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gS 0 0 538 781 rC
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2.91 .291(Towards a Semantics of Desires)J
160 275 :M
f0_12 sf
4.343 .434(George Kiss)J
180 299 :M
f1_12 sf
(HCRL)S
146 311 :M
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161 323 :M
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176 335 :M
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298 275 :M
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281 299 :M
f1_12 sf
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277 311 :M
-.086(University of Nottingham)A
310 323 :M
-.147(Nottingham)A
318 335 :M
-.165(England)A
193 371 :M
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gS 28 30 538 781 rC
283 56 :M
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(2)S
148 122 :M
f0_18 sf
.291(Abstract)A
148 147 :M
f1_12 sf
1.479 .148(As part of an effort to define a unified formal semantics for)J
148 159 :M
-.038(beliefs, desires and action, this paper sketches a model theory for)A
148 171 :M
1.416 .142(the axiological aspects of agent theory: hedonic states, likes,)J
148 183 :M
.843 .084(goals and values. Particular attention is paid to modelling the)J
148 195 :M
-.115(intensity of likes. The main intuition underlying the model theory)A
148 207 :M
.748 .075(is that the axiological aspects of agent theory can be modelled)J
148 219 :M
1.675 .167(through computational generalisations of physical dynamics.)J
148 231 :M
2.729 .273(Computational analogues of force, mass and potential are)J
148 243 :M
.053(offered.)A
90 272 :M
f0_18 sf
.274(Introduction)A
90 297 :M
f1_12 sf
-.096(An important part of agent theory appears to be the notion of desires. Several)A
90 309 :M
-.085(formulations of agent theory have adopted beliefs, desires and intentions as a set of)A
90 321 :M
-.029(basic notions \(the so-called BDI models\). However, to our knowledge, so far)A
90 333 :M
-.153(relatively little has been said explicitly in the AI literature about a theory of desires)A
90 345 :M
.189 .019(\(Cohen and Levesque, 1985 and in press, Moore, 1985a; Kiss, 1988, Shoham, 1989\).)J
90 369 :M
-.12(This paper takes some initial steps towards the explicit formulation and formalisation of)A
90 381 :M
-.062(such a theory. We concentrate on axiological issues, covering hedonic states, likes,)A
90 393 :M
.28 .028(goals and values \(Kiss, 1988, 1990\).)J
90 417 :M
-.062(Among the many issues surrounding desires, we select the question of the )A
f2_12 sf
-.057(intensity)A
f1_12 sf
-.082( of)A
90 429 :M
-.145(the attitude of liking for detailed treatment. We think that likes are not the only attitudes)A
90 441 :M
-.098(that have an intensity aspect. It is common to talk about the strength of beliefs too. We)A
90 453 :M
-.093(hope to extend our approach to those other attitudes as well in the future.)A
90 477 :M
-.149(Differences between the intensities of likes are often called preferences in the literature)A
90 489 :M
-.067(of decision theory, economics and psychology. Preferences are usually taken as the)A
90 501 :M
-.109(primary, primitive, notions in the sense that preferences are directly manifested in the)A
90 513 :M
-.139(choices made by an agent. Likes are therefore treated as )A
f2_12 sf
-.139(relative, comparative attitudes)A
f1_12 sf
(.)S
90 525 :M
-.123(Few disciplines enquire into the mechanisms that might determine such choices and it is)A
90 537 :M
-.133(usually assumed that it is preferences that are directly available to the agent. Absolute)A
90 549 :M
-.1(values of liking are usually recovered from behaviourally expressed preferences by)A
90 561 :M
-.12(some analytical computations from the preferences.)A
90 585 :M
-.121(We would like to proceed in the opposite direction and take absolute likes as primary)A
90 597 :M
-.109(which in turn determine preferences. Our intuition is that an agent has representations)A
90 609 :M
-.077(of how far it likes various things and when faced with a choice, compares the)A
90 621 :M
-.101(intensities of its likes to compute a preference. This need not of course exclude)A
90 633 :M
-.122(mechanisms of context dependence and interaction effects.)A
90 657 :M
-.135(Our longer-term research objective is to formulate a unified formal semantics for)A
90 669 :M
-.072(beliefs, desires and action and to lay foundations for implementation work. This short)A
90 681 :M
-.107(paper has limited aims. Our main concern is to refine the set of intuitions which were)A
90 693 :M
-.055(outlined in Kiss \(1988, 1990, 1991\) and sketch the model theory for a modal logic of)A
90 705 :M
-.108(liking. We defer the definition of the syntax and semantics of the logical language, the)A
90 717 :M
-.101(statement of axioms and the derivation of theorems for another paper.)A
90 741 :M
-.125(The main intuition we wish to convey is that the axiological aspects of agent theory are)A
90 753 :M
-.132(best interpreted in terms of concepts that are computational generalisations of physical)A
90 765 :M
-.091(dynamics. Traditionally in physics dynamics deals with changes of state in a system)A
endp
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-28 -30 :T
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-.066(and with the causes of these changes, usually conceptualised as forces. Modern)A
90 93 :M
-.094(developments have turned dynamics into a more abstract area of study, as we shall)A
90 105 :M
-.048(briefly sketch below.)A
90 129 :M
-.118(We propose that dynamics has a natural place in agent theory, since that theory is vitally)A
90 141 :M
-.079(concerned with \(mental\) states, their properties, and with the dynamics of sequences of)A
90 153 :M
-.119(changes in mental state. The interpretation of knowledge and belief as a state of the)A
90 165 :M
-.06(agent has recently been gaining ground \(Rosenschein, 1986; Halpern and Moses,)A
90 177 :M
-.079(1985\). There have been increasing efforts also in forging a link between knowledge)A
90 189 :M
-.041(and action, \(Moore, 1985b; Cohen and Levesque, in press\), thereby introducing a)A
90 201 :M
-.103(dynamic element, because of the changes caused by action. While these authors have)A
90 213 :M
-.105(been concerned with agent dynamics, in a sense, they have not attempted to link their)A
