fractional-order centrifugal flywheel governor system is q = 0.97, and the system has rich dynamics and produces multiple coexisting attractors. Moreover, the system is controlled (...) by introducing the adaptive controller which is proved by the Lyapunov stability theory. Numerical analysis results verify the effectiveness of the proposed method. (shrink)

In this paper, a discrete-time dynamic duopoly model, with nonlinear demand and cost functions, is established. The properties of existence and local stability of equilibrium points have been verified and analyzed. The stability conditions are also given with the help of the Jury criterion. With changing of the values of parameters, the system shows some new and interesting phenomena in terms to stability and multistability, such as V-shaped stable structures and different shape basins of attraction of coexisting attractors. The (...) eye-shaped structures appear where the period-doubling and period-halving bifurcations occur. Finally, by utilizing critical curves, the changes in the topological structure of basin of attraction and the reason of “holes” formation are analyzed. As a result, the generation of global bifurcation, such as contact bifurcation or final bifurcation, is usually accompanied by the contact of critical curves and boundary. (shrink)

A neural network is a model of the brain’s cognitive process, with a highly interconnected multiprocessor architecture. The neural network has incredible potential, in the view of these artificial neural networks inherently having good learning capabilities and the ability to learn different input features. Based on this, this paper proposes a new chaotic neuron model and a new chaotic neural network model. It includes a linear matrix, a sine function, and a chaotic neural network composed of three chaotic neurons. One (...) of the chaotic neurons is affected by the sine function. The network has rich chaotic dynamics and can produce multiscroll hidden chaotic attractors. This paper studied its dynamic behaviors, including bifurcation behavior, Lyapunov exponent, Poincaré surface of section, and basins of attraction. In the process of analyzing the bifurcation and the basins of attraction, it was found that the network demonstrated hidden bifurcation phenomena, and the relevant properties of the basins of attraction were obtained. Thereafter, a chaotic neural network was implemented by using FPGA, and the experiment proved that the theoretical analysis results and FPGA implementation were consistent with each other. Finally, an energy function was constructed to optimize the calculation based on the CNN in order to provide a new approach to solve the TSP problem. (shrink)

Due to the complex behavior of a multiscroll chaotic system, it is a good candidate for the secure communications. In this paper, by adding an additional variable to the modified Lorenz-type system, a new chaotic system that includes only linear and piecewise items but can generate 4n + 4 scroll chaotic attractors via choosing the various values of natural number n is proposed. Its dynamics including bifurcation, multistability, and symmetric coexisting attractors, as well as various chaotic and periodic behaviors, are (...) analyzed by means of attraction basin, bifurcation diagram, dynamic map, phase portrait, Lyapunov exponent spectrum, and C0 complexity in detail. The mechanism of the occurrence for generating multiscroll chaotic attractors is presented. Finally, this multiscroll chaotic system is implemented by using the Altera Cyclone IV EP4CE10F17C8 FPGA. It is found that this FPGA-based design has an advantage of requiring less resources for 0% of the embedded multipliers and 0% of the PLLs of this FPGA are occupied. (shrink)

In economics there are several complex learning themes and tasks connected with them difficult for deeper understanding of the learning subject. These are the reasons originating serious learning problems for students in the form of Virtual Environment because deeper understanding requires high level mathematical skills. Actually the most important feature for discerning this part of economics is the set of qualitative shapes emerging in discrete dynamic systems when they are undergoing iterations and/or experimentation with parameters and initial coordinates of variables. (...) Among such shapes there are: - trajectories in evolving time; - trajectories in R2 of two variables; - cobweb portraits; - one control parameter bifurcation with first and/or with second variables; - two control parameters bifurcation in R2 ; - cycles; - basin of attraction of two variables; - one Lyapunov’s exponent against some of control parameters; - Lyapunov’s exponents with two control parameters in R2; - absorbing area with possibility to create critical curves and/or attractors. The hope is that products of computational intelligence may help them solve such problems. Naturally, the meant complex economic problems and tasks have discrete, qualitative and nonlinear nature resulting in increased level of difficulties. So with the term used in the head of this paper one has to understand narrowly: “qualitative nonlinear computational economics”. For better understanding the very nature of the problem we are using as appropriate example actual simulation of the model of new ICT products monopolies in virtual laboratory built in the routines setting dominantly in the software iDMC. (shrink)

