statistical mechanics and phase transitions in clustering a new approach to clustering based on statistical physics is presented the problem is formulated as fuzzy clustering and the association probability distribution is obtained by maximizing the entropy at a given average variance the corresponding lagrange multiplier is related to the temperature and motivates a deterministic annealing process where the free energy is minimized at each temperature critical temperatures are derived for phase transitions when existing clusters split it is a hierarchical clustering estimating the most probable cluster parameters at various average variances

convergence of vector quantizers with applications to optimal quantization suppose that a sequence of probability distribution functions f n converges weakly to a distribution function f does the sequence of optimal quantizers for the f n s converge to an optimal quantizer for f if so do the respective distortions converge to the optimal distortion for f sufficient conditions are given to guarantee the convergence for both scalar and vector quantizers with a general class of distortion measures these results are used to prove the existence of minimum rth power distortion vector quantizers and the convergence of a proposed algorithm for constructing optimal quantizers

parity space based fault detection for linear discrete time varying systems with unknown input in this paper a new approach to parity space based fault detection fd is put forward for linear discrete time varying ldtv systems the focus of our study is on solving the problem with heavy online computational burden the main contributions are two folds firstly the problem of parity space based fd is formulated as finding a minimum of quadratic form of unknown input secondly by applying projection in krein space a solution of optimal parity space based fd is obtained via recursively computing innovations it is shown that the reduction of computation cost is achievable especially with the increase of parity space order finally a numerical example is given to demonstrate the application of the proposed method

two counterexamples related to baker s approach to the frame problem abstract andrew baker s approach to reasoning about actions is the most robust circumscriptive approach currently known investigation of its applicability to nondeterministic actions reveals that this approach does not allow us to draw some intuitively plausible conclusions also it does not always generate the proper existence of situations axiom the limitations are traced to an unexpected interference of the axioms encoding observations with the minimization a modification that avoids the shortcomings is suggested

parametrization of optimal fault detection filters this paper is concerned with the fault detection filter design problem for linear time invariant systems subject to disturbance and possible faults to make a tradeoff between fault sensitivity and disturbance sensitivity frameworks such as 2 and are considered it is shown that for and frameworks all optimal fault detection filters can be characterized by an envelope besieged by the special solutions serving as upper and lower bounds furthermore the explicit parametrization is given in terms of a free contractive system parameter this free parameter provides freedom to emphasize fault and disturbance sensitivities at different frequency ranges which can be used to construct new optimal fault detection filter the results are also extended to the optimization over finite frequency range for which the upper and or lower bound of the optimal solution set may not be rational on the other hand it is shown that the solution set of 2 problem is unique up to square inner system finally examples are given to illustrate the results

kernel based equiprobabilistic topographic map formation we introduce a new unsupervised competitive learning rule the kernel based maximum entropy learning rule kmer which performs equiprobabilistic topographic map formation in regular fixed topology lattices for use with nonparametric density estimation as well as nonparametric regression analysis the receptive fields of the formal neurons are overlapping radially symmetric kernels compatible with radial basis functions rbfs but unlike other learning schemes the radii of these kernels do not have to be chosen in an ad hoc manner the radii are adapted to the local input density together with the weight vectors that define the kernel centers so as to produce maps of which the neurons have an equal probability to be active equiprobabilistic maps both an online and a batch version of the learning rule are introduced which are applied to nonparametric density estimation and regression respectively the application envisaged is blind source separation bss from nonlinear noisy mixtures

code vector density in topographic mappings scalar case the author derives some new results that build on his earlier work 1989 of combining vector quantization vq theory and topographic mapping tm theory a vq model with a noisy transmission medium is used to model the processes that occur in tms which leads to the standard tm training algorithm albeit with a slight modification to the encoding process to emphasize this difference the model is called a topographic vector quantizer tvq in the continuum limit of the one dimensional scalar tvq it is found that the density of code vectors is proportional to p x sup a alpha 1 3 assuming that the transmission medium introduces additive noise with a zero mean symmetric monotically decreasing probability density this result is dramatically different from the result that is predicted when the standard tm training algorithm is used with a uniform symmetric neighborhood n n and it is noted that this difference arises entirely from using minimum distortion rather than nearest neighbor encoding

k vectors an alternating minimization algorithm for learning regression functions the k vectors algorithm for learning regression functions proposed here is akin to the well known k means algorithm both algorithms partition the feature space but unlike the k means algorithm the k vectors algorithm aims to reconstruct the response rather than the feature the partitioning rule of the algorithm is based on maximizing the correlation inner product of the feature vector with a set of k vectors and generates polyhedral cells similar to the ones generated by the nearest neighbor rule of the k means algorithm similarly to k means the learning algorithm alternates between two types of steps in the first type of steps k labels are determined via a centroid type rule in the response space which uses a surrogate hinge type loss function to the mean squared error loss function in the second type of steps the k vectors which determine the partition are updated according to a multiclass classification rule in the spirit of support vector machines it is proved that both steps of the algorithm only require solving convex optimization problems and that the algorithm is empirically consistent as the length of the training sequence increases to infinity fixed points of the empirical version of the algorithm tend to fixed points of the population version of the algorithm learnability of the predictor class posit by the algorithm is also established

reasoning about action i a possible worlds approach abstract reasoning about change is an important aspect of commonsense reasoning and planning in this paper we describe an approach to reasoning about change for rich domains where it is not possible to anticipate all situations that might occur the approach provides a solution to the frame problem and to the related problem that it is not always reasonable to explicitly specify all of the consequences of actions the approach involves keeping a single model of the world that is updated when actions are performed the update procedure involves constructing the nearest world to the current one in which the consequences of the actions under consideration hold the way we find the nearest world is to construct proofs of the negation of the explicit consequences of the expected action and to remove a premise in each proof from the current world computationally this construction procedure appears to be tractable for worlds like our own where few things tend to change with each action or where change is regular

global convergence and empirical consistency of the generalized lloyd algorithm the generalized lloyd algorithm for vector quantizer design is analyzed as a descent algorithm for nonlinear programming a broad class of convex distortion functions is considered and any input distribution that has no singular continuous part is allowed a well known convergence theorem is applied to show that iterative applications of the algorithm produce a sequence of quantizers that approaches the set of fixed point quantizers the methods of the theorem are extended to sequences of algorithms yielding results on the behavior of the algorithm when an unknown distribution is approximated by a training sequence of observations it is shown that as the length of the training sequence grows large that 1 fixed point quantizers for the training sequence approach the set of fixed point quantizers for the true distribution and 2 limiting quantizers produced by the algorithm with the training sequence distribution perform no worse than limiting quantizers produced by the algorithm with the true distribution