90 225 :M
-.082(logics to dynamical systems in the physical sense. In this paper we hope to continue)A
90 237 :M
-.116(this trend by filling in more detail about agent dynamics.)A
90 261 :M
-.076(The rest of the paper is organised as follows. We first review some relevant concepts)A
90 273 :M
-.068(from abstract dynamics. Next, we discuss how agent-theoretic concepts can be)A
90 285 :M
-.101(interpreted in such terms. Finally, we formulate computational generalisations of)A
90 297 :M
-.08(physical concepts like potential, force, velocity, etc., and indicate how they can provide)A
90 309 :M
-.112(a framework in which to interpret axiological concepts in agent theory.)A
90 338 :M
f0_18 sf
3.033 .303(Concepts of Abstract Dynamics)J
90 363 :M
f1_12 sf
-.129(The main concepts of recent developments in dynamics deal with the structure of state)A
90 375 :M
-.098(spaces. Abstractly, the theory can be formulated in terms of functional iteration. The)A
90 387 :M
-.099(functions which define dynamical systems are also called mappings or maps. The main)A
90 399 :M
-.108(concern of the abstract theory is with the asymptotic behaviour of iterative mappings.)A
90 411 :M
-.066(The iteration of a function is a discrete process. If the process is continuous, the)A
90 423 :M
-.114(description is often given in the form of differential equations to describe the behaviour)A
90 435 :M
-.079(of the solution over time.)A
90 459 :M
-.097(In a geometric interpretation, the iterative process maps points into points. The points)A
90 471 :M
-.052(correspond to the states of the process. The process is then said to go through a)A
90 483 :M
-.094(trajectory or orbit of points. The main concern of dynamics is to understand the nature)A
90 495 :M
-.1(of all trajectories of a system and to classify them as moving to a fixed point, being)A
90 507 :M
-.087(periodic, asymptotically periodic, etc. We shall now turn to an informal summary of)A
90 519 :M
-.047(some of these concepts. For more detail, see, for example, Abraham and Shaw)A
90 531 :M
-.021(\(1981\), Devaney \(1986\), Thompson and Stewart \(1986\) or Cvitanovic \(1984\).)A
90 543 :M
-.103(Cvitanovic also contains an extensive bibliography. The field is developing very)A
90 555 :M
-.079(rapidly under the designation of chaos theory, which is a specialised branch of)A
90 567 :M
(dynamics.)S
90 591 :M
-.146(The )A
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-.13(state space)A
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-.131( of a system is generally a topological surface \(manifold\) on which the)A
90 603 :M
-.082(possible states of the system are located. This can be just three-dimensional space, or)A
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-.033(some curved surface, for example, like a doughnut \(torus\).)A
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-.126(It is normally assumed that there is a )A
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-.135(force)A
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-.082( )A
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-.124(vector field)A
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-.122( acting at all points of the state)A
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-.088(space. This vector field determines the )A
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-.107(dynamics)A
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-.093( of the system by constraining the)A
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-.156(trajectories)A
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-.16( to certain directions at each point of the state space. When typical or many)A
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-.108(trajectories of the system have been drawn, we get a )A
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-.11(phase portrait)A
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-.113( of the system.)A
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-.121(Closed trajectories produce )A
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-.125(cyclic behaviour)A
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-.125(. Trajectories can otherwise take many)A
90 711 :M
-.022(shapes, like spirals, straight lines or any kind of curve.)A
90 735 :M
-.089(The focus of interest is in the )A
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-.104(asymptotic behaviour)A
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-.082( of trajectories. )A
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-.093(Limit sets)A
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-.095( of state)A
90 747 :M
-.097(spaces are sets of points towards which the trajectories move asymptotically. Limit sets)A
endp
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f1_12 sf
(4)S
90 81 :M
-.077(may be solitary points, or cycles, or more complicated distributions of points. Limit)A
90 93 :M
-.04(sets which are solitary points, are called )A
f2_12 sf
-.041(fixed points)A
f1_12 sf
(.)S
90 117 :M
-.027(Fixed points of functions are points )A
f2_12 sf
(x)S
f1_12 sf
-.027( for which )A
f2_12 sf
-.029(f\(x\)=x)A
f1_12 sf
-.026(. That is, the fixed points are)A
90 129 :M
-.087(mapped into themselves by the function. Fixed points are important in dynamics,)A
90 141 :M
-.077(because they correspond to equilibrium \(steady\) states of systems. Once a system has)A
90 153 :M
-.097(somehow got to a state which is a fixed point, it will not move from that state under the)A
90 165 :M
-.071(iteration of the function )A
f2_12 sf
-.053(f)A
f1_12 sf
(.)S
90 189 :M
-.088(It is of interest to ask how a system may get to a fixed point. The simplest case is that)A
90 201 :M
-.116(the system may start from an initial state that is a fixed point, and there will be no)A
90 213 :M
-.117(further change. More interestingly, trajectories starting at other states may lead to a)A
90 225 :M
-.078(fixed point after a number of transitions. In such cases we say that the fixed point)A
90 237 :M
f2_12 sf
-.161(attracts)A
f1_12 sf
-.161( the trajectory. The set of states from which trajectories lead to an attractive)A
90 249 :M
-.137(fixed point are called the )A
f2_12 sf
-.141(basin of attraction)A