We present a framework for machine implementation of families of non-classical logics with Kripke-style semantics. We decompose a logic into two interacting parts, each a natural deduction system: a base logic of labelled formulae, and a theory of labels characterizing the properties of the Kripke models. By appropriate combinations we capture both partial and complete fragments of large families of non-classical logics such as modal, relevance, and intuitionistic logics. Our approach is modular and supports uniform proofs of soundness, completeness and (...) proof normalization. We have implemented our work in the Isabelle Logical Framework. (shrink)

Издание содержит: хрестоматия; философы; психологи; литературоведы, искусствоведы; мастер изобразительного искусства и др.

В книгу вошли высказывания об искусстве и воображении философов, эстетиков, психологов, искусствоведов и мастеров искусства.

Вниманию читателя предлагаются статьи, посвященные мало исследованным проблемам логики (и психологии) художественного творчества, в частности в работах М. Бахтина. Книга содержит также хрестоматию "Искусство и логика" и предметный указатель.

Ėstetika antichnosti -- Ėstetika srednikh vekov -- Ėstetika vozrozhdenii︠a︡ -- Ėstetika frant︠s︡uzskogo prosveshchenii︠a︡ -- Ėstetika nemet︠s︡kogo prosveshchenii︠a︡ -- Ėstetika angliĭskogo prosveshchenii︠a︡ -- Ėstetika "Buri i natiska" -- Nemet︠s︡kai︠a︡ klassicheskai︠a︡ ėstetika.

In previous work we gave an approach, based on labelled natural deduction, for formalizing proof systems for a large class of propositional modal logics that includes K, D, T, B, S4, S4.2, KD45, and S5. Here we extend this approach to quantified modal logics, providing formalizations for logics with varying, increasing, decreasing, or constant domains. The result is modular with respect to both properties of the accessibility relation in the Kripke frame and the way domains of individuals change between worlds. (...) Our approach has a modular metatheory too; soundness, completeness and normalization are proved uniformly for every logic in our class. Finally, our work leads to a simple implementation of a modal logic theorem prover in a standard logical framework. (shrink)

In previous work, we introduced a version of distributed temporal logic that is well-suited both for verifying security protocols and as a metalogic for reasoning about, and relating, different security protocol models. In this paper, we formally investigate the relationship between our approach and strand spaces, which is one of the most successful and widespread formalisms for analyzing security protocols. We define translations between models in our logic and strand-space models of security protocols, and we compare the results obtained with (...) respect to the level of abstraction that is inherent in each of the formalisms. This allows us to clarify different aspects of strand spaces that are often left implicit, as well as pave the way to transfer results, techniques and tools across the two approaches. (shrink)

Cultural attractor theory (CAT) is a highly visible and audacious approach to studying human cultural evolution. However, the explanatory aims and some central explanatory concepts of CAT remain unclear. Here I remedy these problems. I provide a reconstruction of CAT that recasts it as a theory of forces. I then demonstrate how this reinterpretation of CAT has the resources to generate both cultural distribution and evolvability explanations. I conclude by examining the potential benefits and drawbacks of this reconstruction.

An attractor network was trained to compute from word form to semantic representations that were based on subject‐generated features. The model was driven largely by higher‐order semantic structure. The network simulated two recent experiments that employed items included in its training set (McRae and Boisvert, 1998). In Simulation 1, short stimulus onset asynchrony priming was demonstrated for semantically similar items. Simulation 2 reproduced subtle effects obtained by varying degree of similarity. Two predictions from the model were then tested on (...) human subjects. In Simulation 3 and Experiment 1, the items from Simulation 1 were reversed, and both the network and subjects showed minimally different priming effects in the two directions. In Experiment 2, consistent with attractor networks but contrary to a key aspect of hierarchical spreading activation accounts priming was determined by featural similarity rather than shared superordinate category. It is concluded that semantic‐similarity priming is due to featural overlap that is a natural consequence of distributed representations of word meaning. (shrink)

Concepts from cultural attractor theory are now used in domains far from their original home in anthropology and cultural evolution. Yet these concepts have not been consistently characterised. I here distinguish four ways in which the cultural attractor concept has been used and identify three kinds of factors of attraction typically appealed to. Clarifying these explanatory concepts identifies problems and ambiguities in the work of cultural epidemiologists and commentators alike.

