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gS 0 0 538 781 rC
193 247 :M
f0_18 sf
4.824 .482(Autonomous Agents,)J
189 265 :M
1.987 .199(AI and Chaos Theory)J
f1_9 sf
0 -3 rm
(1)S
0 3 rm
239 293 :M
f0_14 sf
4.15 .415(George Kiss)J
186 317 :M
f1_12 sf
-.106(Human Cognition Research Laboratory)A
230 329 :M
-.128(The Open University)A
194 341 :M
.161 .016(email: gr_kiss@vax.acs.open.ac.uk)J
189 368 :M
f1_14 sf
.264 .026(HCRL Technical Report No. 71)J
231 383 :M
.474 .047(September, 1990)J
-4124 -4125 -1 1 -4122 -4125 1 -4124 -4126 @a
30 678.24 -.24 .24 173.24 678 .24 30 678 @a
30 690 :M
f1_10 sf
(1)S
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.159 .016( In: J.-A. Meyer and S. Wilson \(Eds\) From Animals to Animats, Proceedings of the First International)J
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30 705 :M
-.07(Conference on Simulation of Adaptive Behavior. Cambridge, Massachusetts: MIT Press, 1991)A
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-28 -30 :T
gS 28 30 538 781 rC
292 56 :M
f1_10 sf
(2)S
154 103 :M
f0_12 sf
.337(Abstract)A
76 123 :M
f1_10 sf
.704 .07(Agent theory in AI and related disciplines deals)J
76 134 :M
.462 .046(with the structure and behaviour of autonomous,)J
76 145 :M
.399 .04(intelligent systems, capable of adaptive action to)J
76 156 :M
.13 .013(pursue their interests. In this paper it is proposed)J
76 167 :M
.948 .095(that a natural reinterpretation of agent-theoretic)J
76 178 :M
2.932 .293(intentional concepts like knowing, wanting,)J
76 189 :M
1.188 .119(liking, etc., can be found in process dynamics.)J
76 200 :M
.849 .085(This reinterpretation of agent theory serves two)J
76 211 :M
2.278 .228(purposes. On the one hand we gain a well)J
76 222 :M
1.603 .16(established mathematical theory which can be)J
76 233 :M
1.395 .139(used as the formal mathematical interpretation)J
76 244 :M
.558 .056(\(semantics\) of the abstract agent theory. On the)J
76 255 :M
1.175 .118(other hand, since process dynamics is a theory)J
76 266 :M
1.116 .112(that can also be applied to physical systems of)J
76 277 :M
.836 .084(various kinds, we gain an implementation route)J
76 288 :M
.085 .008(for the construction of artificial agents as bundles)J
76 299 :M
.687 .069(of processes in machines. The paper is intended)J
76 310 :M
.123 .012(as a basis for dialogue with workers in dynamics,)J
76 321 :M
-.018(AI, ethology and cognitive science.)A
58 342 :M
f0_12 sf
(1)S
94 342 :M
.425(Introduction)A
58 362 :M
f1_10 sf
1.406 .141(Agent theory is a branch of artificial intelligence \(Kiss,)J
58 373 :M
.097 .01(1988\). Its domain is the theory, design and implementation)J
58 384 :M
.654 .065(of artificial systems, similar to animals or people, that are)J
58 395 :M
.806 .081(capable of autonomous, rational actions through which to)J
58 406 :M
1.451 .145(pursue their interests and goals. Aspects of this theory)J
58 417 :M
2.111 .211(cover, among other things, how actions are related to)J
58 428 :M
1.327 .133(knowledge, how plans for actions to reach goals can be)J
58 439 :M
.634 .063(formed, how goals are formed, what the role of intentions)J
58 450 :M
.783 .078(for action is, how the state of the world is perceived, and)J
58 461 :M
.167 .017(many others.)J
58 484 :M
.939 .094(The abstract formulation of agent theory can be stated in)J
58 495 :M
.129 .013(many different languages, both informal and formal. Much)J
58 506 :M
.968 .097(current work in this field has made use of formal logical)J
58 517 :M
1.023 .102(languages \(Georgeff and Lansky, 1986\). Although these)J
58 528 :M
.305 .03(specialised logics are convenient and expressive, often it is)J
58 539 :M
.746 .075(dificult to formalise their semantics, or the semantics that)J
58 550 :M
-.003(have been offered have undesirable properties. An example)A
58 561 :M
.649 .065(of this is the possible-world semantics of epistemic logics)J
58 572 :M
.028 .003(which unfortunately makes agents omniscient.)J
58 595 :M
.97 .097(The implementation of theories expressed in such formal)J
58 606 :M
4.424 .442(languages has additional problems. When agent)J
58 617 :M
1.85 .185(implementation is done by direct mechanisation of the)J
58 628 :M
2.444 .244(logic, for example as a theorem-prover, the resulting)J
58 639 :M
2.419 .242(systems turn out to be inefficient. This is a natural)J
58 650 :M
.196 .02(consequence of the expressiveness of the language. On the)J
58 661 :M
1.452 .145(other hand, the languages are sometimes not expressive)J
58 672 :M
1.277 .128(enough to deal with some concepts that seem needed to)J
58 683 :M
3.326 .333(describe agents. An example is the expression of)J
58 694 :M
.372 .037(quantitative magnitudes for describing strength of belief in)J
58 705 :M
-.012(an agent.)A
316 81 :M
.351 .035(Refinement of these logics and their formal semantics, and)J
316 92 :M
1.799 .18(their efficient implementation, is of course an ongoing)J
316 103 :M
3.473 .347(enterprise. This paper is intended as an informal)J
316 114 :M
1.072 .107(preliminary to such work, offering some intuitions about)J
316 125 :M
.007 .001(the interpretation of agent theory through the general theory)J
316 136 :M
-.06(of process dynamics.)A
316 159 :M
2.138 .214(Such an interpretation can also provide a strategy for)J
316 170 :M
3.365 .336(implementation. The situation is analogous to the)J
316 181 :M
-.044(relationship between the abstract Boolean algebra of classes,)A
316 192 :M
.047 .005(the propositional calculus, and hardware logic circuits. The)J
316 203 :M
-.03(abstract algebra is defined in terms of classes and operations)A
316 214 :M
1.005 .101(on them; intersection, union, complementation, etc. One)J
316 225 :M
.263 .026(interpretation of the Boolean algebra is propositional logic,)J
316 236 :M
2.809 .281(where the variables range over propositions and the)J
316 247 :M
1.699 .17(operations are truth-functional manipulations, etc. The)J
316 258 :M
2.044 .204(possibility of implementation arises from the fact that)J
316 269 :M
.784 .078(another interpretation of Boolean algebra can be found in)J
316 280 :M
1.326 .133(the operation of physical electrical circuits. Because of)J
316 291 :M
.617 .062(this, the operation of the circuits can thus be described by)J
316 302 :M
.283 .028(propositional logic, or stated conversely, the circuits are an)J
316 313 :M
.298 .03(implementation of the logic.)J
316 336 :M
.117 .012(Let us represent this by the following schema:)J
316 359 :M
.012 .001(Propositional logic -> Abstract Boolean algebra ->)J
316 370 :M
-.068(Electrical circuits)A
316 393 :M
3.52 .352(This suggests that we should look for an abstract)J
316 404 :M
.291 .029(mathematical theory such that both agent theory and some)J
316 415 :M
.565 .056(suitable physical systems can be interpretations of it. The)J
316 426 :M
-.003(abstract theory can then be used as an intermediary between)A
316 437 :M