f1_12 sf
-.134( of the fixed point. It turns out that a fixed)A
90 261 :M
-.113(point is attractive if the slope \(derivative\) of the function )A
f2_12 sf
-.085(f)A
f1_12 sf
-.115( is less than 1 at the fixed)A
90 273 :M
-.131(point. The magnitude of the slope characterizes the strength of the attractor: the greater)A
90 285 :M
-.094(the strength, the faster the trajectory approaches the fixed point.)A
90 309 :M
-.127(A periodic point is a generalisation of the concept of the fixed point to the case when a)A
90 321 :M
-.115(trajectory cyclically visits a point after every )A
f2_12 sf
-.117(n )A
f1_12 sf
-.116(iterations of the function )A
f2_12 sf
-.086(f)A
f1_12 sf
(.)S
90 345 :M
-.11(If the iteration is run backwards, trajectories would appear to diverge from an attractive)A
90 357 :M
-.095(fixed point. In this situation the fixed point is called a )A
f2_12 sf
-.105(repellor)A
f1_12 sf
-.106(. Such fixed points)A
90 369 :M
-.084(correspond to unstable equilibria in physical systems. Slight disturbance from the)A
90 381 :M
-.12(equilibrium starts the system on a trajectory leading away from the equilibrium state.)A
90 393 :M
-.088(Conversely, attractive fixed points correspond to stable equilibria.)A
90 422 :M
f0_18 sf
2.685 .268(Agent Attributes and Dynamics)J
90 447 :M
f1_12 sf
-.118(We now briefly review how to interpret the agent-theoretic concepts of interest in this)A
90 459 :M
-.083(paper in terms of abstract dynamics.)A
90 481 :M
f0_12 sf
.688(Compositionality.)A
90 505 :M
f1_12 sf
-.145(We assume that complex agents are architecturally compositional both structurally and)A
90 517 :M
-.099(behaviourally. The complex agent structure is produced by assembling simpler)A
90 529 :M
-.097(component elements. Complex agent behaviour is produced through the \(often)A
90 541 :M
-.088(nonlinear\) interactions between the simpler component behaviours. Concurrency,)A
90 553 :M
-.095(parallelism and distributed systems become important issues.)A
90 575 :M
f0_12 sf
2.586 .259(The agent as controller.)J
90 599 :M
f1_12 sf
-.115(We assume that the agent acts as a controller with respect to the world state. The agent)A
90 611 :M
-.088(exerts control by taking actions. We include "doing nothing" as an agent action.)A
90 623 :M
-.109(Taking an evolutionary point of view, we assume that ultimately this control is in the)A
90 635 :M
-.063(interest of fitness for survival. Fitness for survival is dependent on the existence of)A
90 647 :M
-.072(certain world states, or on keeping them within permissible bounds. We assume that)A
90 659 :M
-.102(environmental events produce disturbances in the agent's internal state by causal effects)A
90 671 :M
-.095(conveyed through inputs. Agent action attempts to counteract such disturbances. An)A
90 683 :M
-.135(agent can control the world state either by changing its internal state or by attempting to)A
90 695 :M
-.117(change the external state. For example, the agent may change its beliefs or it may)A
90 707 :M
-.129(locomote to another location.)A
90 731 :M
-.093(We want to distinguish between a system's natural dynamics \(might also be called the)A
90 743 :M
-.103(free dynamics\) which is operating when the agent is executing the "null" action, and the)A
90 755 :M
-.111(constrained dynamics that results from the composition of the free dynamics with the)A
endp
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f1_12 sf
(5)S
90 81 :M
-.112(control dynamics produced by the )A
f2_12 sf
-.113(non-null)A
f1_12 sf
-.105( agent actions. The distinction is motivated)A
90 93 :M
-.1(by recognising that not all events in the world are produced by agent actions. On the)A
90 105 :M
-.078(other hand, agent actions are causing changes of state, but these changes we shall think)A
90 117 :M
-.086(of as either setting up starting states for the free dynamics, or as jumping between)A
90 129 :M
-.098(trajectories of the free dynamics. However, we defer a more detailed explanation of)A
90 141 :M
-.117(our model of agent action to a later paper.)A
90 163 :M
f0_12 sf
3.513 .351(Axiological aspects of agents)J
90 187 :M
f1_12 sf
-.137(Axiological issues are concerned with the directional nature and asymptotic behaviour)A
90 199 :M
-.116(of agent dynamics. The teleological \(goal-directed\) nature of agent behaviour is one of)A
90 211 :M
-.07(the central examples of such issues. In terms of dynamic system theory, the dynamics)A
90 223 :M
-.116(can be described in terms of the movement of the system state )A
f2_12 sf
-.132(towards)A
f1_12 sf
-.124( stable)A
90 235 :M
-.115(equilibrium states and )A
f2_12 sf
-.138(away from)A
f1_12 sf
-.115( unstable equilibrium states. Teleological agent)A
90 247 :M
-.119(behaviour is to be identified with movement towards stable equilibria which are in this)A
90 259 :M
-.107(sense )A
f2_12 sf
-.112(preferred)A
f1_12 sf
-.101( states of the system: we shall say that the agent ")A
f2_12 sf
-.097(likes)A
f1_12 sf
-.106(" to be in these)A
90 271 :M
-.108(states. Aversive agent behaviour is to be identified with movement away from unstable)A
90 283 :M
-.091(equilibria which are in this sense )A
f2_12 sf
-.092(disliked)A
f1_12 sf
-.097( by the agent. In the terminology of dynamic)A
90 295 :M
-.143(system theory, these states are )A
f2_12 sf
-.146(attractors and repellors.)A
f1_12 sf
-.15( Unstable equilibria arise mainly)A
90 307 :M
-.105(through competition between attractors and represent boundaries between the basins of)A
90 319 :M
-.13(attraction of those attractors. Attractors and repellors determine the direction of)A
90 331 :M
-.093(movement, i.e. the direction of agent action. It is natural to interpret the pro- and anti-)A
90 343 :M
-.108(attitudes of agents with this kind of directionality. We assume that due to the)A
90 355 :M
-.116(physiological structuring of living organisms attractors and repellors are created in their)A
90 367 :M
-.086(behavioural space. By analogy, it should be possible to create attractors and repellors)A
90 379 :M
-.091(in non-living computational systems through appropriate construction or programming.)A
90 403 :M
-.1(A related point of view is found in optimisation theory. In this approach the main)A
90 415 :M
-.118(underlying idea is that the states and trajectories of a dynamic system are governed by)A