a maximum entropy approach to nonmonotonic reasoning an approach to nonmonotonic reasoning that combines the principle of infinitesimal probabilities with that of maximum entropy thus extending the inferential power of the probabilistic interpretation of defaults is proposed a precise formalization of the consequences entailed by a conditional knowledge base is provided the computational machinery necessary for drawing these consequences is developed and the behavior of the maximum entropy approach is compared to related work in default reasoning the resulting formalism offers a compromise between two extremes the cautious approach based on the conditional interpretations of defaults and the bold approach based on minimizing abnormalities

impediments to universal preference based default theories research on nonmonotonic and default reasoning has identified several important criteria for preferring alternative default inferences the theories of reasoning based on each of these criteria may uniformly be viewed as theories of rational inference in which the reasoner selects maximally preferred states of belief though researchers have noted some cases of apparent conflict between the preferences supported by different theories it has been hoped that these special theories of reasoning may be combined into a universal logic of nonmonotonic reasoning we show that the different categories of preferences conflict more than has been realized and adapt formal results from social choice theory to prove that every universal theory of default reasoning will violate at least one reasonable principle of rational reasoning our results can be interpreted as demonstrating that within the preferential framework we cannot expect much improvement on the rigid lexicographic priority mechanisms that have been proposed for conflict resolution

on an unsupervised learning rule for scalar quantization following the maximum entropy principle in this paper we observe that a particular class of rational function rf approximations may be viewed as feedforward networks like the radial basis function rbf network the training of the rf network may be performed using a linear adaptive filtering algorithm we illustrate the application of the rf network by considering two nonlinear signal processing problems the first problem concerns the one step prediction of a time series consisting of a pair of complex sinusoid in the presence of colored non gaussian noise simulated data were used for this problem in the second problem we use the rf network to build a nonlinear dynamic model of sea clutter radar backscattering from a sea surface here real life data were used for the study

comments on on a novel unsupervised competitive learning algorithm for scalar quantization this note propose an alternative to a neural network for designing scaler quantizers proposed by van hulle and martinez ibid vol 5 p 498 501 may 1994 it also points out that the performance measure used is of limited applicability

a matrix factorization solution to the h h fault detection problem in this paper we give a matrix factorization solution to the h h fault detection fd problem for linear time invariant dynamic systems an h h fd filter minimizes the sensitivity of the residual signal to disturbances while maintaining a minimum level of sensitivity to faults more specifically it minimizes the largest singular value over the extended imaginary axis of the transfer matrix from the disturbance to the residual signal vectors subject to the constraint that the singular values of the transfer matrix from the fault to the residual vectors are larger than or equal to 1 we show through the use of matrix function factorizations and completions that the problem reduces to a nonstandard model matching problem which is then solved under a mild assumption concerning the rank of a matrix function we also give an illustrative example

on a novel unsupervised competitive learning algorithm for scalar quantization this letter presents a novel unsupervised competitive learning rule called the boundary adaptation rule bar for scalar quantization it is shown both mathematically and by simulations that bar converges to equiprobable quantizations of univariate probability density functions and that in this way it outperforms other unsupervised competitive learning rules

on the characterization and uniqueness of centroidal voronoi tessellations vector quantization is a classical signal processing technique with significant applications in data compression pattern recognition clustering and data stream mining it is well known that for critical points of the quantization energy the tessellation of the domain is a centroidal voronoi tessellation however for dimensions greater than one rigorously verifying a given centroidal voronoi tessellation is a local minimum can prove difficult using variational techniques we give a full characterization of the second variation of a centroidal voronoi tessellation and give sufficient conditions for a centroidal voronoi tessellation to be a local minimum in addition the conditions under which a centroidal voronoi tessellation for a given density and domain is unique have been elusive for dimensions greater than one we prove that there does not exist a unique two generator centroidal voronoi tessellation for dimensions greater than one

a unifying action calculus mccarthy s situation calculus is arguably the oldest special purpose knowledge representation formalism designed to axiomatize knowledge of actions and their effects four decades of research in this area have led to a variety of alternative formalisms while some approaches can be considered instances or extensions of the classical situation calculus like reiter s successor state axioms or the fluent calculus there are also special planning languages like adl and approaches based on a linear rather than branching time structure like the event calculus the co existence of many different calculi has two main disadvantages the formal relations among them is a largely open issue and a lot of today s research concerns the transfer of specific results from one approach to another in this paper we present a unifying action calculus which encompasses well defined classes of all of the aforementioned formalisms our calculus not only facilitates comparisons and translations between specific approaches it also allows to solve interesting problems for various calculi at once we exemplify this by providing a general calculus independent solution to a problem of practical relevance which is intimately related to mccarthy s quest for elaboration tolerant formalisms the modularity of domain axiomatizations

from statistical knowledge bases to degrees of belief an intelligent agent will often be uncertain about various properties of its environment and when acting in that environment it will frequently need to quantify its uncertainty for example if the agent wishes to employ the expected utility paradigm of decision theory to guide its actions it will need to assign degrees of belief subjective probabilities to various assertions of course these degrees of belief should not be arbitrary but rather should be based on the information available to the agent this paper describes one approach for inducing degrees of belief from very rich knowledge bases that can include information about particular individuals statistical correlations physical laws and default rules we call our approach the random worlds method the method is based on the principle of indifference it treats all of the worlds the agent considers possible as being equally likely it is able to integrate qualitative default reasoning with quantitative probabilistic reasoning by providing a language in which both types of information can be easily expressed our results show that a number of desiderata that arise in direct inference reasoning from statistical information to conclusions about individuals and default reasoning follow directly from the semantics of random worlds for example random worlds captures important patterns of reasoning such as specificity inheritance indifference to irrelevant information and default assumptions of independence furthermore the expressive power of the language used and the intuitive semantics of random worlds allow the method to deal with problems that are beyond the scope of many other nondeductive reasoning systems

optimal bi level quantization and its application to multilevel quantization a special form of optimal quantization optimal bilevel quantization is studied a fixed point method is embedded in a search scheme to find all the locally optimal bilevel quantizers resulting in an algorithm for computing the globally optimal bilevel quantizer some interesting relations between the optimal bilevel quantizer and the mean and the median of the density function p x are explored efficient algorithms for computing optimal bilevel quantizers are proposed the application of these results to optimal quantization in general is discussed