1.08 .108(agent logic and the physical systems that can be used as)J
316 448 :M
3.316 .332(efficient implementations. This paper explores the)J
316 459 :M
.857 .086(possibility of using abstract dynamics as such an abstract)J
316 470 :M
-.004(theory and physical dynamic systems as implementations of)A
316 481 :M
.13 .013(agents, as shown by the schema:)J
316 504 :M
-.003(Agent theory -> Abstract Dynamics -> Physical dynamic)A
316 515 :M
.056(systems)A
316 538 :M
3.656 .366(A theoretical foundation has already been laid by)J
316 549 :M
3.795 .38(Rosenschein \(1985, 1986, 1989\) for the epistemic)J
316 560 :M
1.183 .118(\(informational\) analysis of agents regarded as processes.)J
316 571 :M
-.011(We propose that Rosenschein's framework is to be extended)A
316 582 :M
1.304 .13(in two senses. First, the process-based interpretation of)J
316 593 :M
.591 .059(agents is to be extended from the epistemic to praxiologic)J
316 604 :M
2.149 .215(\(action-related\) and axiologic \(value-related\) concepts.)J
316 615 :M
.339 .034(Second, processes are to be analysed in terms of their state)J
316 626 :M
.592 .059(space dynamics in addition to the correlative relationships)J
316 637 :M
-.037(between states of a process and an environment.)A
316 658 :M
f0_12 sf
(2)S
352 658 :M
2.586 .259(Concepts in Agent theory)J
316 678 :M
f1_10 sf
2.193 .219(The main idea an agent theory attempts to capture is)J
316 689 :M
.207 .021(purposiveness: that agents execute actions in order to reach)J
316 700 :M
2.191 .219(goals. Refinements of the theory are concerned with)J
316 711 :M
1 .1(optimality issues. Rational agents are often described as)J
316 722 :M
.139 .014(executing actions which maximally satisfy their goals.)J
endp
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-.044(To provide more structure, agents are also often described in)A
58 92 :M
3.055 .305(mentalistic, intentional terms by attributing to them)J
58 103 :M
1.096 .11(\(propositional\) attitudes. Some of the main examples of)J
58 114 :M
.343 .034(such attitudes, perhaps a minimal set of them, are wanting,)J
58 125 :M
-.03(knowing, liking \(related to preferring\), and intending.)A
58 148 :M
2.26 .226(The common-sense interpretation of these concepts is)J
58 159 :M
.11 .011(briefly as follows. Knowledge characterizes how the world)J
58 170 :M
.56 .056(is, from the agent's point of view. Likes characterise how)J
58 181 :M
1.387 .139(the agent likes the world to be. Wants characterise the)J
58 192 :M
.058 .006(agent's commitment to reach a goal. Intentions characterise)J
58 203 :M
.199 .02(the commitment of an agent to an action.)J
58 224 :M
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94 224 :M
2.827 .283(Concepts of Abstract Dynamics)J
58 244 :M
f1_10 sf
.715 .072(The main concepts of dynamics deal with the structure of)J
58 255 :M
.933 .093(state spaces. Abstractly, the theory can be formulated in)J
58 266 :M
.797 .08(terms of functional iteration. The functions which define)J
58 277 :M
.389 .039(dynamical systems are also called mappings or maps. The)J
58 288 :M
.554 .055(main concern of the abstract theory is with the asymptotic)J
58 299 :M
2.742 .274(behaviour of iterative mappings. The iteration of a)J
58 310 :M
.316 .032(function is a discrete process. If the process is continuous,)J
58 321 :M
1.31 .131(the description is often given in the form of differential)J
58 332 :M
1.322 .132(equations to describe the behaviour of the solution over)J
58 343 :M
.182(time.)A
58 366 :M
1.375 .138(In a geometric interpretation, the iterative process maps)J
58 377 :M
.829 .083(points into points. The points correspond to the states of)J
58 388 :M
1.776 .178(the process. The process is then said to go through a)J
58 399 :M
.023 .002(trajectory or orbit of points. The main concern of dynamics)J
58 410 :M
-.012(is to understand the nature of all trajectories of a system and)A
58 421 :M
.283 .028(to classify them as moving to a fixed point, being periodic,)J
58 432 :M
1.812 .181(asymptotically periodic, etc. We shall now turn to an)J
58 443 :M
1.101 .11(informal summary of some of these concepts. For more)J
58 454 :M
2.646 .265(detail, see, for example, Abraham and Shaw \(1981\),)J
58 465 :M
3.309 .331(Devaney \(1986\), Thompson and Stewart \(1986\), or)J
58 476 :M
.71 .071(Cvitanovic \(1984\). Cvitanovic also contains an extensive)J
58 487 :M
-.036(bibliography. The field is developing very rapidly under the)A
58 498 :M
.595 .059(designation of chaos theory, which is a specialised branch)J
58 509 :M
-.059(of dynamics.)A
58 532 :M
1.598 .16(The )J
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2.606 .261(state space)J
f1_10 sf
1.737 .174( of a system is generally a topological)J
58 543 :M
1.97 .197(surface \(manifold\) on which the possible states of the)J
58 554 :M
1.561 .156(system are located. This can be just three-dimensional)J
58 565 :M
-.008(space, or some curved surface, for example, like a doughnut)A
58 576 :M
-.021(\(torus\).)A
58 599 :M
.472 .047(It is normally assumed that there is a )J
f2_10 sf
.774 .077(vector field)J
f1_10 sf
.475 .048( acting at)J
58 610 :M
.757 .076(all points of the state space. This vector field determines)J
58 621 :M
.176 .018(the )J
f2_10 sf
.079(dynamics)A
f1_10 sf
.219 .022( of the system by constraining the )J
f2_10 sf
.07(trajectories)A
58 632 :M
f1_10 sf
.268 .027(to certain directions at each point of the state space. When)J
58 643 :M
.12 .012(typical or many trajectories of the system have been drawn,)J
58 654 :M
-.028(we get a )A
f2_10 sf
-.029(phase portrait)A
f1_10 sf
-.03( of the system.)A
58 676 :M
.538 .054(Closed trajectories produce )J
f2_10 sf
.712 .071(cyclic behaviour)J
f1_10 sf
.453 .045(. Trajectories)J
58 687 :M
.486 .049(can otherwise take many shapes, like spirals, straight lines)J
58 698 :M
-.029(or any kind of curve.)A
58 720 :M
1.279 .128(The focus of interest is in the )J
f2_10 sf
3.152 .315(asymptotic behaviour)J
f1_10 sf
.988 .099( of)J
58 731 :M
1.294 .129(trajectories. )J
f2_10 sf
1.685 .168(Limit sets)J
f1_10 sf
1.093 .109( of state spaces are sets of points)J
316 81 :M
.312 .031(towards which the trajectories move asymptotically. Limit)J
316 92 :M
.362 .036(sets may be solitary points, or cycles, or more complicated)J
316 103 :M
2.305 .23(distributions of points. Limit sets which are solitary)J
316 114 :M
.072 .007(points, are called )J
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.105 .011(fixed points)J
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(.)S
316 136 :M
1.353 .135(Fixed points of functions are points )J
f2_10 sf
.403(x)A
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.966 .097( for which )J
f2_10 sf
.38(f\(x\)=x)A
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(.)S
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.268 .027(That is, the fixed points are mapped into themselves by the)J
316 158 :M
.411 .041(function. Fixed points are important in dynamics, because)J