90 427 :M
-.144(some principle that can be expressed mathematically as finding the stationary value)A
90 439 :M
-.107(\(usually maximisation or minimisation\) of an "objective" \(or goal\) function. There is a)A
90 451 :M
-.111(great deal of work on the application of such optimality principles to evolutionary,)A
90 463 :M
-.075(ecological, economic and behavioural processes. We wish to look upon this approach)A
90 475 :M
-.128(in the same spirit and regard the extrema of the objective function as specifications of)A
90 487 :M
-.11(the attractors and repellors of the state space. In its application to the description of)A
90 499 :M
-.125(behavioural or economical processes the objective function is usually called utility.)A
90 511 :M
-.1(Note that utility is here a descriptive aspect, revealed by the observation of behaviour.)A
90 523 :M
-.117(In other applications to evolutionary processes the objective function is taken to be)A
90 535 :M
-.088(fitness for survival. We are of course more concerned with individual agent behaviour)A
90 547 :M
-.092(and hence with utility in this paper. In summary, from the viewpoint of optimality)A
90 559 :M
-.093(theory, the agent is maximising utility.)A
90 583 :M
-.081(In a utilitarian framework utility would be some function of hedonic states, i.e. pleasure)A
90 595 :M
-.125(and pain. One might speculate that pleasure and pain are related to fitness and have)A
90 607 :M
-.147(been incorporated in the architecture of organisms to make available to the individual)A
90 619 :M
-.105(some state variable that can be used as an indicator of fitness. Such an interpretation)A
90 631 :M
-.1(would not be unnatural in the case of pain as an indicator of damage and hence loss of)A
90 643 :M
-.085(fitness and pleasure as an indicator of health and hence of maximisation of fitness. For)A
90 655 :M
-.116(the time being, we adopt this utilitarian framework and assume that the agent is)A
90 667 :M
-.102(maximising a hedonic function.)A
90 691 :M
-.107(The )A
f2_12 sf
-.111(values)A
f1_12 sf
-.105( of an agent correspond to global \(high-dimensional\) attractors and repellors)A
90 703 :M
-.1(of the composite dynamics. We think of values as global attractors which may never be)A
90 715 :M
-.115(reached or closely approached by trajectories, due to the topological structure of the)A
90 727 :M
-.141(state space created by the competition between them. In complex agents explicit)A
90 739 :M
-.072(representations of values form a value system.)A
endp
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f1_12 sf
(6)S
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-.146(A )A
f2_12 sf
-.133(goal)A
f1_12 sf
-.119( of an agent corresponds to a local \(low-dimensional\) attractor in a basin of)A
90 93 :M
-.113(attraction of the composite dynamics. We think of goals as attractors which are reached)A
90 105 :M
-.096(or closely approached by nearby trajectories.)A
90 129 :M
-.073(To support our intuitions, we wish to use a mechanical analogy. According to this)A
90 141 :M
-.09(analogy the intensity of a desire \(liking\) should correspond to some abstract "force of)A
90 153 :M
-.123(attraction" acting on the agent, producing acceleration of state change.)A
90 177 :M
-.137(Similar conceptual frameworks have already been used in mechanical engineering and)A
90 189 :M
-.059(in robotics \(see Koditschek, 1989 for a review\). In mechanics it is well known that the)A
90 201 :M
-.116(total energy of a dissipative system \(expressed by the Hamiltonian\) will monotonically)A
90 213 :M
-.114(decrease and will be asymptotically stable. A known technique in robot control)A
90 225 :M
-.106(engineering is to use feedback control which amounts to following the gradients of total)A
90 237 :M
-.091(energy. This technique has been used for robot arm control. Direct utilisation of the)A
90 249 :M
-.117(potential field has been used for path planning with obstacle avoidance in mobile robots)A
90 261 :M
-.027(\(Barraquand and Latombe, in press\).)A
90 285 :M
-.109(In our mechanical analogy too, the forces would be derived from a potential field and)A
90 297 :M
-.086(the agent is assumed to follow the gradients of the potential. From the point of view of)A
90 309 :M
-.101(optimisation theory, the objective function is used as the potential. The description of)A
90 321 :M
-.124(such a potential therefore amounts to the specification of a goal which is the)A
90 333 :M
-.134(asymptotically stable equilibrium state of the agent. We can also represent a )A
f2_12 sf
-.184(value)A
90 345 :M
-.058(system)A
f1_12 sf
-.052( in this analogy as additional potentials, with opposite sign, superimposed on the)A
90 357 :M
-.129(potential created by the goal. In the robot navigational applications such potentials are)A
90 369 :M
-.077(used to represent obstacles to be avoided while moving towards the goal state. In our)A
90 381 :M
-.078(analogy these obstacles correspond to elements of the value system, expressed as)A
90 393 :M
-.085("prohibitions". The analogy is reasonable in the light of value systems often being)A
90 405 :M
-.043(expressed in the form of prohibitions \(laws, regulations, etc\). Presumably positive)A
90 417 :M
-.077(values \(obligations\) could always be re-expressed in a negated form.)A
90 441 :M
-.04(Finally, the usefulness of knowledge for an agent is, of course, in guiding action)A
90 453 :M
-.077(towards a goal. In process dynamics terms the agent needs knowledge in order to tell)A
90 465 :M
-.082(what trajectory to follow. However, we shall pursue the interpretation of epistemic)A
90 477 :M
-.086(concepts in a dynamics framework in another paper.)A
90 506 :M
f0_18 sf
3.114 .311(Model theory)J
90 531 :M
f1_12 sf
-.101(In this section we review some of the fundamental concepts that we need for our model)A
90 543 :M
-.055(theory: space, time, state, and process \(trajectory\). Our formulation draws on and)A
90 555 :M
-.063(extends previous work by Rosenschein and Kaelbling \(1986\) on agents as situated)A
90 567 :M
-.068(automata and by Halpern and Moses \(1990\) on knowledge in distributed systems. Our)A
90 579 :M
-.079(main concern is the formal characterisation of a process \(or trajectory\). For this, we)A