Memristor is the fourth basic electronic element discovered in addition to resistor, capacitor, and inductor. It is a nonlinear gadget with memory features which can be used for realizing chaotic, memory, neural network, and other similar circuits and systems. In this paper, a novel memristor-based fractional-order chaotic system is presented, and this chaotic system is taken as an example to analyze its dynamic characteristics. First, we used Adomian algorithm to solve the proposed fractional-order chaotic system and yield a chaotic phase (...) diagram. Then, we examined the Lyapunov exponent spectrum, bifurcation, SE complexity, and basin of attraction of this system. We used the resulting Lyapunov exponent to describe the state of the basin of attraction of this fractional-order chaotic system. As the local minimum point of Lyapunov exponential function is the stable point in phase space, when this stable point in phase space comes into the lowest region of the basin of attraction, the solution of the chaotic system is yielded. In the analysis, we yielded the solution of the system equation with the same method used to solve the local minimum of Lyapunov exponential function. Our system analysis also revealed the multistability of this system. (shrink)

This article proposes complementing actor-network theory (ANT) with Niklas Luhmann’s communication theory, in order to overcome one of ANT’s major shortcomings, namely, the lack of a conceptual repertoire to describe virtual processes such as sense-making. A highly problematic consequence of ANT’s actualism is that it cannot explain the differentiation of economic, legal, scientific, touristic, religious, medical, artistic, political and other qualities of actual entities, assemblages and relationships. By recasting Luhmann’s theory of functionally differentiated communication forms and sense-making as dealing with (...) different types of virtual attractors calling for actualizations in concrete assemblages, I propose a symmetrical understanding of societal differentiation processes as based on the co-production of virtual attractors and actual assemblages. (shrink)

Contemporary complexity sciences claim a literal, non-metaphorical applicability to physical, economic, social and cultural events. They envision the development of a general social or historical physics. Conversely, in the social sciences and humanities, complexity sciences have been typically treated as a source of new metaphors or tropes to be used in theory-building. Can there be a critical social or historical physics that is not a world-view and that does not treat science as a source of metaphors? The Lorenz attractor (...) figures centrally in the history of complexity science as a popular image of ‘deterministic chaos’ and the ‘butterfly effect’, as an indication of how far complexity science has progressed in the last two decades, and, as this article argues, as an event whose multiplicity of interpretations attests to the problem it raises, the problem of generality associated with complexity. Via the Lorenz attractor, the article examines three attempts to treat complexity non-metaphorically in recent theoretical work (Delanda; Massumi; Stengers). In these accounts, the attractor performs several different functions. It forms part of a re-engineered concept of multiplicity, it helps conceptualize feeling or sensitivity, and it raises the general problem of practice in theory-building. (shrink)

This article is devoted to the characterization of the basin of attraction of pattern solutions for some slow–fast reaction–diffusion systems with a symmetric property and an underlying oscillatory reaction part. We characterize some subsets of initial conditions that prevent the dynamical system to evolve asymptotically toward solutions which are homogeneous in space. We also perform numerical simulations that illustrate theoretical results and give rise to symmetric and non-symmetric pattern solutions. We obtain these last solutions by choosing particular random initial conditions.