316 169 :M
.75 .075(they correspond to equilibrium \(steady\) states of systems.)J
316 180 :M
.32 .032(Once a system has somehow got to a state which is a fixed)J
316 191 :M
.231 .023(point, it will not move from that state under the iteration of)J
316 202 :M
.324 .032(the function )J
f2_10 sf
.059(f)A
f1_10 sf
(.)S
316 224 :M
1.31 .131(It is of interest to ask how a system may get to a fixed)J
316 235 :M
.467 .047(point. The simplest case is that the system may start from)J
316 246 :M
1.105 .111(an initial state that is a fixed point, and there will be no)J
316 257 :M
.671 .067(further change. More interestingly, trajectories starting at)J
316 268 :M
1.268 .127(other states may lead to a fixed point after a number of)J
316 279 :M
1.935 .193(transitions. In such cases we say that the fixed point)J
316 290 :M
f2_10 sf
.606(attracts)A
f1_10 sf
2.075 .208( the trajectory. The set of states from which)J
316 301 :M
.842 .084(trajectories lead to an attractive fixed point are called the)J
316 312 :M
f2_10 sf
1.597 .16(basin of attraction)J
f1_10 sf
.888 .089( of the fixed point. It turns out that a)J
316 323 :M
1.764 .176(fixed point is attractive if the slope \(derivative\) of the)J
316 334 :M
.754 .075(function )J
f2_10 sf
.111(f)A
f1_10 sf
.483 .048( is less than 1 at the fixed point. The magnitude)J
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.694 .069(of the slope characterizes the strength of the attractor: the)J
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.226 .023(greater the strength, the faster the trajectory approaches the)J
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2.196 .22(fixed point. Two different kinds of behaviour in the)J
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-.008(neighbourhood of a fixed point are illustrated in Figure 1.)A
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.112 .011(Figure 1. Attractive fixed points)J
316 557 :M
.961 .096(A periodic point is a generalisation of the concept of the)J
316 568 :M
.492 .049(fixed point to the case when a trajectory cyclically visits a)J
316 579 :M
.123 .012(point after every )J
f2_10 sf
.054 .005(n )J
f1_10 sf
.13 .013(iterations of the function )J
f2_10 sf
(f)S
f1_10 sf
(.)S
316 601 :M
.468 .047(If the iteration is run backwards, trajectories would appear)J
316 612 :M
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316 623 :M
1.488 .149(the fixed point is called a )J
f2_10 sf
.51(repellor)A
f1_10 sf
1.665 .166(. Such fixed points)J
316 634 :M
2.292 .229(correspond to unstable equilibria in physical systems.)J
316 645 :M
1.041 .104(Slight disturbance from the equilibrium starts the system)J
316 656 :M
1.303 .13(on a trajectory leading away from the equilibrium state.)J
316 667 :M
1.674 .167(Conversely, attractive fixed points correspond to stable)J
316 678 :M
-.082(equilibria.)A
316 700 :M
1.535 .153(An interesting situation is shown in Fig. 2. There is a)J
316 711 :M
1.349 .135(limit point which is attractive for points on the left and)J
316 722 :M
1.718 .172(repelling for points on the right. The two heavy lines)J
316 733 :M
.776 .078(show trajectories which are not in the basins of attraction)J
endp
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.059 .006(and repulsion, and are deflected by the presence of the limit)J
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1.257 .126(point without going through it. This illustrates how the)J
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58 114 :M
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58 125 :M
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f1_10 sf
-.058(Figure 2. Deflected trajectories)A
58 356 :M
f0_12 sf
(4)S
94 356 :M
2.641 .264(Dynamics and Information)J
58 376 :M
f1_10 sf
1.999 .2(Dynamics and information theory are connected. The)J
58 387 :M
.96 .096(connection with the concept of information can be found)J
58 398 :M
1.546 .155(when we consider the information needed to )J
f2_10 sf
.384(specify)A
f1_10 sf
.874 .087( or)J
58 409 :M
f2_10 sf
.274(measure)A
f1_10 sf
.688 .069( the state of a dynamic system at a point in time.)J
58 420 :M
.677 .068(For example, when we want to start up a dynamic system)J
58 431 :M
1.413 .141(from some initial state, we need to specify that starting)J
58 442 :M
.383 .038(state to some degree of precision. Conversely, if we try to)J
58 453 :M
.188 .019(find out what the state of the system is at some later instant)J
58 464 :M
1.62 .162(of time, we can only measure its state to some limited)J
58 475 :M
2.396 .24(degree accuracy, determined by the resolution of our)J
58 486 :M
.357 .036(measuring instruments or sense organs. We can then speak)J
58 497 :M
3.489 .349(of the amount of information needed to make the)J
58 508 :M
.148 .015(specification, or the amount of information gained from the)J
58 519 :M
-.073(measurement.)A
58 541 :M
.738 .074(The convergence and divergence of trajectories near limit)J
58 552 :M
3.293 .329(sets are associated with information gain and loss.)J
58 563 :M
2.937 .294(Divergence of trajectories is associated with greater)J
58 574 :M
2.72 .272(uncertainty about the actual state of the system and)J
58 585 :M
.232 .023(therefore with information loss, as can be seen from Figure)J
58 596 :M
1.337 .134(3. Consider the trajectories that go through the smaller)J
58 607 :M
1.24 .124(circular area on the left. In order to specify or locate a)J
58 618 :M
.946 .095(particular trajectory, we have to specify the position of a)J
58 629 :M
1.301 .13(point within this area. The accuracy of specification or)J
58 640 :M
.541 .054(measurement defines a coordinate grid over the area. The)J
58 651 :M
.823 .082(amount of information involved is that needed to select a)J
58 662 :M
.143 .014(cell in this grid. The larger circular area on the right shows)J
58 673 :M
.205 .021(the effect of divergence in the phase space. If the accuracy)J
58 684 :M
.491 .049(of specification or measurement remains constant, a larger)J
58 695 :M
.04 .004(amount of information is needed to specify the location of a)J
58 706 :M
1.131 .113(trajectory, and a larger amount of information is yielded)J
58 717 :M
1.835 .184(when the state is measured, because there are a larger)J
58 728 :M
.091 .009(number of cells in the grid.)J
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.151 .015(Figure 3. Information loss in divergent flow)J
316 297 :M
2.945 .294(Since diverging flows involve a progressive loss of)J
316 308 :M
1.928 .193(information about the state of the system they lead to)J
316 319 :M
.113 .011(sensitive dependence on the initial conditions \(the so-called)J
316 330 :M
1.138 .114("butterfly effect": the flapping of a butterfly's wings can)J
316 341 :M
4.305 .43(cause a cyclone later\). Although the system is)J
316 352 :M
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.062(deterministic)A