90 591 :M
-.082(need formal notions of time, space and state. We describe each in turn briefly.)A
90 613 :M
f2_12 sf
-.091(Time )A
f1_12 sf
-.075(is analysed as consisting of a set of instants )A
f2_12 sf
-.112(T)A
f1_12 sf
-.079( and a total ordering relation < over)A
90 625 :M
f2_12 sf
.917(T)A
f1_12 sf
(.)S
90 649 :M
f2_12 sf
-.102(Space)A
f1_12 sf
-.08( will be regarded as a set of locations )A
f2_12 sf
-.119(L)A
f1_12 sf
-.088(. We shall not assume any specific)A
90 661 :M
-.007(topology over )A
f2_12 sf
(L)S
f1_12 sf
-.006(, but wish to partition )A
f2_12 sf
(L)S
f1_12 sf
-.007( into subsets, which we shall call )A
f2_12 sf
-.007(systems)A
f1_12 sf
(. In)S
90 673 :M
-.118(particular we shall want to distinguish the set of locations that constitute an agent from)A
90 685 :M
-.098(the set of locations that constitute the agent's environment. Sometimes we shall call)A
90 697 :M
-.105(these the set of internal and external locations, respectively.)A
90 721 :M
f2_12 sf
-.088(States )A
f1_12 sf
-.094(are defined as functions from locations to data values. We assume that for every)A
90 733 :M
-.111(location )A
f2_12 sf
-.076(l )A
f1_12 sf
-.092( in )A
f2_12 sf
-.16(L)A
f1_12 sf
-.104(, there is a set of data values )A
f2_12 sf
-.208(D)A
f2_10 sf
0 2 rm
-.067(l)A
0 -2 rm
f1_12 sf
-.112( that this location can take. We)A
90 745 :M
-.079(distinguish between global and local states as follows. Global states are functions)A
90 757 :M
-.102(which assign to every location )A
f2_12 sf
-.071(l)A
f1_12 sf
-.099( a data value from the appropriate set )A
f2_12 sf
-.184(D)A
f2_10 sf
0 2 rm
-.059(l)A
0 -2 rm
f1_12 sf
-.101(. Given a set of)A
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f1_12 sf
(7)S
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-.031(locations )A
f2_12 sf
(L)S
f1_12 sf
-.032(, we define )A
f2_12 sf
-.05(GS)A
f2_10 sf
0 -3 rm
(L)S
0 3 rm
f1_10 sf
0 -3 rm
( )S
0 3 rm
f1_12 sf
-.03(to be the set of possible global states. Clearly, if the)A
90 97 :M
-.043(number of locations is )A
f2_12 sf
-.053(n)A
f1_12 sf
-.04( then )A
f2_12 sf
-.065(GS)A
f2_10 sf
0 -3 rm
-.031(L )A
0 3 rm
f1_12 sf
-.043(can be regarded as an )A
f2_12 sf
-.053(n)A
f1_12 sf
-.042(-dimensional space. If )A
f2_12 sf
-.04(g )A
f1_12 sf
-.048(is a)A
90 109 :M
-.09(global state, then )A
f2_12 sf
-.121(g)A
f1_12 sf
-.08(\()A
f2_12 sf
-.067(l)A
f1_12 sf
-.094(\) denotes the data value assigned to location )A
f2_12 sf
-.067(l)A
f1_12 sf
-.09( by )A
f2_12 sf
-.121(g)A
f1_12 sf
(.)S
90 133 :M
-.1(A local state is a function which assigns appropriate data values to a subset )A
f2_12 sf
-.129(Loc)A
f1_12 sf
-.11( of the)A
90 147 :M
-.046(set of locations. The set of all possible local states over )A
f2_12 sf
-.062(Loc)A
f1_12 sf
-.048( is denoted )A
f2_12 sf
-.066(LS)A
f2_10 sf
0 -3 rm
-.052(Loc)A
0 3 rm
f1_12 sf
(.)S
90 171 :M
f2_12 sf
-.116(Processes)A
f1_12 sf
-.101( are defined as temporal sequences of states. Since the concept of state is tied)A
90 183 :M
-.091(to that of space through locations taking on data values, it is natural to regard processes)A
90 195 :M
-.059(as occupying a spatio-temporal region. Following Rosenschein and Kaelbling \(1986\),)A
90 207 :M
-.081(we capture these intuitions in two steps. First, at each instant in time a process can be)A
90 219 :M
-.086(regarded as occupying a set of locations. Second, each occupied location takes on a)A
90 231 :M
-.07(specific data value. We thus have two functions. The first is a function from )A
f2_12 sf
-.072(T )A
f1_12 sf
-.139(to)A
90 243 :M
-.085(subsets of )A
f2_12 sf
-.123(L)A
f1_12 sf
-.09( determining the occupied locations, while the second associates data)A
90 255 :M
-.077(values with these locations. We can thus generalise the notion of state to processes.)A
90 267 :M
-.126(The state of a process at time )A
f2_12 sf
-.087(t )A
f1_12 sf
-.129(is determined by the set of locations occupied at )A
f2_12 sf
-.091(t)A
f1_12 sf
-.186( and)A
90 279 :M
-.096(their data values.)A
90 303 :M
-.033(Just as we did with states, we distinguish global and local processes. Global processes)A
90 315 :M
-.043(are temporal sequences of global states. Thus, global processes occupy, and assign)A
90 327 :M
-.106(data values to, all locations at every instant in time. Halpern and Moses call such a)A
90 339 :M
-.056(global process a "run" of a system. A global process or run can be regarded as one)A
90 351 :M
-.027(possible way the world can unfold over time, or a "possible world". Formally, a run is)A
90 365 :M
-.049(a function from )A
f2_12 sf
-.049(T )A
f1_12 sf
-.044(into )A
f2_12 sf
-.074(GS)A
f2_10 sf
0 -3 rm
-.056(L)A
0 3 rm
f1_12 sf
-.046(. We denote the set of all runs by )A
f2_12 sf
-.074(R)A
f1_12 sf
-.051( and an individual run)A
90 377 :M
-.127(by )A
f2_12 sf
-.119(r)A
f1_12 sf
-.117(. Then )A
f2_12 sf
-.119(r)A
f1_12 sf
-.102(\()A
f2_12 sf
-.085(t)A
f1_12 sf
-.112(\) gives the state of the run )A
f2_12 sf
-.119(r)A
f1_12 sf
-.093( at )A
f2_12 sf
-.085(t)A
f1_12 sf
-.112(, and )A
f2_12 sf
-.119(r)A
f1_12 sf
-.102(\()A
f2_12 sf
-.085(t)A
f1_12 sf
-.102(\)\()A
f2_12 sf
-.085(l)A
f1_12 sf
-.121(\) gives the data value of location)A
90 389 :M
f2_12 sf
(l)S
f1_12 sf
-.06( assigned by the run )A
f2_12 sf
-.06(r)A
f1_12 sf
-.049( to )A
f2_12 sf
(l)S
f1_12 sf
(.)S
90 413 :M
-.101(Local processes occupy only a subset of )A
f2_12 sf
-.138(L)A
f1_12 sf
-.097( at each instant in time and are thus a)A
90 425 :M
-.061(sequence of local states. Local processes can also be thought of as subprocesses of a)A
90 441 :M
-.072(global process. Formally, the spatial region occupied by a local process is a function )A
f4_12 sf
(p)S
90 454 :M
f1_12 sf
-.046(from )A
f2_12 sf
-.059(T)A
f0_12 sf
( )S
f1_12 sf
-.045(and )A
f2_12 sf
-.046(R )A
f1_12 sf
-.038(into )A
f2_12 sf
-.049(Powerset)A
f1_12 sf
(\()S
f2_12 sf
-.059(L)A
f1_12 sf
-.041(\). The state of the process is then given by a function)A
90 470 :M
f2_12 sf
(s)S
f1_12 sf
(\()S
f4_12 sf
(p)S
f1_12 sf
(,)S
f2_12 sf
(r,t)S
f1_12 sf
.004 0(\), which is a set of pairs: {<)J
f2_12 sf
(l, r)S
f1_12 sf
(\()S
f2_12 sf
(t)S
f1_12 sf
(\)\()S
f2_12 sf
(l)S
f1_12 sf
(\)> | )S
f2_12 sf
(l )S
f4_12 sf
(\316p)S
f1_12 sf
(\()S
f2_12 sf
(r, t)S
f1_12 sf
(\)}. This)S
90 483 :M
