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Qualitative Simulation
 Artificial Intelligence
, 2001
"... Qualitative simulation predicts the set of possible behaviors... ..."
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Cited by 421 (31 self)
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Qualitative simulation predicts the set of possible behaviors...
Qualitative Velocity and Ball Interception
, 2002
"... In many approaches for qualitative spatial reasoning, navigation of an agent in a more or less static environment is considered (e.g. in the doublecross calculus [13]). However, in general, the environment is dynamic, which means that both the agent itself and also other objects and agents in th ..."
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Cited by 47 (7 self)
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In many approaches for qualitative spatial reasoning, navigation of an agent in a more or less static environment is considered (e.g. in the doublecross calculus [13]). However, in general, the environment is dynamic, which means that both the agent itself and also other objects and agents in the environment may move. Thus, in order to perform spatial reasoning, not only (qualitative) distance and orientation information is needed (as e.g. in [1]), but also information about (relative) velocity of objects (see e.g. [2]). Therefore, we will introduce concepts for qualitative and relative velocity: (quick) to left, neutral, (quick) to right. We investigate the usefulness of this approach in a case study, namely ball interception of simulated soccer agents in the RoboCup [11]. We compare a numerical approach where the interception point is computed exactly, a strategy based on reinforcement learning, a method with qualitative velocities developed in this paper, and the nave method where the agent simply goes directly to the actual ball position.
A Qualitative Approach to Rigid Body Mechanics
, 1988
"... In order for a program to interact with the world as well as people do, we must provide it with a great deal of commonsense about the way things work. Reasoning 'about the geometric interactions ad motions of objects is an important part of that commons.ns.. Some of the most complex problems we solv ..."
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Cited by 21 (0 self)
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In order for a program to interact with the world as well as people do, we must provide it with a great deal of commonsense about the way things work. Reasoning 'about the geometric interactions ad motions of objects is an important part of that commons.ns.. Some of the most complex problems we solve involve reasoning about mechanical devices, such as gears, cams, and docks. Qualitative mechanics is the symbolic analysis of the motions and the geometric in terations of physical objects. This thesis describes a theory for analysis of rigid body mechanisms, an important subset of qualitative mechanics problems. This theory has been implemented ad tested on several mechanisms including a mechanical clock. Beginning with drawings of the parts involved we compute a discrete symbolic description showing changes in position and motion of the parts of the mechanism as well as its global behavior.
Qualitative Simulation: Then and Now
, 1993
"... ion, Soundness, and Incompleteness Once the abstraction relations from ODEs to QDEs, and from continuously differentiable functions to qualitative behaviors, are carefully defined 1 , the mathematical results are relatively straightforward. We can view an ordinary differential equation solver as ..."
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Cited by 17 (1 self)
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ion, Soundness, and Incompleteness Once the abstraction relations from ODEs to QDEs, and from continuously differentiable functions to qualitative behaviors, are carefully defined 1 , the mathematical results are relatively straightforward. We can view an ordinary differential equation solver as a theoremprover for theorems of a special form: DiffEqs ` ODE State(t 0 ) ! Beh: (1) A qualitative simulation algorithm can also be viewed as a specialpurpose theoremprover: QSIM ` QDE QState(t 0 ) ! or(QBeh 1 ; : : : QBeh n ): (2) The soundness theorem says that when QSIM proves a theorem of form (2), it is true: that is, for any ODE described by the QDE, and State(t 0 ) described by QState(t 0 ), the solution Beh to the ODE is described by one of the qualitative behaviors, QBeh 1 ; : : : QBeh n . The constraint filtering algorithm makes the proof very simple: all possible real transitions from one qualitative state to the next are proposed, and only impossible ones are filtered out...
A dynamic systems perspective on qualitative simulation
 Artificial Intelligence
, 1990
"... This paper examines qualitative simulation (QS) from the phase space perspective of dynamic systems theory. QS consists of two steps: transition analysis determines the sequence of qualitative states that a system traverses and global interpretation derives its longterm behavior. I recast transitio ..."