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.183 .018(, it becomes )J
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.066(unpredictable)A
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.176 .018( in the long run due)J
316 363 :M
.558 .056(to this information loss.)J
316 385 :M
3.223 .322(As far as practical applications are concerned, this)J
316 396 :M
1.412 .141(phenomenon can be used for )J
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2.15 .215(amplification and control)J
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1.986 .199(purposes in information processing: a small change in)J
316 418 :M
2.305 .23(initial conditions can produce a large change in later)J
316 429 :M
1.542 .154(behaviour. The converse effect, gain of information in)J
316 440 :M
.66 .066(convergent flows, produces insensitive dependence on the)J
316 451 :M
-.034(initial conditions and can therefore be used for )A
f2_10 sf
-.036(classification)A
316 462 :M
1.417 .142(or recognition)J
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.99 .099( processes in information processing. The)J
316 473 :M
1.047 .105(convergence of trajectories to a fixed point serves as the)J
316 484 :M
.653 .065(recognition of the starting points in the basin of attraction)J
316 495 :M
.213 .021(as belonging to the same class.)J
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2.364 .236(Agent Attributes and Dynamics)J
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.303 .03(We now turn to the central proposal of this paper, which is)J
316 547 :M
1.299 .13(to interpret agent-theoretic concepts in terms of abstract)J
316 558 :M
-.103(dynamics.)A
316 580 :M
2.511 .251(Rosenschein \(1985\) has already interpreted agents as)J
316 591 :M
1.362 .136(processes and offered an operationalisation of epistemic)J
316 602 :M
1.377 .138(attitudes in terms of states of a process. The epistemic)J
316 613 :M
.687 .069(interpretation of states hinges on there being a correlation)J
316 624 :M
.251 .025(between states of the environment \(the world\) and states of)J
316 635 :M
.25 .025(the agent. When such a correlation exists, the agent is said)J
316 646 :M
1.205 .12(to know a fact that can be stated as a description of the)J
316 657 :M
-.094(corresponding world state.)A
316 679 :M
.137 .014(This interpretation of knowledge as states of a process does)J
316 690 :M
.213 .021(not yet offer any insight into why the correlations exist and)J
316 701 :M
.832 .083(what their nature is, nor is there any principle that would)J
316 712 :M
.65 .065(describe the dynamics of the process that is said to be the)J
316 723 :M
-.031(agent.)A
endp
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2.05 .205(Complex agents are architecturally compositional both)J
58 92 :M
-.027(structurally and behaviourally. The complex agent structure)A
58 103 :M
1.221 .122(is produced by assembling simpler component elements.)J
58 114 :M
3.726 .373(Complex agent behaviour is produced through the)J
58 125 :M
.183 .018(interactions between the simpler component behaviours. A)J
58 136 :M
1.849 .185(vital point is that agents are )J
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.645(nonlinear)A
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1.985 .199( systems. The)J
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1.521 .152(importance of this is in the fact that )J
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2.398 .24(only in nonlinear)J
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.027(systems)A
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.049 .005( will )J
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.024(qualitatively)A
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.105 .01( new phenomena arise through the)J
58 169 :M
.668 .067(interactions between components. In linear systems these)J
58 180 :M
.729 .073(interactions will be merely additive accumulations of size)J
58 191 :M
.731 .073(\(scaling\), without new features. Nonlinearity leads to the)J
58 202 :M
.621 .062(appearance of new features in the )J
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.182(global)A
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.632 .063( behaviour of the)J
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.071 .007(system which were not present in the behaviour of the )J
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.025(local)A
58 224 :M
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.829 .083(components and are not just the additive accumulation of)J
58 235 :M
(the component behaviours.)S
58 257 :M
.863 .086(Concurrency, parallelism and distributed systems become)J
58 268 :M
1.211 .121(important because structural and behavioural complexity)J
58 279 :M
.324 .032(only emerge as the result of iterative accumulation of local)J
58 290 :M
1.029 .103(components. The local components can be identical and)J
58 301 :M
2.29 .229(simple in the computations they carry out. Complex)J
58 312 :M
.058 .006(structures appear as the result of the many interactions. For)J
58 323 :M
.848 .085(real-time operation the execution of the numerous )J
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.262(simple)A
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2.518 .252(identical steps)J
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1.338 .134( can be, and needs to be, parallel. Long)J
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.073 .007(behavioural trajectories can then be computed in essentially)J
58 356 :M
1.479 .148(a single step in the limit of parallelism, or increasingly)J
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2.042 .204(serially between a single-processor and the maximally)J
58 378 :M
.88 .088(parallel system. Proportional speed-up is thus obtainable)J
58 389 :M
.573 .057(by adding more processors. This contrasts with the rather)J
58 400 :M
1.748 .175(more limited gains that can be obtained in the case of)J
58 411 :M
4.492 .449(carrying out complex structured computations on)J
58 422 :M
.285 .029(multiprocessor systems.)J
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1.27 .127(The dynamics of the agent process are of importance in)J
58 455 :M
5.828 .583(relation to all three aspects of agent theory:)J
58 466 :M
-.009(epistemological, praxiological and axiological.)A
58 488 :M
.635 .063(The epistemic issues are concerned with the way states of)J
58 499 :M
2.079 .208(the environment process determine states of the agent)J
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-.086(process and hence produce the correlations referred to above.)A
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2.828 .283(The trajectory of a part of the environment process)J
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.704 .07(\(abstractly in a phase-space, concretely in physical space\))J
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1.773 .177(enters into the region within the boundary of an agent)J