-.109(notation emphasizes that the data values of the local process depend on the run of which)A
90 495 :M
.074 .007(it is a subprocess.)J
90 519 :M
-.082(The foregoing define processes in a very general way. For many applications simpler)A
90 531 :M
-.093(special cases are sufficient and are conceptually easier to handle. For the purposes of)A
90 543 :M
-.079(the rest of this paper we introduce )A
f2_12 sf
-.083(fixed-location processes)A
f1_12 sf
-.092(, which occupy the same)A
90 555 :M
-.093(locations at every instant in time. Thus, fixed-location processes do not move spatially)A
90 567 :M
-.129(and the only change that takes place at successive instants of time is that the fixed)A
90 579 :M
-.109(locations take on different data values.)A
90 603 :M
-.109(In the agent-theoretic use of this model we shall analyse complex agents into sets of)A
90 615 :M
-.071(\(fixed-location\) processes. This is the usual picture of a distributed, concurrent)A
90 627 :M
-.091(computing system. The component processes in such a system interact with each other)A
90 639 :M
-.066(through constraint relationships, implemented as message or signal passing.)A
90 651 :M
-.127(Connectionist architectures can also be interpreted in such a model; here the messages)A
90 663 :M
-.069(are values, usually in the real number or boolean data domains. Thus our framework is)A
90 675 :M
-.092(very general and can be used for analysing a wide variety of system architectures.)A
90 699 :M
-.101(We now show how this model theory can accommodate the notion of an "accessible)A
90 711 :M
-.055(world", which we will need for the construction of a modal logic of desires. A process)A
90 727 :M
f4_12 sf
-.124(p)A
f1_12 sf
-.085( only occupies a subset of the set of all locations at time )A
f2_12 sf
-.063(t)A
f1_12 sf
-.083(. It is therefore possible for)A
90 744 :M
-.11(different runs to assign the same state to )A
f4_12 sf
-.158(p)A
f1_12 sf
-.088( at )A
f2_12 sf
-.08(t)A
f1_12 sf
-.11(. We shall call such runs )A
f2_12 sf
-.122(alternative runs)A
90 761 :M
f1_12 sf
-.075(with respect to )A
f4_12 sf
-.108(p)A
f1_12 sf
-.071( at time )A
f2_12 sf
-.051(t. )A
f1_12 sf
-.078(Thus, the runs )A
f2_12 sf
-.076(r)A
f1_12 sf
-.076( and )A
f2_12 sf
-.056(r' )A
f1_12 sf
-.078(are alternative runs with respect to)A
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f1_12 sf
(8)S
90 85 :M
-.007(process )A
f4_12 sf
(p)S
f1_12 sf
-.006( at time )A
f2_12 sf
(t )S
f1_12 sf
(if )S
f2_12 sf
(s)S
f1_12 sf
(\()S
f4_12 sf
(p)S
f1_12 sf
(,)S
f2_12 sf
(r,t)S
f1_12 sf
(\) = )S
f2_12 sf
(s)S
f1_12 sf
(\()S
f4_12 sf
(p)S
f1_12 sf
(,)S
f2_12 sf
(r',t)S
f1_12 sf
-.007(\). If we identify a process with an agent situated)A
90 98 :M
-.094(in the world, the alternative runs can be regarded as different states of affairs which are)A
90 110 :M
-.089(indistinguishable as far as the state of the agent is concerned. This construction gives)A
90 122 :M
-.103(us a way to interpret the epistemic operator in our logic.)A
90 144 :M
f0_12 sf
2.421 .242(State Transition Functions and State Space)J
90 168 :M
f1_12 sf
-.104(In order to introduce dynamics into the model theory, we introduce state transition)A
90 180 :M
-.076(functions. Let )A
f2_12 sf
-.081(L )A
f1_12 sf
-.075(be the set of locations. Then a state transition function for )A
f2_12 sf
-.081(L )A
f1_12 sf
-.095( can be)A
90 192 :M
-.079(defined in general as a function which maps every state of )A
f2_12 sf
-.111(L)A
f1_12 sf
-.074( into a new state of )A
f2_12 sf
-.111(L)A
f1_12 sf
(.)S
90 206 :M
-.051(Formally, a state transition function )A
f2_12 sf
-.035(f )A
f1_12 sf
-.049(for a set of locations )A
f2_12 sf
-.074(L)A
f1_12 sf
-.051( is a function from )A
f2_12 sf
-.081(GS)A
f2_10 sf
0 -3 rm
(L)S
0 3 rm
90 220 :M
f1_12 sf
-.062(into )A
f2_12 sf
-.105(GS)A
f2_10 sf
0 -3 rm
-.079(L)A
0 3 rm
f1_12 sf
-.065(. Clearly transition functions over )A
f2_12 sf
-.095(L)A
f1_12 sf
-.069( define the behaviour of the global)A
90 232 :M
.146(process.)A
90 256 :M
-.07(In specific cases, the new states of locations in )A
f2_12 sf
-.104(L)A
f1_12 sf
-.078( may not depend on the previous states)A
90 268 :M
-.071(of all the locations in )A
f2_12 sf
-.108(L)A
f1_12 sf
-.075(, but only on a subset of them. For certain architectures, like)A
90 280 :M
-.133(cellular automata, the transition function is defined for each location separately as a)A
90 292 :M
-.098(function of only the immediate neighbours of that location. For logic circuits too, the)A
90 304 :M
-.102(transition function of a location is usually only a function of a small subset of specified)A
90 316 :M
-.036(locations.)A
90 340 :M
-.078(Each state )A
f2_12 sf
-.077(s)A
f1_12 sf
-.076( of the agent process is a substate of a state of one of the possible runs)A
90 352 :M
-.047(\(trajectories\) of the global process. The set of possible runs as been denoted )A
f2_12 sf
-.104(R.)A
90 364 :M
f1_12 sf
-.1(Trajectories in )A
f2_12 sf
-.162(R)A
f1_12 sf
-.101( are generated by the iterated application of a transition function )A
f2_12 sf
-.074(f)A
f1_12 sf
-.066(, )A
f2_12 sf
-.103(s)A
f2_10 sf
0 2 rm
-.061(i)A
0 -2 rm
f1_10 sf
0 2 rm
-.235(+1)A
0 -2 rm
90 376 :M
f1_12 sf
-.027(= )A
f2_12 sf
(f)S
f1_12 sf
(\()S
f2_12 sf
(s)S
f2_10 sf
0 2 rm
(i)S
0 -2 rm
f1_12 sf
-.025(\). The transition function )A
f2_12 sf
(f)S
f1_12 sf
-.027( represents the changes brought about by the agent's)A
90 388 :M
-.111(actions, including doing nothing. Recall that the changes may be either internal or)A
90 400 :M
-.125(external to the agent.)A
90 424 :M
-.107(We shall be concerned with nonlinear functions )A
f2_12 sf
-.072(f)A
f1_12 sf
-.101( which have attractive limit sets. In)A
90 439 :M
-.085(the case of a limit set which is just a single point, we have a fixed point )A
f2_12 sf
-.087(s)A
f2_10 sf
0 2 rm
-.073(fixed)A
0 -2 rm
f1_14 sf
-.065(,)A
f1_12 sf
-.095( such that)A
90 451 :M
f2_12 sf
(f)S
f1_12 sf
(\()S
f2_12 sf
(s)S
f2_10 sf
0 2 rm
-.036(fixed)A
0 -2 rm
f1_12 sf
-.039(\) = )A
f2_12 sf
(s)S
f2_10 sf
0 2 rm
-.036(fixed)A
0 -2 rm
f1_12 sf
-.041(. Here )A
f2_12 sf
(s)S
f2_10 sf
0 2 rm
-.036(fixed)A
0 -2 rm
f1_14 sf
( )S
f1_12 sf
-.04(is an attractor.)A
f1_10 sf
( )S
f1_12 sf
-.042( For all attractors there is an open set, called)A
90 467 :M
-.123(the domain of attraction )A