a game theoretic approach to h control for time varying systems a representation formula for all controllers that satisfy an mathcal l infty type constraint is derived for time varying systems it is now known that a formula based on two indefinite algebraic riccati equations may be found for time invariant systems over an infinite time support see j c doyle et al ieee trans automat control ac 34 1989 pp 831 847 k glover and j c doyle systems control lett 11 1988 pp 167 172 k glover et al siam j control optim 29 1991 pp 283 324 m green et al siam j control optim 28 1990 pp 1350 1371 d j n limebeer et al in proc ieee conf on decision and control austin tx 1988 g tadmor math control systems signal processing 3 1990 pp 301 324 in the time varying case two indefinite riccati differential equations are required a solution to the design problem exists if these equations have a solution on the optimization interval the derivation of the representation formula illustrated in this paper mak

nonmonotonic logic and temporal projection abstract nonmonotonic formal systems have been proposed as an extension to classical first order logic that will capture the process of human default reasoning or plausible inference through their inference mechanisms just as modus ponens provides a model for deductive reasoning but although the technical properties of these logics have been studied in detail and many examples of human default reasoning have been identified for the most part these logics have not actually been applied to practical problems to see whether they produce the expected results we provide axioms for a simple problem in temporal reasoning which has long been identified as a case of default reasoning thus presumably amenable to representation in nonmonotonic logic upon examining the resulting nonmonotonic theories however we find that the inferences permitted by the logics are not those we had intended when we wrote the axioms and in fact are much weaker this problem is shown to be independent of the logic used nor does it depend on any particular temporal representation upon analyzing the failure we find that the nonmonotonic logics we considered are inherently incapable of representing this kind of default reasoning the first part of the paper is an expanded version of one that appeared in the 1986 aaai proceedings the second part reports on several responses to our result that have appeared since the original paper was published

nondegeneracy and weak global convergence of the lloyd algorithm in mathbb r d the lloyd algorithm originated in the context of optimal quantization and represents a fixed point iteration for computing an optimal quantizer reducing average distortion at every step it constructs a voronoi partition of the domain and replaces each generator with the centroid of the corresponding voronoi cell optimal quantization is obtained in the case of a centroidal voronoi tessellation cvt which is a special voronoi tessellation of a domain omega in mathbb r d having the property that the generators of the voronoi diagram are also the centers of mass with respect to a given density function rho geq 0 of the corresponding voronoi cells the lloyd iteration is currently the most popular and elegant algorithm for computing cvts and optimal quantizers but many questions remain about its convergence especially in d dimensional spaces d 1 in this paper we prove that any limit point of the lloyd iteration in any dimensional spaces is nondegenerate provided that omega is a convex and bounded set and rho belongs to l 1 omega and is positive almost everywhere this ensures that the fixed point map remains closed and hence the standard theory of descent methods guarantees weak global convergence of the lloyd iteration to the set of nondegenerate fixed point quantizers while previously only conjectured the convergence properties of the lloyd iteration are rigorously justified under such minimal regularity assumptions on the density functional the results presented in this paper go beyond existing convergence theories for cvts and optimal quantization related algorithms and should be of interest to both the mathematical and engineering communities

characterization of ℋ index for linear time varying systems the increasing interest in index in fault detection has led to some recent development in time domain investigation this paper at first presents a necessary and sufficient condition of the index in finite time horizon for linear time varying systems it is shown that the feasibility of the index which is given when the index is greater than a predefined value is equivalent to the existence of a certain backward differential riccati equation under a constraint the square system as a special case is discussed the corresponding results are extended to systems with unknown initial condition with a modified definition of the index the condition for weighted index to emphasize the signal effect at different time instant is also derived by transformation the result is also compared with the famous bounded real lemma the connection with the linear time invariant lti case is also discussed finally examples are given to illustrate the main results

non monotonic logic i abstract non monotonic logical systems are logics in which the introduction of new axioms can invalidate old theorems such logics are very important in modeling the beliefs of active processes which acting in the presence of incomplete information must make and subsequently revise assumptions in light of new observations we present the motivation and history of such logics we develop model and proof theories a proof procedure and applications for one non monotonic logic in particular we prove the completeness of the non monotonic predicate calculus and the decidability of the non monotonic sentential calculus we also discuss characteristic properties of this logic and its relationship to stronger logics logics of incomplete information and truth maintenance systems

statistical theory of learning curves under entropic loss criterion the present paper elucidates a universal property of learning curves which shows how the generalization error training error and the complexity of the underlying stochastic machine are related and how the behavior of a stochastic machine is improved as the number of training examples increases the error is measured by the entropic loss it is proved that the generalization error converges to h0 the entropy of the conditional distribution of the true machine as h0 m 2t while the training error converges as h0 m 2t where t is the number of examples and m shows the complexity of the network when the model is faithful implying that the true machine is in the model m is reduced to m the number of modifiable parameters this is a universal law because it holds for any regular machine irrespective of its structure under the maximum likelihood estimator similar relations are obtained for the bayes and gibbs learning algorithms these learning curves show the relation among the accuracy of learning the complexity of a model and the number of training examples

generalized metrics and uniquely determined logic programs the introduction of negation into logic programming brings the benefit of enhanced syntax and expressibility but creates some semantical problems specifically certain operators which are monotonic in the absence of negation become non monotonic when it is introduced with the result that standard approaches to denotational semantics then become inapplicable in this paper we show how generalized metric spaces can be used to obtain fixed point semantics for several classes of programs relative to the supported model semantics and investigate relationships between the underlying spaces we employ our methods allow the analysis of classes of programs which include the acyclic locally hierarchical and acceptable programs amongst others and draw on fixed point theorems which apply to generalized ultrametric spaces and to partial metric spaces

uniqueness of locally optimal quantizer for log concave density and convex error weighting function it is desired to encode a random variable x using an n level quantizer q to minimize the expected distortion e rho x q x i where the error weighting function rho is convex strictly increasing and continuously differentiable it is shown that if x has a log concave density then there exists a unique locally optimal quantizer q ast and lloyd s method i may be used to find q ast trushkin had earlier shown this result for the error weighting functions rho t equiv t and rho t euiv t 2

a computational model for metric spaces for every metric space x we define a continuous poset bx such that x is homeomorphic to the set of maximal elements of bx with the relative scott topology the poset bx is a dcpo iff x is complete and continuous iff x is separable the computational model bx is used to give domain theoretic proofs of banach s fixed point theorem and of two classical results of hutchinson on a complete metric space every hyperbolic iterated function system has a unique non empty compact attractor and every iterated function system with probabilities has a unique invariant measure with bounded support we also show that the probabilistic power domain of bx provides an continuous computational model for measure theory on a separable complete metric space x