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1.472 .147(system and then continues as part of the agent process.)J
58 565 :M
.588 .059(Since this part of the agent process is causally determined)J
58 576 :M
.742 .074(by the environment process by means of the state-to-state)J
58 587 :M
2.157 .216(transitions, the required epistemic correlations will be)J
58 598 :M
.287 .029(produced. In automata-theoretic terms these are inputs. In)J
58 609 :M
.203 .02(agent-theoretic terms these are sensations \(at the boundary\))J
58 620 :M
.127 .013(or perceptions \(further inside the agent\) or cognitions \(deep)J
58 631 :M
.819 .082(inside the agent\). Looking at this another way, the agent)J
58 642 :M
.82 .082(process is simply a part of a global world process and its)J
58 653 :M
.148 .015(states are parts of the world states. )J
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.138 .014(An agent is just a )J
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10 f4_1 :p
20.261 :m
.066(local)A
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96.772 :m
-.007(phenomenon within the )A
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25.557 :m
(global)S
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10 f3_1 :p
60.712 :m
-.007( world process.)A
58 688 :M
1.943 .194(Praxiological issues are concerned with the way agent)J
58 699 :M
1.029 .103(processes eventually \(at the boundary of the agent\) exert)J
58 710 :M
.312 .031(causal influence on the environment process. In automata-)J
58 721 :M
.185 .019(theoretic terms, these are outputs. In agent-theoretic terms,)J
316 81 :M
1.052 .105(these are actions \(at the boundary\), volitions, willings or)J
316 92 :M
-.021(intentions \(progressively deeper within the agent\).)A
316 114 :M
.497 .05(Axiological issues are concerned with the dynamics of the)J
316 125 :M
-.029(agent-process trajectory in its phase-space and, in particular,)A
316 136 :M
.303 .03(with the directional nature of the process. The teleological)J
316 147 :M
.323 .032(nature of agent behaviour is one of the central examples of)J
316 158 :M
1.967 .197(such issues. In terms of nonlinear system theory, the)J
316 169 :M
.113 .011(dynamics can be described in terms of the movement of the)J
316 180 :M
1.138 .114(system state )J
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.339(towards)A
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1.081 .108( stable equilibrium states and )J
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.517(away)A
316 191 :M
.606(from)A
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2.09 .209( unstable equilibrium states. Teleological agent)J
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.208 .021(behaviour is to be identified with movement towards stable)J
316 213 :M
1.152 .115(equilibria which are in this sense )J
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.343(preferred)A
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.956 .096( states of the)J
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1.813 .181(system: the agent )J
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.444(likes)A
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1.469 .147( to be in these states. Aversive)J
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1.134 .113(agent behaviour is to be identified with movement away)J
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.303 .03(from unstable equilibria which are in this sense )J
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.079(disliked)A
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.213 .021( by)J
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.905 .09(the agent. In the terminology of dynamic system theory,)J
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-.028(these states are )A
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-.03(attractors and repellors.)A
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-.031( Unstable equilibria)A
316 279 :M
1.275 .127(arise mainly through competition between attractors and)J
316 290 :M
1.364 .136(represent boundaries between the basins of attraction of)J
316 301 :M
-.019(those attractors.)A
316 323 :M
-.093(The correspondence between the various main characteristics)A
316 334 :M
.262 .026(of )J
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.138(purposive)A
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.618 .062( agents and dynamic process-related concepts)J
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-.054(can be sketched as follows:)A
325 368 :M
(\245)S
343 368 :M
-.056(Agents correspond to atomic or structured processes.)A
325 390 :M
(\245)S
343 390 :M
4.904 .49(What the agent knows corresponds to the)J
343 401 :M
.124 .012(information contents of a state.)J
325 423 :M
(\245)S
343 423 :M
.228 .023(An agent's actions correspond to a change of state in)J
343 434 :M
-.016(the state space.)A
325 456 :M
(\245)S
343 456 :M
.513 .051(The likes and dislikes of an agent correspond to the)J
343 467 :M
.385 .038(global \(high-dimensional\) attractors and repellors of)J
343 478 :M
3.147 .315(the state-space. In complex agents these are)J
343 489 :M
.116 .012(elements of a value system.)J
325 511 :M
(\245)S
343 511 :M
1.84 .184(A goal of an agent corresponds to a local \(low-)J
343 522 :M
-.009(dimensional\) attractor in a basin of attraction.)A
325 544 :M
(\245)S
343 544 :M
(A want of an agent corresponds to a )S
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(trajectory)S
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( which)S
343 555 :M
3.268 .327(converges to a local attractor in its basin of)J
343 566 :M
-.026(attraction.)A
325 588 :M
(\245)S
343 588 :M
1.18 .118(Hedonic states of pleasure and pain correspond to)J
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2.359 .236(satisfaction and dissatisfaction of the constraint)J
343 610 :M
.549 .055(system constituted by the attractors and repellors of)J
343 621 :M
.015 .001(the state-space, i.e. to )J
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(distance)S
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.017 .002( from them.)J
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.498 .05(Following Rosenschein's conceptual framework, processes)J
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2.347 .235(will be regarded as trajectories over time and spatial)J
316 678 :M
.371 .037(locations. A trajectory is specified by a function )J
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.22 .022(w : L)J
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.061 .006( )J
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.147(\264)A
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.061 .006( )J
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.741 .074(-> )J
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.607(D)A