f2_12 sf
-.225(D)A
f1_12 sf
-.109(, such that for all states )A
f2_12 sf
-.1(s )A
f5_12 sf
-.222(\316)A
f2_12 sf
-.127( D )A
f1_12 sf
-.117(the iterated application of )A
f2_12 sf
(f)S
90 480 :M
f1_12 sf
-.109(eventually carries the state into )A
f2_12 sf
-.113(s)A
f2_10 sf
0 2 rm
-.095(fixed)A
0 -2 rm
f1_12 sf
(.)S
90 504 :M
-.119(We distinguish global attractors from local attractors. The transition function may)A
90 516 :M
-.113(assign the same state to a subset of locations at different times. We call such a local)A
90 528 :M
-.124(fixed state a local attractor. By analogy to global domains of attractions we can define a)A
90 540 :M
-.115(local domain of attraction in a straightforward manner.)A
90 562 :M
f0_12 sf
4.106 .411(Hedonic Functions)J
90 586 :M
f1_12 sf
-.09(In order to use the model theory for the interpretation of desires, we introduce hedonic)A
90 598 :M
-.089(functions. Intuitively, the hedonic function specifies the amount of pleasure or pain an)A
90 614 :M
-.074(agent experiences in some state. The hedonic function )A
f2_12 sf
-.092(h)A
f4_10 sf
0 -3 rm
-.085(p)A
0 3 rm
f1_12 sf
-.07( of a process )A
f4_12 sf
-.101(p)A
f1_12 sf
-.081( maps states)A
90 627 :M
-.11(into hedonic data values. The domain of hedonic data values )A
f2_12 sf
-.195(H)A
f1_12 sf
-.104( is a partially ordered)A
90 639 :M
-.119(set, containing a distinguished element )A
f2_12 sf
-.113(neutral, )A
f1_12 sf
-.125(corresponding to a neutral hedonic data)A
90 651 :M
-.142(value. All other hedonic data values are either hedonically greater than or smaller than)A
90 663 :M
f2_12 sf
-.136(neutral)A
f1_12 sf
-.13(. The hedonic relational operator will be denoted by <)A
f2_10 sf
0 2 rm
-.152(Hed)A
0 -2 rm
f1_12 sf
-.138(. We shall assume that)A
90 675 :M
-.119(the hedonic state of an agent depends only on the local state of the agent. As indicated)A
90 687 :M
-.118(below, we will interpret the hedonic state as a computational analogue of potential field,)A
90 699 :M
-.122(with a potential of zero corresponding to the hedonic )A
f2_12 sf
-.127(neutral)A
f1_12 sf
(.)S
90 723 :M
-.129(The hedonic state results from the superposition of attractive and repelling potentials at)A
90 735 :M
-.1(the point corresponding to the current state. These potentials are produced by the)A
90 747 :M
-.08(agent's value system and by the current goal. The contributions of individual attractors)A
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f1_12 sf
(9)S
90 84 :M
-.018(and repellors can be separately computed as )A
f2_12 sf
(h)S
f4_10 sf
0 -3 rm
(p)S
0 3 rm
f1_12 sf
(\()S
f2_12 sf
(s,)S
f2_14 sf
(s)S
f2_9 sf
0 4 rm
-.013(fixed)A
0 -4 rm
0 8 rm
(i)S
0 -8 rm
f1_12 sf
-.017(\), where )A
f2_14 sf
(s)S
f2_9 sf
0 4 rm
-.013(fixed)A
0 -4 rm
0 8 rm
(i)S
0 -8 rm
0 4 rm
( )S
0 -4 rm
f1_14 sf
(is)S
f1_36 sf
( )S
f1_12 sf
-.019(the fixed)A
90 102 :M
-.097(point state corresponding to attractor )A
f2_12 sf
-.07(i)A
f1_12 sf
(.)S
90 126 :M
-.108(As is usual in utilitarian agent theories, we assume that an agent acts in order to)A
90 138 :M
-.146(maximise its hedonic state. The computation the agent executes to determine its action)A
90 150 :M
-.12(is therefore the optimisation of the hedonic function. Maxima of the hedonic function)A
90 162 :M
-.099(correspond to limit sets in the state space of the agent.)A
90 184 :M
f0_12 sf
2.708 .271(Computational Analogues of Force, Mass and Potential)J
90 210 :M
f1_12 sf
-.084(We assume that for each point )A
f2_12 sf
-.079(s)A
f1_12 sf
-.065( in )A
f2_12 sf
-.125(GS)A
f2_10 sf
0 -3 rm
-.095(L)A
0 3 rm
f1_12 sf
-.085( we can define the distance)A
90 225 :M
f2_12 sf
-.092(d)A
f1_12 sf
-.061(\()A
f2_12 sf
-.072(s)A
f1_12 sf
-.046(, )A
f2_14 sf
-.084(s)A
f2_10 sf
0 2 rm
-.06(fixed)A
0 -2 rm
f1_12 sf
-.072(\) as the distance between the point )A
f2_12 sf
-.072(s)A
f1_12 sf
-.071( and the fixed point )A
f2_14 sf
-.084(s)A
f2_10 sf
0 2 rm
-.06(fixed)A
0 -2 rm
f1_12 sf
-.074(. If we regard)A
90 239 :M
f2_12 sf
-.094(GS)A
f2_10 sf
0 -3 rm
-.052(L )A
0 3 rm
f1_12 sf
-.059(as an )A
f2_12 sf
-.077(n)A
f1_12 sf
-.062(-dimensional space, then this could be euclidean distance. If we interpret)A
90 251 :M
-.121(each function iteration of the transition function )A
f2_12 sf
-.084(f )A
f1_12 sf
-.129(as a unit of time then we can define)A
90 263 :M
-.087(the velocity at )A
f2_12 sf
-.091(s)A
f1_12 sf
-.087( as the distance )A
f2_12 sf
-.117(d)A
f1_12 sf
-.078(\()A
f2_12 sf
-.091(s)A
f1_12 sf
-.059(, )A
f2_12 sf
-.065(f)A
f1_12 sf
-.078(\()A
f2_12 sf
-.091(s)A
f1_12 sf
-.078(\)\))A
f2_12 sf
-.059(, )A
f1_12 sf
-.09(since this will be the distance travelled in unit)A
90 275 :M
-.124(time. The definition of a force vector )A
f3_12 sf
-.215(F)A
f1_12 sf
-.118( acting at the point )A
f2_12 sf
-.126(s)A
f1_12 sf
-.14( follows the mechanical)A
90 287 :M
-.102(analogy and is the product of acceleration and mass. It is natural to interpret mass in)A
90 299 :M
-.08(our computational domain as some measure of the size of the state )A
f2_12 sf
-.056(s. )A
f1_12 sf
-.094(For example, we)A
90 311 :M
-.067(can take the number of locations occupied by the agent process, )A
f2_12 sf
-.083(n)A
f1_12 sf
-.067(, as this measure.)A
90 323 :M
.086(Then,)A
90 347 :M
f2_12 sf
.108 .011( )J
f1_12 sf
.108 .011( )J
f3_12 sf
.316(F)A
f1_12 sf
.158(\()A
f2_12 sf
.184(s)A
f1_12 sf
.198 .02(, )J
f2_12 sf
.184(s)A
f2_10 sf
0 2 rm
.154(fixed)A
0 -2 rm
f1_12 sf
.271 .027(\) = n \245 )J
f2_12 sf
.237(d)A
f1_12 sf
.158(\()A
f2_12 sf
.184(s)A
f1_12 sf
.198 .02(, )J
f2_12 sf
.132(f)A
f1_12 sf
.158(\()A
f2_12 sf
.132(f)A
f1_12 sf
.158(\()A
f2_12 sf
.184(s)A
f1_12 sf
.334 .033(\)\)\) - )J
f2_12 sf
.237(d)A
f1_12 sf
.158(\()A
f2_12 sf
.184(s)A
f1_12 sf
.198 .02(, )J
f2_12 sf
.132(f)A
f1_12 sf
.158(\()A
f2_12 sf
.184(s)A
f1_12 sf
.217(\)\).)A
90 371 :M
-.076(The analogy can then be even further extended by defining force, as in physics, as the)A
90 383 :M
.425 .043(gradient of a potential, )J
f3_12 sf
.385 .038(F = grad)J
f1_12 sf
.067 .007( )J
f2_12 sf
.289(H.)A
90 407 :M
f1_12 sf
-.119(The joint effect of two or more fixed points at )A
f2_12 sf
-.098(s )A
f1_12 sf
-.125(can then be reflected by vector addition)A
90 419 :M
-.051(of the forces acting at )A
f2_12 sf
-.054(s)A
f1_12 sf