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Cited by 11 (1 self)
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This paper examines qualitative simulation (QS) from the phase space perspective of dynamic systems theory. QS consists of two steps: transition analysis determines the sequence of qualitative states that a system traverses and global interpretation derives its longterm behavior. I recast transition analysis as a search problem in phase space and replace the assorted transition rules with two algebraic conditions. The first condition determines transitions between arbitrarily shaped regions in phase space, as opposed to QS which only handles ndimensional rectangles. It also provides more accurate results by considering only the boundaries between regions. The second condition determines whether nearby trajectories approach a fixed point asymptotically. It obtains better results than QS by exploiting local stability properties. I recast global interpretation as a search for attractors in phase space and present a global interpretation algorithm for systems whose local behavior determines global behavior uniquely. 'This research was performed while I was in the Clinical Decision Making Group oftheM.I.T. Laboratory
The Logic of Occurrence
, 1987
"... A general problem in qualitative physics is determining the consequences of assumptions about the behavior of a system. If the space of behaviors is represented by an envisionment, many such consequences can be represented by pruning states from the envisionment. This paper provides a formal logic o ..."
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Cited by 10 (3 self)
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A general problem in qualitative physics is determining the consequences of assumptions about the behavior of a system. If the space of behaviors is represented by an envisionment, many such consequences can be represented by pruning states from the envisionment. This paper provides a formal logic of occurrence which justifies the algorithms involved and provides a language for relating specific histories to envisionments. The concepts and axioms are general enough to be applicable to any system of qualitative physics. We further propose the concept of transverse quantities as a general solution to qualitative versions of Zeno's paradox. The utility of these ideas is illustrated by a rational reconstruction of the pruning algorithms used in FROB, a working AI program. December, 1 Introduction A goal of qualitative physics is to predict the behavior of physical systems. One technique, envisioning, generates all possible behaviors of a system, relative to a particular set of backgroun...
Order of Magnitude Reasoning in Qualitative Differential Equations
, 1987
"... We present a theory that combines order of magnitude reasoning with envisionment of qualitative differential equations. Such a theory can be used to reason qualitatively about dynamical systems containing parameters of widely varying magnitudes. We present an a mathematical analysis of envisionment ..."
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Cited by 8 (2 self)
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We present a theory that combines order of magnitude reasoning with envisionment of qualitative differential equations. Such a theory can be used to reason qualitatively about dynamical systems containing parameters of widely varying magnitudes. We present an a mathematical analysis of envisionment over orders of magnitude, including a complete categorization of adjacent pairs of qualitative states. We show how this theory can be applied to simple problems, we give an algorithm for generating a complete envisionment graph, and we discuss the implementation of this algorithm in a running program.
HigherOrder Derivative Constraints in Qualitative Simulation
 Artificial Intelligence
, 1991
"... Qualitative simulation is a useful method for predicting the possible qualitatively distinct behaviors of an incompletely known mechanism described by a system of qualitative differential equations (QDEs). Under some circumstances, sparse information about the derivatives of variables can lead to in ..."
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Cited by 7 (3 self)
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Qualitative simulation is a useful method for predicting the possible qualitatively distinct behaviors of an incompletely known mechanism described by a system of qualitative differential equations (QDEs). Under some circumstances, sparse information about the derivatives of variables can lead to intractable branching (or "chatter") representing uninteresting or even spurious distinctions among qualitative behaviors. The problem of chatter stands in the way of real applications such as qualitative simulation of models in the design or diagnosis of engineered systems. One solution to this problem is to exploit information about higherorder derivatives of the variables. We demonstrate automatic methods for identification of chattering variables, algebraic derivation of expressions for secondorder derivatives, and evaluation and application of the sign of second and thirdorder derivatives of variables, resulting in tractable simulation of important qualitative models. Caution is requir...
Articles A New Direction in AI Toward a Computational Theory of Perceptions
"... ■ Humans have a remarkable capability to perform a wide variety of physical and mental tasks without any measurements and any computations. Familiar examples are parking a car, driving in city traffic, playing golf, cooking a meal, and summarizing a story. In performing such tasks, humans use percep ..."
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■ Humans have a remarkable capability to perform a wide variety of physical and mental tasks without any measurements and any computations. Familiar examples are parking a car, driving in city traffic, playing golf, cooking a meal, and summarizing a story. In performing such tasks, humans use perceptions of time, direction, speed, shape, possibility, likelihood, truth, and other attributes of physical and mental objects. Reflecting the bounded ability of the human brain to resolve detail, perceptions are intrinsically imprecise. In more concrete terms, perceptions are fgranular, meaning that (1) the boundaries of perceived classes are unsharp and (2) the values of attributes are granulated, with a granule being a clump of values
for the degreeof Doctor of PhilosophyModel Based Reasoning of Device Behavior with Causal Ordering
, 1988
"... m Computer Science ..."