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.958 .096(, where )J
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.467(T)A
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.732 .073( is a set of times, )J
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.467(L)A
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.9 .09( is a set of locations of)J
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1.888 .189(some physical system and each location )J
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.576(a)A
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1.35 .135( can take on)J
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1.041 .104(values from some set )J
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.526(D)A
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0 -2 rm
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.546 .055(. )J
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.165 .017( )J
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.526(D)A
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.888 .089( is the union taken over all)J
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1.883 .188(sets )J
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.726(a)A
0 -2 rm
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1.736 .174(. An agent will be taken to be a process or a)J
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.945 .094(structured set of processes. The structuring is defined in)J
58 92 :M
-.002(terms of constraints between the process states.)A
58 114 :M
.462 .046(Interpreting goals as local attractors can be seen as a more)J
58 125 :M
.138 .014(special case of trajectories being shaped by the existence of)J
58 136 :M
.903 .09(attractors and repellors in the state space. Attractors and)J
58 147 :M
1.799 .18(repellors determine the direction of movement, i.e. the)J
58 158 :M
.523 .052(direction of agent action. It is natural to interpret the pro-)J
58 169 :M
.379 .038(and anti-attitudes of agents with this kind of directionality.)J
58 180 :M
.169 .017(Movement according to attractors and repellors leads to the)J
58 191 :M
.742 .074(notion of the movement )J
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.182(satisfying)A
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.829 .083( the constraints applied)J
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2.068 .207(by them. We propose to tie this notion of constraint)J
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.085 .008(satisfaction to the notion of hedonic satisfaction in complex)J
58 224 :M
1.462 .146(agents. Pleasure and pain constrain agent action in the)J
58 235 :M
.856 .086(same structural sense as attractors and repellors constrain)J
58 246 :M
.156 .016(dynamic systems. We assume that due to the physiological)J
58 257 :M
.589 .059(structuring of living organisms attractors and repellors are)J
58 268 :M
.04 .004(created in their behavioural space. By analogy, it should be)J
58 279 :M
1.749 .175(possible to create attractors and repellors in non-living)J
58 290 :M
.4 .04(computational systems through appropriate construction or)J
58 301 :M
.006(programming.)A
58 323 :M
.895 .089(Wants in agent theory express the notion that an agent is)J
58 334 :M
.516 .052(committed to carrying out some action or series of actions)J
58 345 :M
2.643 .264(to reach a goal. This commitment can be naturally)J
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1.284 .128(interpreted as embarking on a trajectory towards a local)J
58 367 :M
.478 .048(attractor in a basin. Weaker forms of desire, like wishing,)J
58 378 :M
2.258 .226(can be interpreted as a belief that some goal state is)J
58 389 :M
.321 .032(attractive, without commitment to actions.)J
58 411 :M
1.075 .107(For simplicity we do not distinguish here between belief)J
58 422 :M
.733 .073(and knowledge as epistemic states of an agent. Adopting)J
58 433 :M
2.019 .202(the theory proposed by Rosenschein \(1985, 1986\), we)J
58 444 :M
(interpret knowledge as the information content of an agent's)S
58 455 :M
.925 .093(state. The information content expresses the relationship)J
58 466 :M
-.019(between an agent's internal state and the corresponding state)A
58 477 :M
3.447 .345(of the environment. An agent is said to know a)J
58 488 :M
1.12 .112(proposition )J
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.321 .032(p )J
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.627 .063(in a situation in which its internal state is )J
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.199(s)A
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(,)S
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.525 .052(if in all possible situations in which the agent is in state )J
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.165(s)A
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(,)S
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.368(p)A
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1.032 .103( is satisfied by the environment. Recall that agents are)J
58 521 :M
.547 .055(interpreted as processes, so that agent states correspond to)J
58 532 :M
2.093 .209(process states. An agent can only tell what state the)J
58 543 :M
1.058 .106(environment is in by examining parts of its own internal)J
58 554 :M
.312 .031(state, i.e. the state of its sensory apparatus. Since there are)J
58 565 :M
.168 .017(causal constraints between the state of the environment and)J
58 576 :M
1.386 .139(the state of the agent, the agent's internal state contains)J
58 587 :M
.273 .027(information about the environment. What the agent knows)J
58 598 :M
3.576 .358(is the discriminatory power of this information in)J
58 609 :M
.551 .055(distinguishing between possible states of the environment.)J
58 620 :M
3.818 .382(The agent's knowledge defines what states of the)J
58 631 :M
1.217 .122(environment are indistinguishable from each other. The)J
58 642 :M
.711 .071(more the agent knows, the smaller these indistinguishable)J
58 653 :M
-.132(equivalence classes.)A
58 675 :M
2.384 .238(In this framework reasoning can be shown to be the)J
58 686 :M
1.091 .109(concentration of information from a set of locations to a)J
58 697 :M
.476 .048(smaller set of locations, and also to be the making explicit)J
58 708 :M
1.476 .148(of the information contained implicitly in the larger set)J
58 719 :M
.496 .05(\(Rosenschein and Kaelbling, 1986\). Agent states can thus)J
58 730 :M
.863 .086(be thought of as being ordered in terms of the amount of)J
316 81 :M
.831 .083(explicit infomation they contain. The greater the explicit)J
316 92 :M
1.55 .155(information content, the more precisely the state of the)J
316 103 :M
.085 .008(world is known.)J
316 125 :M
.572 .057(The usefulness of knowledge for an agent is, of course, in)J
316 136 :M
.538 .054(guiding action towards a goal. In process dynamics terms)J
