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Autonomous Agents, AI and Chaos Theory
"... Agent theory in AI and related disciplines deals with the structure and behaviour of autonomous, intelligent systems, capable of adaptive action to pursue their interests. In this paper it is proposed that a natural reinterpretation of agenttheoretic intentional concepts like knowing, wanting, liki ..."
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Cited by 12 (1 self)
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Agent theory in AI and related disciplines deals with the structure and behaviour of autonomous, intelligent systems, capable of adaptive action to pursue their interests. In this paper it is proposed that a natural reinterpretation of agenttheoretic intentional concepts like knowing, wanting, liking, etc., can be found in process dynamics. This reinterpretation of agent theory serves two purposes. On the one hand we gain a well established mathematical theory which can be used as the formal mathematical interpretation (semantics) of the abstract agent theory. On the other hand, since process dynamics is a theory that can also be applied to physical systems of various kinds, we gain an implementation route for the construction of artificial agents as bundles of processes in machines. The paper is intended as a basis for dialogue with workers in dynamics, AI, ethology and cognitive science. 1 Introduction Agent theory is a branch of artificial intelligence (Kiss, 1988). Its domain is...
Prior Information and Generalized Questions
, 1996
"... In learning problems available information is usually divided into two categories: examples of function values (or training data) and prior information (e.g. a smoothness constraint). ..."
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Cited by 7 (4 self)
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In learning problems available information is usually divided into two categories: examples of function values (or training data) and prior information (e.g. a smoothness constraint).
An extension of Markov partitions for a certain toral endomorphism
, 1999
"... We define and construct Markov partition for a certain toral endomorphism and then we use it to obtain a symbolic representation of the semidynamical system induced by the endomorphism. Research supported in part by Polish Scientific Grant No.2 P03A 029 12 and the PRODYN programme of the European ..."
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We define and construct Markov partition for a certain toral endomorphism and then we use it to obtain a symbolic representation of the semidynamical system induced by the endomorphism. Research supported in part by Polish Scientific Grant No.2 P03A 029 12 and the PRODYN programme of the European Science Foundation Contents 1 Introduction 2 2 Acknowledgements 3 3 Definition of the extended Markov partition 4 4 Main results 6 5 Proof of the existence of the extended Markov partition 6 6 Proof of the theorem on the correspondence to a onesided subshift of finite type 9 7 A new method of obtaining the transition rule 12 8 Final remarks 12 9 Adler and Weiss' method fails in the case of an endomorphism 13 10 Why do we choose such an extension of Markov partitions? 14 10.1 The aim of the construction of the extended Markov partition . . 14 10.2 Properties that are significant for Markov partitions . . . . . . . 15 1 1 Introduction The increasing interest in the theory of symbolic d...
The Correspondence Principle and Structural Stability in NonMaximum Systems
, 2004
"... The correspondence principle suggests a link between asymptotic stability properties of equilibria of economic models and the equilibrium response to data that describe the model or the model environment. However, this link has been impaired by a logicalmathematical deficiency. This paper, by intro ..."
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The correspondence principle suggests a link between asymptotic stability properties of equilibria of economic models and the equilibrium response to data that describe the model or the model environment. However, this link has been impaired by a logicalmathematical deficiency. This paper, by introducing a conceptual requirement of (local) structural stability as part of the principle hypotheses, rectifies the relation between qualitative properties of equilibria and the analysis of variations. Two related examples are given. The first completes Dierkers’ proof of a unique equilibrium in regular Arrow–Debreu economies, where all price systems are locally stable relative to a tâtonnement process. The second validates linear approximation analysis of deterministic continuous time rational expectation models. The paper’s focus on local analysis makes it possible to handle potentially difficult problems in a straightforward manner.
Time Series of Rational Partitions and Complexity of Onedimensional Processes
"... Abstract. Time series based on couples of partitions, and a related reduction algorithm, are used to develop indicators of complexity for general onedimensional processes with discretizable states. After introducing the calculation scheme, we provide algorithms for some typical examples (cellular a ..."
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Abstract. Time series based on couples of partitions, and a related reduction algorithm, are used to develop indicators of complexity for general onedimensional processes with discretizable states. After introducing the calculation scheme, we provide algorithms for some typical examples (cellular automata and iterated maps). Experiments show the sensitivity of these indicatorsto complexity in the intuitive sense, and to hidden features distinguishing complexity from ordinary randomness. 1. Rational partitions The concept of a rational partition (rpartition) was introduced in [1], with the purpose of estimating the complexity of objects or situations endowed, in a broad sense, with a dynamics (cellular automata (CAs) , mappings, shifts, patterns depending on a parameter, and so on). The idea illustrated there may be summarized in the following main points. • Inasmuch as finite measurable partitions in probability spaces give a