the suprem architecture a new intelligent paradigm abstract we investigate the model theory of the notion of circumscription and find completeness theorems that provide a partial converse to a result of mccarthy we show that the circumscriptive theorems are precisely the truths of the minimal models in the case of various classes of theories and for various versions of circumscription we also present an example of commonsense reasoning in which first order circumscription does not achieve the intuitive and desired minimization

self organization as an iterative kernel smoothing process kohonen s self organizing map when described in a batch processing mode can be interpreted as a statistical kernel smoothing problem the batch som algorithm consists of two steps first the training data are partitioned according to the voronoi regions of the map unit locations second the units are updated by taking weighted centroids of the data falling into the voronoi regions with the weighing function given by the neighborhood then the neighborhood width is decreased and steps 1 2 are repeated the second step can be interpreted as a statistical kernel smoothing problem where the neighborhood function corresponds to the kernel and neighborhood width corresponds to kernel span to determine the new unit locations kernel smoothing is applied to the centroids of the voronoi regions in the topological space this interpretation leads to some new insights concerning the role of the neighborhood and dimensionality reduction it also strengthens the algorithm s connection with the principal curve algorithm a generalized self organizing algorithm is proposed where the kernel smoothing step is replaced with an arbitrary nonparametric regression method

controlling the magnification factor of self organizing feature maps the magnification exponents occurring in adaptive map formation algorithms like kohonen s self organizing feature map deviate for the information theoretically optimal value 1 as well as from the values that optimize e g the mean square distortion error 1 3 for one dimensional maps at the same time models for categorical perception such as the perceptual magnet effect which are based on topographic maps require negative magnification exponents 0 we present an extension of the self organizing feature map algorithm which utilizes adaptive local learning step sizes to actually control the magnification properties of the map by change of a single parameter maps with optimal information transfer with various minimal reconstruction errors or with an inverted magnification can be generated analytic results on this new algorithm are complemented by numerical simulations

conditional entailment bridging two approaches to default reasoning abstract in recent years two conceptually different interpretations of default expressions have been advanced extensional interpretations in which defaults are regarded as prescriptions for extending one s set of beliefs and conditional interpretations in which defaults are regarded as beliefs whose validity is bound to a particular context the two interpretations possess virtues and limitations that are practically orthogonal to each other the conditional interpretations successfully resolve arguments of different specificity e g penguins don t fly in spite of being birds but fail to capture arguments of irrelevance e g concluding red birds fly from birds fly the opposite is true for the extensional interpretations this paper develops a new account of defaults called conditional entailment which combines the benefits of the two interpretations like prioritized circumscriptions conditional entailment resolves arguments by enforcing priorities among defaults however instead of having to be specified by the user these priorities are extracted automatically from the knowledge base similarly conditional entailment possesses a sound and complete proof theory based on interacting arguments and amenable to implementation in conventional atmss

an lmi approach to minimum sensitivity analysis with application to fault detection this paper systematically studies the minimum input sensitivity analysis problem the lowest level of sensitivity of system outputs to system inputs is defined as an h index a full characterization of the h index is given first in terms of matrix equalities and inequalities and then in terms of linear matrix inequalities lmis as a dual of the bounded real lemma a related problem of input observability is also studied with new necessary and sufficient conditions given which are necessary for a fault detection system to have a nonzero worst case fault sensitivity the above results are applied to the problem of fault detection filter analysis with numerical examples given to show the effectiveness of the proposed approaches

on convergence of lloyd s method i although lloyd s method i for optimal quantization was proposed more than thirty years ago and has been frequently referred to in the literature its convergence has so far not been shown this correspondence proves that lloyd s method i converges for a large class of error measures if the density function is continuous positive and defined on a finite interval the proof is done by modeling the behavior of a continuous optimization algorithm by a finite state machine

best asymptotic normality of the kernel density entropy estimator for smooth densities in the random sampling setting we estimate the entropy of a probability density distribution by the entropy of a kernel density estimator using the double exponential kernel under mild smoothness and moment conditions we show that the entropy of the kernel density estimator equals a sum of independent and identically distributed i i d random variables plus a perturbation which is asymptotically negligible compared to the parametric rate n sup 1 2 an essential part in the proof is obtained by exhibiting almost sure bounds for the kullback leibler divergence between the kernel density estimator and its expected value the basic technical tools are doob s submartingale inequality and convexity jensen s inequality

the formation of topographic maps that maximize the average mutual information of the output responses to noiseless input signals this article introduces an extremely simple and local learning rule for to pographic map formation the rule called the maximum entropy learning rule mer maximizes the unconditional entropy of the map s output for any type of input distribution the aim of this article is to show that mer is a viable strategy for building topographic maps that maximize the average mutual information of the output responses to noiseless input signals when only input noise and noise added input signals are available

estimating renyi entropy of discrete distributions it was shown recently that estimating the shannon entropy h p of a discrete k symbol distribution p requires theta k log k samples a number that grows near linearly in the support size in many applications h p can be replaced by the more general renyi entropy of order alpha and h alpha p we determine the number of samples needed to estimate h alpha p for all alpha showing that alpha requires a super linear roughly k 1 alpha samples noninteger alpha 1 requires a near linear k samples but perhaps surprisingly integer alpha 1 requires only theta k 1 1 alpha samples furthermore developing on a recently established connection between polynomial approximation and estimation of additive functions of the form sum x f p x we reduce the sample complexity for noninteger values of alpha by a factor of log k compared with the empirical estimator the estimators achieving these bounds are simple and run in time linear in the number of samples our lower bounds provide explicit constructions of distributions with different renyi entropies that are hard to distinguish

exponential rate of convergence for lloyd s method i for a random variable with finite second moment and log concave density a unique quantizer exists which produces the minimum expected encoding error using squared error distortion an algorithm given by lloyd lloyd s method i yields a sequence of quantizers which converges to the optimum quantizer using results of fleischer it is shown that the convergence takes place exponentially fast if the logarithm of the density is not piecewise affine as a consequence the number of iterations of lloyd s algorithm needed to obtain the optimum distortion correct to n decimal places approaches infinity no faster than linearly in n another consequence is that if the output of a stationary information source at each time is distributed according to the given density the source output can be encoded at each time i using the quantizer obtained on the i th iteration of lloyd s method obtaining the same asymptotic behavior one would have obtained if the optimum quantizer had been used to encode at each time

acyclic logic programs and the completeness of sldnf resolution abstract this paper investigates the class of acyclic programs programs with the usual hierarchical condition imposed on ground instances of atoms rather than predicate symbols the acyclic condition seems to naturally capture much of the recursion that occurs in practice and many programs that arise in practical programming satisfy this condition we prove completeness of sldnf resolution for the acyclic programs and discuss several other desirable properties exhibited by programs belonging to this class