This book is open access under a CC BY-NC 2.5 license. This book offers a devastating look at deeply flawed development processes driven by international finance, African governments and the global consulting industry. It examines major river basin development underway in the semi-arid borderlands of Ethiopia, Kenya and South Sudan and its disastrous human rights consequences for a half-million indigenous people. The volume traces the historical origins of Gibe III megadam construction along the Omo River in Ethiopia-in turn, enabling irrigation (...) for commercial-scale agricultural development and causing radical reduction of downstream Omo and (Kenya's) Lake Turkana waters. Presenting case studies of indigenous Dasanech and northernmost Turkana livelihood systems and Gibe III linked impacts on them, the author predicts agropastoral and fishing economic collapse, region-wide hunger with exposure to disease epidemics, irreversible natural resource destruction and cross-border interethnic armed conflict spilling into South Sudan. The book identifies fundamental failings of government and development bank impact assessments, including their distortion or omission of mandated transboundary assessment, cumulative effects of the Gibe III dam and its linked Ethiopia-Kenya energy transmission 'highway' project, key hydrologic and human ecological characteristics, major earthquake threat in the dam region and widespread expropriation and political repression. Violations of internationally recognized human rights, especially by the Ethiopian government but also the Kenyan government, are extensive and on the increase-with collaboration by the development banks, in breach of their own internal operational procedures. A policy crossroads has now emerged. The author presents the alternative to the present looming catastrophe-consideration of development suspension in order to undertake genuinely independent transboundary assessment and a plan for continued development action within a human rights framework-forging a sustainable future for the indigenous peoples now directly threatened and for their respective eastern Africa states. Claudia Carr's book is a treasure of detailed information gathered over many years concerning river basin development of the Omo River in Ethiopia and its impact on the peoples of the lower Omo Basin and the Lake Turkana region in Kenya. It contains numerous maps, charts, and photographs not previously available to the public. The book is highly critical of the environmental and human rights implications of the Omo River hydropower projects on both the local ethnic communities in Ethiopia and on the downstream Turkana in Kenya. David Shinn Former Ambassador to Ethiopia and to Burkina Faso Adjust Professor of International Affairs, The George Washington University, Washington D.C. (shrink)

In this paper, we address the model of global attractor formulated in the form of evolution differential inclusions with second order in Banach spaces. Firstly, based on the fixed point theorem, the existence result of mild solutions is deduced. Then, by implementing the measure of noncompactness, the existence of global attractor associated with m -semiflow is validated. Finally, a concrete application of the main result is demonstrated to enhance the practical signification.

Every immediate memory is unique; it is therefore unlikely to consist of an attractor or even a combination of attractors. In the present state of knowledge about the chemistry of synaptic transmission, there is no reason to look beyond neurons that directly receive sensory afferents for the afterdischarges that correspond to active memories.

In this article, physiological and pathological forms of excitability are studied in a two-dimensional electrical model of excitable cell endowed with a generic inward persistent conductance. Bifurcation analysis of the model is performed as a function of the maximal inward persistent conductance, the input current, or the voltage dependency of the activation function. Several discharge modes are exhibited, including: (1) a basic mode that corresponds to a resting potential and production of action potential; (2) bistability between resting potential and self-sustained (...) spiking; (3) a pacemaker mode of discharge; and (4) bistability between resting potential and plateau potential. These behaviours can be compared to experimentally described physiological and pathological forms of excitability that depend upon inward persistent conductances. In the results obtained, attractors allow for a qualitative description of physiological and pathological states. However, it is not possible to obtain an unambiguous identification of particular ''physiological attractors'' or ''pathological attractors''. In the perspective of the theory of dynamical systems, we suggest that pathological states can be modelled in two different ways, i.e. by bifurcation (as in the present model) or by perturbation. We also highlight some other theoretical concepts that may be relevant to a theoretical description of pathology. (shrink)

Spatio-temporal neuro-dynamics is a quickly developing field of brain research and Tsuda's work is a significant contribution toward establishing theoretical foundations in this area. It is conceivable that the fragmented attractor landscapes and dynamical memory patterns identified earlier in various K-sets are biologically plausible manifestations of attractor ruins, chaotic itinerancy, and Cantor encoding as applied to sensory information processing.

Philosophers of science today by and large reject the cataclysmic and irrational interpretation of the scientific enterprise claimed by Kuhn. Many computational models have been implemented to rationally study the conceptual change in science. In this recent tradition a key role is played by the concept of abduction as a mechanism by which new explanatory hypotheses are introduced. Nevertheless some problems in describing the most interesting abductive issues rise from the classical computational approach. It describes a cognitive process (and so (...) abduction) by the manipulation of internal symbolic representations of external world. This view assumes a discrete set of representations fixed in discrete time jumps, and cannot adequately account for the issue of anticipation and causation of a new hypothesis. An integration of the traditional computational view with some ideas developed inside the so-called dynamical approach can suggest some important insights. The concept of attractor is very significant. It permits a description of the abductive generation of new hypotheses in terms of a catastrophic rearrangement of the parameters responsible for the behavior of the system. (shrink)