-.055(. Let us denote two such forces by )A
f3_12 sf
-.092(F)A
f2_10 sf
0 2 rm
(i)S
0 -2 rm
f1_12 sf
-.054( and )A
f3_12 sf
-.092(F)A
f2_10 sf
0 2 rm
(j)S
0 -2 rm
f1_12 sf
-.056( for two different)A
90 431 :M
-.095(fixed points. The joint effect is then)A
90 447 :M
f3_12 sf
(F)S
f1_12 sf
( = )S
f3_12 sf
(F)S
f2_10 sf
0 2 rm
(i)S
0 -2 rm
f1_12 sf
( )S
f4_12 sf
(\305)S
f1_12 sf
( )S
f3_12 sf
(F)S
f2_10 sf
0 2 rm
(j)S
0 -2 rm
f1_10 sf
0 2 rm
( )S
0 -2 rm
f1_12 sf
.043 .004(where )J
f4_12 sf
(\305)S
f1_12 sf
.046 .005( denotes vector addition.)J
90 472 :M
-.096(We can now assess the relative strengths of two attractors by comparing the magnitudes)A
90 487 :M
-.024(of the two forces and say that )A
f2_12 sf
-.028(Greater)A
f1_12 sf
(\( )S
f2_14 sf
(s)S
f2_9 sf
0 4 rm
-.018(fixed)A
0 -4 rm
0 8 rm
(i)S
0 -8 rm
0 4 rm
( )S
0 -4 rm
f1_12 sf
(, )S
f2_14 sf
(s)S
f2_9 sf
0 4 rm
-.018(fixed)A
0 -4 rm
0 8 rm
(j)S
0 -8 rm
f1_12 sf
-.017(\) if |)A
f3_12 sf
(F)S
f2_10 sf
0 2 rm
(i)S
0 -2 rm
f1_12 sf
-.018(| > |)A
f3_12 sf
(F)S
f2_10 sf
0 2 rm
(j)S
0 -2 rm
f1_12 sf
(|.)S
90 517 :M
-.116(The intuitive agent theoretic interpretation of these concepts is then as follows. As)A
90 529 :M
-.099(stated before, the potential is interpreted as the hedonic state. Components of the)A
90 541 :M
-.094(potential correspond to the values of the agent. The forces correspond to the intensity)A
90 553 :M
-.078(of liking. The concept of relative intensity, or preference, is based on the comparison)A
90 565 :M
-.119(of forces. We model the activity of the agent as following gradients in a potential field)A
90 577 :M
-.039(produced by the superposition of all the forces, i.e. values, acting on the agent.)A
90 589 :M
-.079(Gradient following corresponds to hedonic maximisation.)A
90 618 :M
f0_18 sf
.699(Conclusions)A
90 643 :M
f1_12 sf
-.131(We have described some intuitions about the interpretation of axiological aspects of)A
90 655 :M
-.086(agent theory in terms of concepts from physical dynamics. The first steps have been)A
90 667 :M
-.097(taken towards formalisation by sketching a model theory. This model theory can be)A
90 679 :M
-.094(used straightforwardly for the construction of a logical language in which to reason)A
90 691 :M
-.069(about an agent's hedonic state, likes, goals and values. We believe that the model)A
90 703 :M
-.123(theory can also be used for an integrated interpretation of axiological, epistemic and)A
90 715 :M
-.097(praxiological aspects of agent theory.)A
90 739 :M
-.08(As indicated in Kiss \(1991\), such a model theory can also offer a link between)A
90 751 :M
-.083(concerns for formalisation and concerns for implementation strategies. As shown by)A
90 763 :M
-.1(Rosenschein's work on situated automata theory and the implementation language)A
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f1_12 sf
(10)S
90 81 :M
-.147(REX, there is a complementary relationship between a mathematical model and a)A
90 93 :M
-.108(physical phenomenon, both of which can be taken as alternative interpretations of a)A
90 105 :M
-.065(logic. When this is the case, the logic can be used for reasoning about a design, the)A
90 117 :M
-.126(mathematical model provides the semantics of that reasoning, while the physical)A
90 129 :M
-.134(phenomena \(or their computational analogues\) can be used for the implementation of)A
90 141 :M
-.061(the design. Our motivation for this work is thus not just formalisation, but)A
90 153 :M
-.135(implementation as well.)A
90 182 :M
f0_18 sf
.675(References)A
90 207 :M
f1_12 sf
.114 .011(Abraham, R. H. and Shaw, C. D. \(1981\). )J
f2_12 sf
.159 .016(Dynamics, the Geometry of Behavior, Parts)J
144 219 :M
(1-4)S
f1_12 sf
-.008( . Santa Cruz, CA: Aerial Press.)A
90 243 :M
-.007(Barraquand, J. and Latombe, J.-L. \(In press\). Robot motion planning:a distributed)A
144 255 :M
-.124(representation approach. )A
f2_12 sf
-.128(International Journal of Robotics Research)A
f1_12 sf
(.)S
90 279 :M
.034 .003(Cohen, P. R. and Levesque, H. \(1985\). Speech acts and rationality. )J
f2_12 sf
.062 .006(Proceedings of)J
144 291 :M
-.097(the 23rd Annual Meeting of the Association for Computational Linguistics.)A
90 315 :M
f1_12 sf
.038 .004(Cohen, P.R. and Levesque, H. \(in press\). Rational interaction as a basis for)J
144 327 :M
.221 .022(communication. In P. R. Cohen, J. Morgan, & M. E. Pollack \(Ed.\),)J
144 339 :M
f2_12 sf
-.067(Intentions in Communication)A
f1_12 sf
-.068( Cambridge, Massachusetts: MIT Press.)A
90 363 :M
-.023(Cvitanovic, P. \(1984\). )A
f2_12 sf
-.024(Universality in Chaos. )A
f1_12 sf
-.026(Bristol: Adam Hilger,)A
90 387 :M
-.019(Devaney, R. L. \(1986\). )A
f2_12 sf
-.02(An Introduction to Chaotic Dynamical Systems)A
f1_12 sf
-.02( . Menlo Park,)A
144 399 :M
-.127(CA: Benjamin/Cummings.)A
90 423 :M
-.015(Halpern, J. Y. and Moses, Y. \(1985\). A guide to the modal logics of knowledge and)A
144 435 :M
-.067(belief: preliminary draft. )A
f2_12 sf
-.072(Proceedings of the 9th IJCAI. )A
f1_12 sf
-.085(Los Altos, CA:)A
144 447 :M
.045(Kaufmann.)A
90 471 :M
.041 .004(Halpern, J. Y. and Moses, Y. \(1990\). Knowledge and common knowledge in a)J
144 483 :M
-.085(distributed environment. )A
f2_12 sf
-.09(Journal of the Association for Computing)A
144 495 :M
.046(Machinery)A
f1_12 sf
(, )S
f2_12 sf
.047(37)A
f1_12 sf
.226 .023(\(3\), 549-587.)J
90 519 :M
.061 .006(Kiss, G. R. \(1988\). )J
f2_12 sf
.092 .009(Some aspects of agent theory)J
f1_12 sf
.126 .013( Report HLD/OU/WP/GRK/24,)J
144 531 :M
-.012(HCRL, The Open University.)A
90 555 :M
.135 .013(Kiss, G.R. \(1990\). Value mechanisms in a theory of agents. In J.R. Galliers \(Ed\),)J
144 567 :M
f2_12 sf
-.202(Proceedings of the first belief representation and agent architectures)A
144 579 :M
-.023(workshop. )A
f1_12 sf
-.024(Technical Report 194, University of Cambridge, Computer)A
144 591 :M
-.03(Laboratory.)A
90 615 :M
-.028(Kiss, G. R. \(1991\). Autonomous agents, AI and chaos theory. )A
f2_12 sf
-.028(First International)A
144 627 :M
-.07(Conference on Simulation of Adaptive Behavior: From Animals to Animats.)A
144 639 :M
f1_12 sf
(1990. Cambridge: MIT Press.)S
90 663 :M
-.033(Koditschek, D. E. \(1989\). Robot planning and control via potential functions. In)A
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