316 147 :M
-.008(the agent needs knowledge in order to tell what trajectory to)A
316 158 :M
2.092 .209(follow. In areas of the state space where trajectories)J
316 169 :M
.528 .053(diverge, there is sensitive dependence on the current state,)J
316 180 :M
.483 .048(so even small errors in determining a trajectory may mean)J
316 191 :M
.464 .046(missing the goal later. In areas where the flow converges,)J
316 202 :M
.728 .073(little knowledge is needed: the agent can't help taking the)J
316 213 :M
.31 .031(right action.)J
316 234 :M
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352 234 :M
2.785 .278(Brief Notes on Other Issues)J
316 254 :M
f1_10 sf
2.215 .222(This section presents brief notes on some conjectures)J
316 265 :M
-.008(relating agent theory to dynamics. These notes are intended)A
316 276 :M
.143 .014(as a basis for discussion about these issues with others both)J
316 287 :M
1.01 .101(in the areas of dynamics, AI and cognitive science. The)J
316 298 :M
3.367 .337(notes will be revised and expanded as a result of)J
316 309 :M
-.005(discussions.)A
316 330 :M
f2_12 sf
.5(6.1)A
352 330 :M
-.285(Learning)A
316 350 :M
f1_10 sf
.147 .015(Learning consists in shaping the phase-space of the system.)J
316 361 :M
1.97 .197(For example, goal-directed and aversive behaviour are)J
316 372 :M
-.089(produced by introducing attractors and repellers in the phase-)A
316 383 :M
.044 .004(space. Shaping of the phase-space is produced by changing)J
316 394 :M
.487 .049(the computational mapping between environmental inputs,)J
316 405 :M
3.363 .336(internal state, and agent outputs. The behavioural)J
316 416 :M
2.39 .239(trajectories of an agent are produced by the iterative)J
316 427 :M
5.293 .529(computation of this mapping using the current)J
316 438 :M
2.511 .251(environmental inputs and current internal state. The)J
316 449 :M
.125 .012(attractors and repellers can be both implicitly and explicitly)J
316 460 :M
.46 .046(represented in the structures that define this computational)J
316 471 :M
.162 .016(mapping. It is reasonable to assume that low level learning)J
316 482 :M
2.951 .295(of the kind produced by conditioning is implicitly)J
316 493 :M
2.275 .228(represented, while learning procedures from linguistic)J
316 504 :M
-.048(descriptions is explicitly represented.)A
316 525 :M
f2_12 sf
.5(6.2)A
352 525 :M
3.179 .318(Linking Cognition to Action at Fixed)J
316 537 :M
-.133(Points)A
316 557 :M
f1_10 sf
1.028 .103(Concepts of dynamics are also applicable to some of the)J
316 568 :M
2.266 .227(internal processes taking place inside agents. In this)J
316 579 :M
.395 .04(section I briefly discuss two proposals: \(a\) that the process)J
316 590 :M
1.504 .15(of constructing increasingly abstract representations has)J
316 601 :M
1.033 .103(fixed points, and \(b\) that for maximal generality the two)J
316 612 :M
1.015 .101(processes of cognition and action are best linked to each)J
316 623 :M
.082 .008(other at fixed points of the cognition process.)J
316 645 :M
1.29 .129(One role of the cognitive and perceptual processes is to)J
316 656 :M
2.854 .285(obtain representations of the environment. I regard)J
316 667 :M
1.505 .15(representations as approximations, because they contain)J
316 678 :M
2.129 .213(less information than the objects they represent. Such)J
316 689 :M
2.11 .211(approximations are more economical than the original)J
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.639 .064(objects, because they abstract away from irrelevant detail.)J
316 711 :M
.053 .005(It is often pointed out in the literature of psychology and AI)J
316 722 :M
1.061 .106(that perceptual processing proceeds through a number of)J
316 733 :M
1.827 .183(levels in terms of the abstractness or generality of the)J
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-.012(representations used. I assume that the iterative progression)A
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3.495 .35(through such levels of mapping into more general)J
58 103 :M
1.13 .113(representations has limits which are fixed points. These)J
58 114 :M
1.178 .118(fixed points are irreducibly abstract concepts. I want to)J
58 125 :M
.731 .073(emphasize, that I do not mean irreducibility to properties.)J
58 136 :M
1.568 .157(If reduction to properties is possible, the properties are)J
58 147 :M
.119 .012(themselves represented at the most abstract level. My most)J
58 158 :M
.863 .086(abstract conception of a dog has still properties like legs,)J
58 169 :M
.051 .005(but the legs are the most abstract kind that I have available.)J
58 191 :M
-.033(Action patterns are produced by using a mapping to produce)A
58 202 :M
2.862 .286(patterns on the "surface" of the agent starting from)J
58 213 :M
.637 .064(representations inside. This surface is the set of actuators)J
58 224 :M
1.983 .198(or transducers of the agent. In terms of directionality,)J
58 235 :M
1.163 .116(actions are an "inside-out process" in terms of causation)J
58 246 :M
.108 .011(from agent to environment.)J
58 268 :M
1.232 .123(Cognitive and action patterns are best linked together at)J
58 279 :M
1.133 .113(increasing levels of condensed representation in order to)J
58 290 :M
.404 .04(achieve economy and generality. The most economic way)J
58 301 :M
.955 .096(of doing this is to place the linkage at fixed points. The)J
58 312 :M
.126 .013(progression from cognition to action \(and back to cognition)J
58 323 :M
.251 .025(again via the environmental feedback loop\) is via the focus)J
58 334 :M
.128 .013(of fixed points where the representation from cognition and)J
58 345 :M
1.131 .113(the representation for action are at the same level: when)J
58 356 :M
1.728 .173(looked upon from the cognitive point of view, it is an)J
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.412 .041(appropriately abstract representation of a situation )J
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.168 .017(as it is )J
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2.107 .211(when looked upon from the action point of view, the)J
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.483 .048(representation is of a situation )J
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.292 .029(as it is to be)J
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.356 .036( as the result of)J
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1.417 .142(the action, when appropriately expanded. The result of)J
58 411 :M
.19 .019(condensation through cognition is a fixed point. This fixed)J
58 422 :M
.283 .028(point is then used as the starting point \(or parameter value\))J
58 433 :M
.338 .034(for expansion into an action pattern. The usefulness of the)J
58 444 :M
1.08 .108(fixed-point representation is in its economy both in size,)J
58 455 :M
1.517 .152(and also in its abstractness: many similar situations are)J
58 466 :M