design and analysis of optimal noisy channel quantization with random index assignment this paper studies the design of vector quantization on noisy channels and its high rate asymptotic performance given a tandem source channel coding system with vector quantization block channel coding and random index assignment a closed form formula is first derived for computing the average end to end distortion eed of the system which reveals a structural factor called the scatter factor of a noisy channel quantizer based on this formula we propose a noisy channel quantization design method by minimizing the eed experiments and simulations show that quantizers jointly designed with channel conditions significantly reduce the eed when compared with quantizers designed separately without reference to channel conditions which reveals a practical and effective design for noisy channel quantization as to simplify the channel model by considering a random index assignment furthermore we have presented the high rate asymptotic analysis of the eed for the tandem system while convergence analysis of the iterative algorithm is included in the appendix

active logic semantics for a single agent in a static world for some time we have been developing and have had significant practical success with a time sensitive contradiction tolerant logical reasoning engine called the active logic machine alma the current paper details a semantics for a general version of the underlying logical formalism active logic central to active logic are special rules controlling the inheritance of beliefs in general and of beliefs about the current time in particular very tight controls on what can be derived from direct contradictions email protected p and mechanisms allowing an agent to represent and reason about its own beliefs and past reasoning furthermore inspired by the notion that until an agent notices that a set of beliefs is contradictory that set seems consistent and the agent therefore reasons with it as if it were consistent we introduce an apperception function that represents an agent s limited awareness of its own beliefs and serves to modify inconsistent belief sets so as to yield consistent sets using these ideas we introduce a new definition of logical consequence in the context of active logic as well as a new definition of soundness such that when reasoning with consistent premises all classically sound rules remain sound in our new sense however not everything that is classically sound remains sound in our sense for by classical definitions all rules with contradictory premises are vacuously sound whereas in active logic not everything follows from a contradiction

how does a box work a study in the qualitative dynamics of solid objects this paper is an in depth study of qualitative physical reasoning about one particular scenario using a box to carry a collection of objects from one place to another specifically we consider the plan plan1 load objects ucargo into box obox one by one carry obox from location l1 to location l2 we present qualitative constraints on the shape starting position and material properties of ucargo and obox and on the characteristics of the motion that suffice to make it virtually certain that plan1 can be successfully executed we develop a theory consisting mostly of first order statements together with two default rules that supports an inference of the form if conditions xyz hold and the agent attempts to carry out plan1 then presumably he will succeed our theory is elaboration tolerant in the sense that carrying out the analogous inference for carrying objects in boxes with lids in boxes with small holes or on trays can reuse much of the same knowledge the theory integrates reasoning about continuous time euclidean space commonsense dynamics of solid objects and semantics of partially specified plans

k means type algorithms a generalized convergence theorem and characterization of local optimality the k means algorithm is a commonly used technique in cluster analysis in this paper several questions about the algorithm are addressed the clustering problem is first cast as a nonconvex mathematical program then a rigorous proof of the finite convergence of the k means type algorithm is given for any metric it is shown that under certain conditions the algorithm may fail to converge to a local minimum and that it converges under differentiability conditions to a kuhn tucker point finally a method for obtaining a local minimum solution is given

dynamical system design from a control perspective finite frequency positive realness approach nonminimum phase zeros are well known to limit the best achievable control performance when the control gain is allowed to be arbitrarily high on the other hand the phase crossover appears to be a limiting factor for performance when high gain controllers are not allowed in particular the positive realness in a finite frequency range seems crucial for achieving good performance in the presence of control constraints this paper will first give multiple reasons to support this conjecture and then develop a systematic method for designing mechanical systems to achieve the finite frequency positive real ffpr property specifically we present a state space characterization of the ffpr property by generalizing the well known kalman yakubovich popov lemma to deal with a class of frequency domain inequalities that are required to hold within a finite frequency interval the result is further extended for uncertain systems to give a sufficient condition for satisfaction of a robust ffpr property the nominal ffpr result is interpreted in the time domain in terms of input output signals finally we show that certain sensor actuator placement problems to achieve the ffpr property can be reduced to finite dimensional convex problems involving linear matrix inequalities the method is applied to the shape design of a swing arm for magnetic storage devices with the objective of maximizing the control bandwidth achievable with a limited actuator power

regression modeling in back propagation and projection pursuit learning we study and compare two types of connectionist learning methods for model free regression problems 1 the backpropagation learning bpl and 2 the projection pursuit learning ppl emerged in recent years in the statistical estimation literature both the bpl and the ppl are based on projections of the data in directions determined from interconnection weights however unlike the use of fixed nonlinear activations usually sigmoidal for the hidden neurons in bpl the ppl systematically approximates the unknown nonlinear activations moreover the bpl estimates all the weights simultaneously at each iteration while the ppl estimates the weights cyclically neuron by neuron and layer by layer at each iteration although the bpl and the ppl have comparable training speed when based on a gauss newton optimization algorithm the ppl proves more parsimonious in that the ppl requires a fewer hidden neurons to approximate the true function to further improve the statistical performance of the ppl an orthogonal polynomial approximation is used in place of the supersmoother method originally proposed for nonlinear activation approximation in the ppl

on fixed points of multivalued functions on complete lattices and their application to generalized logic programs unlike monotone single valued functions multivalued mappings may have zero one or possibly infinitely many minimal fixed points the contribution of this work is twofold first we overview and investigate the existence and computation of minimal fixed points of multivalued mappings whose domain is a complete lattice and whose range is its power set second we show how these results are applied to a general form of logic programs where the truth space is a complete lattice we show that a multivalued operator can be defined whose fixed points are in one to one correspondence with the models of the logic program

nonmonotonic causal theories the nonmonotonic causal logic defined in this paper can be used to represent properties of actions including actions with conditional and indirect effects nondeterministic actions and concurrently executed actions it has been applied to several challenge problems in the theory of commonsense knowledge we study the relationship between this formalism and other work on nonmonotonic reasoning and knowledge representation and discuss its implementation called the causal calculator

sufficient conditions for uniqueness of a locally optimal quantizer for a class of convex error weighting functions sufficient conditions are presented for uniqueness of a locally optimal quantizer being a stationary point of the quantization distortion measure e f x eta the expected value of an error weighting function f x eta where x is a random variable to be quantized where the probability density function p x describing x is continuous and positive on some finite or infinite interval and zero outside it and where eta is the quantization error the function f x eta is assumed convex and symmetric in eta and zero only for eta 0 it is shown that in the cases of f x eta eta 2 and f x eta eta the simple condition of concavity of in p x is sufficient for uniqueness of a locally optimal quantizer

faithful representation of separable distributions a geometric approach to data representation incorporating information theoretic ideas is presented the task of finding a faithful representation where the input distribution is evenly partitioned into regions of equal mass is addressed for input consisting of mixtures of statistically independent sources we treat independent component analysis ica as a computational geometry problem first we consider the separation of sources with sharply peaked distribution functions where the ica problem becomes that of finding high density directions in the input distribution second we consider the more general problem for arbitrary input distributions where ica is transformed into the task of finding an aligned equipartition by modifying the kohonen self organized feature maps we arrive at neural networks with local interactions that optimize coding while simultaneously performing source separation the local nature of our approach results in networks with nonlinear ica capabilities

a time domain approach to robust fault detection of linear time varying systems this paper gives the optimal solutions to several robust fault detection problems such as 2 and problems for linear time varying systems in a time domain which extends the previous results on linear time invariant systems in a frequency domain it is shown that all three problems have the same optimal detection filter and the filter is a simple observer obtained by solving a standard differential riccati equation finally an example is given to illustrate our results

ℋ index for discrete time stochastic systems with markovian jump and multiplicative noise abstract in this paper we discuss the index problem for stochastic linear discrete time systems subject to markovian jump and multiplicative noise for which a necessary and sufficient condition for an index larger than 0 is given in finite time horizon it is shown that the index larger than a given value is equivalent to the solvability of a certain generalized difference riccati equation gdre what we have obtained generalizes the results of deterministic systems to stochastic models moreover the index problem for s q u a r e systems in infinite horizon is also studied finally some examples are presented to illustrate the effectiveness of the proposed theoretical results

provably correct theories of action we investigate logical formalization of the effects of actions in the situation calculus we propose a formal criterion against which to evaluate theories of deterministic actions we show how the criterion provides us a formal foundation upon which to tackle the frame problem as well as its variant in the context of concurrent actions our main technical contributions are in formulating a wide class of monotonic causal theories that satisfy the criterion and showing that each such theory can be reformulated succinctly in circumscription

modeling a dynamic and uncertain world i symbolic and probabilistic reasoning about change abstract intelligent agency requires some ability to predict the future an agent must ask itself what is presently its best course of action given what it now knows about what the world will be like when it intends to act this paper presents a system that uses a probabilistic model to reason about the effects of an agent s proposed actions on a dynamic and uncertain world computing the probability that relevant propositions will hold at a specified point in time the model allows for incomplete information about the world the occurrence of exogenous unplanned events unreliable sensors and the possibility of an imperfect causal theory the system provides an application program with answers to questions of the form is the probability that will hold in the world at time t greater than it is unique among algorithms for probabilistic temporal reasoning in that it tries to limit its inference according to the proposition time and probability threshold provided by the application the system will also notify the application if subsequent evidence invalidates its answer to a query

input output norms in general linear systems upper bounds on the induced norm of the input output operators in linear systems with l2 input and output signals are provided the main idea is to transform the original problem into a parametized set of indefinite lq optimization problems using the classical maximum principle the existence of solutions to the latter is equivalent to the solvability of a boundary value hamiltonian system or equivalenty of an indefinite riccati equation our time domain approach enables the treatment of a very general linear set up including time varying infinite dimensional finite and infinite horizon systems

probabilistic horn abduction and bayesian networks this paper presents a simple framework for horn clause abduction with probabilities associated with hypotheses the framework incorporates assumptions about the rule base and independence assumptions amongst hypotheses it is shown how any probabilistic knowledge representable in a discrete bayesian belief network can be represented in this framework the main contribution is in finding a relationship between logical and probabilistic notions of evidential reasoning this provides a useful representation language in its own right providing a compromise between heuristic and epistemic adequacy it also shows how bayesian networks can be extended beyond a propositional language this paper also shows how a language with only unconditionally independent hypotheses can represent any probabilistic knowledge and argues that it is better to invent new hypotheses to explain dependence rather than having to worry about dependence in the language

nonmonotonic reasoning in the framework of situation calculus abstract most of the solutions proposed to the yale shooting problem have either introduced new nonmonotonic reasoning methods generally involving temporal priorities or completely reformulated the domain axioms to represent causality explicitly this paper presents a new solution based on the idea that since the abnormality predicate takes a situational argument it is important for the meanings of the situations to be held constant across the various models being compared this is accomplished by a simple change in circumscription policy when ab is circumscribed result rather than holds is allowed to vary in addition we need an axiom ensuring that every consistent situation is included in the domain of discourse ordinary circumscription will then produce the intuitively correct answer beyond its conceptual simplicity the solution proposed here has additional advantages over the previous approaches unlike the approach that uses temporal priorities it can support reasoning backward in time as well as forward and unlike the causal approach it can handle ramifications in a natural manner

elements of generalized ultrametric domain theory generalized ultrametric spaces are a common generalization of preorders and ordinary ultrametric spaces as was observed by lawvere 1973 guided by his enriched categorical view on ultra metric spaces we generalize the standard notions of cauchy sequence and limit in an ultra metric space and of adjoint pair between preorders this leads to a solution method for recursive domain equations that combines and extends the standard order theoretic smyth and plotkin 1982 and metric america and rutten 1989 approaches

brief paper optimal fault detection for linear discrete time varying systems this paper deals with the problem of observer based fault detection for linear discrete time varying ldtv systems a problem formulation is first proposed to address the optimization of the fault detection filter fdf design which is expressed in terms of maximizing a finite horizon h h or h h performance index this formulation can be applied to fdf design of ldtv systems subject to l 2 norm bounded unknown inputs or stochastic noise sequences it is shown that a unified optimal solution to the fdf can be obtained by solving the discrete time riccati equation and the optimal fdf is not unique a numerical example is given to illustrate the proposed method

answer set programming and plan generation abstract the idea of answer set programming is to represent a given computational problem by a logic program whose answer sets correspond to solutions and then use an answer set solver such as smodels or dlv to find an answer set for this program applications of this method to planning are related to the line of research on the frame problem that started with the invention of formal nonmonotonic reasoning in 1980

quantizer monotonicities and globally optimal scalar quantizer design new monotonicity properties of optimal scalar quantizers are discussed these monotonicities reveal a globally optimal scalar quantizer structure depending on the probability mass functions and on the number of quantizer levels by incorporating the monotone quantizer structure into a dynamic programming process the time complexities of previous algorithms for designing globally optimal scalar quantizers can be significantly reduced for very general classes of distortion measures