-.021(conceptually classified together for the purposes of identical)A
58 477 :M
.581 .058(or similar action. Generalisation over similar situations is)J
58 488 :M
-.025(thus obtained, producing economy.)A
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94 509 :M
-.022(Problem Solving)A
58 529 :M
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.535 .053(Problem solving can be interpreted as a trajectory towards)J
58 540 :M
.487 .049(stable equilibria, as has been discussed in relation to goals)J
58 551 :M
.858 .086(earlier in this paper. Alternative paths to an attractor are)J
58 562 :M
1.711 .171(disjunctive solutions, while points on a single path are)J
58 573 :M
.118 .012(conjunctive subgoals.)J
58 595 :M
.206 .021(The problem-solving metaphor can possibly be extended to)J
58 606 :M
.591 .059(logical inference, as is done in intuitionistic logic. It may)J
58 617 :M
3.32 .332(be natural to interpret the existence of a proof as)J
58 628 :M
-.011(convergence to a maximal informational state.)A
58 650 :M
1.676 .168(Axioms could be interpreted as fixed points since they)J
58 661 :M
-.083(require no further proof process.)A
58 683 :M
2.862 .286(Reasoning is seen as finding a path from the point)J
58 694 :M
-.032(corresponding to a formula to a fixed point corresponding to)A
58 705 :M
1.223 .122(an axiom. The path is the proof process, consisting of a)J
58 716 :M
1.24 .124(sequence of transformations of the formula according to)J
316 81 :M
2.648 .265(derivation rules. The derivation rules correspond to)J
316 92 :M
-.004(reasoning actions of an agent.)A
316 114 :M
1.314 .131(Alternatively, formulas to be proved can be regarded as)J
316 125 :M
1.63 .163(problems to be solved, with constituent subformulas as)J
316 136 :M
.305 .03(subgoals. The informational state of the agent increases as)J
316 147 :M
3.555 .356(more and more constituents are proved. Such an)J
316 158 :M
.403 .04(interpretation has been used by Kripke \(1965\) to provide a)J
316 169 :M
.884 .088(semantics for intuitionistic logic. It will be of interest to)J
316 180 :M
1.373 .137(analyse the dynamics of changes in informational states)J
316 191 :M
.133 .013(along the lines suggested in this paper.)J
316 212 :M
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352 212 :M
1.061 .106(Process Dynamics as an Implementation)J
316 224 :M
-.141(Strategy)A
316 244 :M
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.788 .079( The theoretical framework proposed represents agents as)J
316 255 :M
-.054(processes \(or bundles of processes\) and constraints acting on)A
316 266 :M
.583 .058(these processes, producing the appropriate dynamics. This)J
316 277 :M
.67 .067(suggests that the implementation should be in the form of)J
316 288 :M
1.374 .137(machines recursively composed of parts. Machines can)J
316 299 :M
1.221 .122(generally be described as bundles of processes, with the)J
316 310 :M
-.008(machine structure acting as constraints on the processes.)A
316 332 :M
1.061 .106(Rosenschein and Kaelbling \(1986\) has offered a detailed)J
316 343 :M
.87 .087(formalisation of this concept by modelling machines as a)J
316 354 :M
.346 .035(pair of processes \(input and output\), subject to behavioural)J
316 365 :M
1.21 .121(constraints. The constraints impose a structuring on the)J
316 376 :M
1.839 .184(state-space of the output process that can occur in the)J
316 387 :M
2.165 .216(machine, producing what we call a dynamics for that)J
316 398 :M
.659 .066(process. Having a dynamics )J
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.224(means)A
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.749 .075( being constrained, so)J
316 409 :M
.079 .008(that not all possible state trajectories are possible, and those)J
316 420 :M
2.434 .243(that are possible must take a shape that satisfies the)J
316 431 :M
(constrains.)S
316 453 :M
.562 .056(Convenient high-level languages need to be developed for)J
316 464 :M
1.013 .101(expressing the constraint system in order to facilitate the)J
316 475 :M
1.754 .175(design of artificial agents. Rosenschein and Kaelbling)J
316 486 :M
2.458 .246(\(1986, 1989\) have developed one example of such a)J
316 497 :M
2.946 .295(language, REX, and its extension to the declarative)J
316 508 :M
1.3 .13(specification of goals, GAPPS. This language has been)J
316 519 :M
2.033 .203(used in robotics by Rosenschein and by the author in)J
316 530 :M
1.908 .191(developing agents as intelligent interfaces to computer)J
316 541 :M
-.115(software.)A
316 562 :M
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.8(Conclusions)A
316 582 :M
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2.704 .27(This paper has taken the first steps in providing an)J
316 593 :M
2.47 .247(interpretation of agent theoretic concepts in terms of)J
316 604 :M
1.23 .123(process dynamics concepts. If successful, this approach)J
316 615 :M
1.336 .134(could have the double advantage that it provides both a)J
316 626 :M
3.259 .326(mathematical theory which is already known to be)J
316 637 :M
1.228 .123(successful in other application domains like physics and)J
316 648 :M
3.058 .306(biology, and it also gives a hint at implementation)J
316 659 :M
-.019(strategy.)A
316 680 :M
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352 680 :M
.672(References)A
316 700 :M
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2.03 .203(Abraham, R.H. and Shaw, C.D. \(1981\) Dynamics, the)J
338 711 :M
1.086 .109(Geometry of Behavior, Parts 1-4. Santa Cruz, CA:)J
338 722 :M
-.007(Aerial Press.)A
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80 161 :M
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80 230 :M
6.86 .686(implementation strategy. )J
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5.67 .567(Project )J
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2.003(Report)A
80 241 :M
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2.149 .215(Kripke, S. \(1965\) Semantical analysis of intuitionistic)J
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1.624 .162(and robotics. New Generation Computing, 3, 345-)J
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4.65 .465(of digital machines with provable epistemic)J
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3.317 .332(reasoning about knowledge. Proc. of the 1986)J
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2.558 .256(Rosenschein, S. and Kaelbling, L. \(1989\) Integrating)J
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3.552 .355(Space Telerobotics Conference, Pasadena, CA.)J
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1.25 .125(automata from environment descriptions. In: Proc.)J
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.125(1989.)A
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1.849 .185(Thompson, J.M.T. and Stewart, H.B. \(1986\) Nonlinear)J
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