ℋ index for continuous time stochastic systems with markov jump and multiplicative noise this paper investigates the problem of index for stochastic linear continuous time systems involving markov jump and multiplicative noise a set of generalized differential riccati equations gdres are presented and it is shown that the solvability of gdres is necessary and sufficient for the feasibility of an index larger than 0 our results extend the corresponding deterministic cases to stochastic systems furthermore the infinite horizon index problem for square systems is considered finally the effectiveness of the obtained results is tested by two examples

learning gaussian mixture models with entropy based criteria in this paper we address the problem of estimating the parameters of gaussian mixture models although the expectation maximization em algorithm yields the maximum likelihood ml solution its sensitivity to the selection of the starting parameters is well known and it may converge to the boundary of the parameter space furthermore the resulting mixture depends on the number of selected components but the optimal number of kernels may be unknown beforehand we introduce the use of the entropy of the probability density function pdf associated to each kernel to measure the quality of a given mixture model with a fixed number of kernels we propose two methods to approximate the entropy of each kernel and a modification of the classical em algorithm in order to find the optimum number of components of the mixture moreover we use two stopping criteria a novel global mixture entropy based criterion called gaussianity deficiency gd and a minimum description length mdl principle based one our algorithm called entropy based em ebem starts with a unique kernel and performs only splitting by selecting the worst kernel attending to gd we have successfully tested it in probability density estimation pattern classification and color image segmentation experimental results improve the ones of other state of the art model order selection methods

the fixed point theory of strictly causal functions we ask whether strictly causal components form well defined systems when arranged in feedback configurations the standard interpretation for such configurations induces a fixed point constraint on the function modeling the component involved we define strictly causal functions formally and show that the corresponding fixed point problem does not always have a well defined solution we examine the relationship between these functions and the functions that are strictly contracting with respect to a generalized distance function on signals and argue that these strictly contracting functions are actually the functions that one ought to be interested in we prove a constructive fixed point theorem for these functions introduce a corresponding induction principle and study the related convergence process

generalized ultrametric spaces in quantitative domain theory domains and metric spaces are two central tools for the study of denotational semantics in computer science but are otherwise very different in many fundamental aspects a construction that tries to establish links between both paradigms is the space of formal balls a continuous poset which can be defined for every metric space and that reflects many of its properties on the other hand in order to obtain a broader framework for applications and possible connections to domain theory generalized ultrametric spaces gums have been introduced in this paper we employ the space of formal balls as a tool for studying these more general metrics by using concepts and results from domain theory it turns out that many properties of the metric can be characterized via its formal ball space furthermore we can state new results on the topology of gums as well as two new fixed point theorems which may be compared to the priesz crampe and ribenboim theorem and the banach fixed point theorem respectively deeper insights into the nature of formal ball spaces are gained by applying methods from category theory our results suggest that while being a useful tool for the study of gums the space of formal balls does not provide the hoped for general connection to domain theory

representing action indeterminacy and ramifications abstract we define and study a high level language for describing actions more expressive than the action language a introduced by gelfond and lifschitz the new language ar allows us to describe actions with indirect effects ramifications nondeterministic actions and actions that may be impossible to execute it has symbols for nonpropositional fluents and for the fluents that are exempt from the commonsense law of inertia temporal projection problems specified using the language ar can be represented as nested abnormality theories based on the situation calculus

inductive situation calculus temporal reasoning has always been a major test case for knowledge representation formalisms in this paper we develop an inductive variant of the situation calculus in id logic classical logic extended with inductive definitions this logic has been proposed recently and is an extension of classical logic it allows for a uniform representation of various forms of definitions including monotone inductive definitions and non monotone forms of inductive definitions such as iterated induction and induction over well founded posets we show that the role of such complex forms of definitions is not limited to mathematics but extends to commonsense knowledge representation in the id logic axiomatization of the situation calculus fluents and causality predicates are defined by simultaneous induction on the well founded poset of situations the inductive approach allows us to solve the ramification problem for the situation calculus in a uniform and modular way our solution is among the most general solutions for the ramification problem in the situation calculus using previously developed modularity techniques we show that the basic variant of the inductive situation calculus without ramification rules is equivalent to reiter style situation calculus

defeasible reasoning with variable degrees of justification the question addressed in this paper is how the degree of justification of a belief is determined a conclusion may be supported by several different arguments the arguments typically being defeasible and there may also be arguments of varying strengths for defeaters for some of the supporting arguments what is sought is a way of computing the on sum degree of justification of a conclusion in terms of the degrees of justification of all relevant premises and the strengths of all relevant reasons i have in the past defended various principles pertaining to this problem in this paper i reaffirm some of those principles but propose a significantly different final analysis specifically i endorse the weakest link principle for the computation of argument strengths according to this principle the degree of justification an argument confers on its conclusion in the absence of other relevant arguments is the minimum of the degrees of justification of its premises and the strengths of the reasons employed in the argument i reaffirm my earlier rejection of the accrual of reasons according to which two arguments for a conclusion can result in a higher degree of justification than either argument by itself this paper diverges from my earlier theory mainly in its treatment of defeaters first it argues that defeaters that are too weak to defeat an inference outright may still diminish the strength of the conclusion second in the past i have also denied that multiple defeaters can result in the defeat of an argument that is not defeated by any of the defeaters individually in this paper i urge that there are compelling examples that support a limited version of this collaborative defeat the need to accommodate diminishers and collaborative defeat has important consequences for the computation of degrees of justification the paper proposes a characterization of degrees of justification that captures the various principles endorsed and constructs an algorithm for computing them

asymptotic distribution theory for nonparametric entropy measures of serial dependence entropy is a classical statistical concept with appealing properties establishing asymptotic distribution theory for smoothed nonparametric entropy measures of dependence has so far proved challenging in this paper we develop an asymptotic theory for a class of kernel based smoothed nonparametric entropy measures of serial dependence in a time series context we use this theory to derive the limiting distribution of granger and lin s 1994 normalized entropy measure of serial dependence which was previously not available in the literature we also apply our theory to construct a new entropy based test for serial dependence providing an alternative to robinson s 1991 approach to obtain accurate inferences we propose and justify a consistent smoothed bootstrap procedure the naive bootstrap is not consistent for our test our test is useful in for example testing the random walk hypothesis evaluating density forecasts and identifying important lags of a time series it is asymptotically locally more powerful than robinson s 1991 test as is confirmed in our simulation an application to the daily s p 500 stock price index illustrates our approach

motivated action theory a formal theory of causal reasoning when we reason about change over time it causation provides an implicit preference we prefer sequences of situations in which one situation leads causally to the next rather than sequences in which one situation follows another at random and without causal connections in this paper we explore the problem of temporal reasoning reasoning about change over time and the crucial role that causation plays in our intuitions we examine previous approaches to temporal reasoning and their shortcomings in light of this analysis we propose a new system for it causal reasoning motivated action theory which builds upon causation as a crucial preference criterion motivated action theory solves the traditional problems of both forward and backward reasoning and additionally provides a basis for a new theory of explanation

topographic map formation by maximizing unconditional entropy a plausible strategy for online unsupervised competitive learning and nonparametric density estimation an unsupervised competitive learning rule called the vectorial boundary adaptation rule vbar is introduced for topographic map formation since vbar is aimed at producing an equiprobable quantization of the input space it yields a nonparametric model of the input probability density function furthermore since equiprobable quantization is equivalent to unconditional entropy maximization we argue that this is a plausible strategy for maximizing mutual information shannon information rate in the case of online learning we use mutual information as a tool for comparing the performance of our rule with kohonen s self organizing feature map algorithm

nonmonotonic logic ii nonmonotonic modal theories tradmonal logics suffer from the monotomclty problem new axioms never mvahdate old theorems one way to get nd of this problem ts to extend traditional modal logic in the following way the operator m usually read possible is extended so that mp is true whenever p is consistent with the theory then any theorem of this form may be mvahdated if p s added as an axiom this extension results m nonmonotomc versions of the systems t 4 and 5 these systems are complete in that a theorem is provable in a theory based on one of them just if it is true m all noncommittal models of that theory where a noncommittal model ts one m which as many thmgs are possible as possible nonmonotomc 4 is probably the most interesting of the three since it is stronger than ordinary 4 but has all the usual inferential machinery of 4 there is a straightforward proof procedure for the sententlal subset of nonmonotomc 4 this approach to nonmonotonlc logic may be applied to several problems in knowledge representation for aruficml mtelhgence its main advantages over competmg approaches are that tt factors out problems of resource hmltattons and allows the symbol m to appear m any context since m is a meaningful part of the language

ramification and causality abstract in formal systems for reasoning about actions the ramification problem denotes the problem of handling indirect effects these effects are not explicitly represented in action specifications but follow from general laws describing dependencies among components of the world state an adequate treatment of indirect effects requires a suitably weakened version of the general law of persistence it also requires a method to avoid unintuitive changes suggested by the aforementioned dependency laws we propose a solution to the ramification problem that uses directed relations between two single effects stating the circumstances under which the occurrence of the first causes the second we argue for the necessity of an approach based on causality by elaborating the limitations of common paradigms employed to handle ramifications the principle of categorization and the policy of minimal change our abstract solution is realized on the basis of a particular action calculus namely the fluent calculus

a logic for default reasoning the need to make default assumptions is frequently encountered in reasoning about incompletely specified worlds inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations it is this property which leads to the non monotonicity of any logic of defaults in this paper we propose a logic for default reasoning we then specialize our treatment to a very large class of commonly occuring defaults for this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover finally we provide criteria under which the revision of derived beliefs must be effected

on the design of optimal noisy channel scalar quantizer with random index assignment the general approach in a noisy channel scalar quantizer design is an iterative descent algorithm which guarantees only a locally optimal solution while sufficient conditions under which the local optimum becomes a global optimum are known in the noiseless channel case such sufficient conditions were not derived for the noisy counterpart moreover efficient globally optimal design techniques for general discrete distributions in the noiseless case exist however they seem not to extend to the noisy scenario when a fixed index assignment is assumed recently the design of noisy channel scalar quantizer with random index assignment ria was proposed using a locally optimal iterative algorithm in this paper we derive sufficient conditions for the uniqueness of a local optimum which thus guarantee the global optimality of the solution these sufficient conditions are satisfied for a log concave probability density function which is additionally symmetric around its mean furthermore we show that assuming an ria the globally optimal design for general discrete sources can also be carried out efficiently

a new iterative approach for multi objective fault detection observer design and its application to a hypersonic vehicle abstractthis paper addresses the multi objective fault detection observer design problems for a hypersonic vehicle owing to the fact that parameters variations modelling errors and disturbances are inevitable in practical situations system uncertainty is considered in this study by fully utilising the orthogonal space information of output matrix some new understandings are proposed for the construction of lyapunov matrix sufficient conditions for the existence of observers to guarantee the fault sensitivity and disturbance robustness in infinite frequency domain are presented in order to further relax the conservativeness slack matrices are introduced to fully decouple the observer gain with the lyapunov matrices in finite frequency range iterative linear matrix inequality algorithms are proposed to obtain the solutions the simulation examples which contain a monte carlo campaign illustrate that the new methods can effectively reduce the design conservativeness compared with the existing methods

qualitative probabilities for default reasoning belief revision and causal modeling abstract this paper presents a formalism that combines useful properties of both logic and probabilities like logic the formalism admits qualitative sentences and provides symbolic machinery for deriving deductively closed beliefs and like probability it permits us to express if then rules with different levels of firmness and to retract beliefs in response to changing observations rules are interpreted as order of magnitude approximations of conditional probabilities which impose constraints over the rankings of worlds inferences are supported by a unique priority ordering on rules which is syntactically derived from the knowledge base this ordering accounts for rule interactions respects specificity considerations and facilitates the construction of coherent states of beliefs practical algorithms are developed and analyzed for testing consistency computing rule ordering and answering queries imprecise observations are incorporated using qualitative versions of jeffrey s rule and bayesian updating with the result that coherent belief revision is embodied naturally and tractably finally causal rules are interpreted as imposing markovian conditions that further constrain world rankings to reflect the modularity of causal organizations these constraints are shown to facilitate reasoning about causal projections explanations actions and change

explaining updates by minimal sums human reasoning about developments of the world involves always an assumption of inertia we discuss two approaches for formalizing such an assumption based on the concept of an explanation 1 there is a general preference relation given on the set of all explanations and 2 there is a notion of a distance between models and explanations are preferred if their sum of distances is minimal each distance dist naturally induces a preference relation dist we show exactly under which conditions the converse is true as well and therefore both approaches are equivalent modulo these conditions our main result is a general representation theorem in the spirit of kraus lehmann and magidor copyright 2001 elsevier science b v

estimation of the entropy and information of absolutely continuous random variables a method is proposed for estimating the entropy and the mutual information of absolutely continuous random vectors and an upper bound of the mean risks for the proposed estimators under strong mixing conditions is given