Incorporating new information into a knowledge base is an important problem which has been widely investigated. In this paper, we study this problem in a formal framework for reasoning about actions and change. In this framework, action domains are described in an action language whose semantics is based on the notion of causality. Unlike the formalisms considered in the related work, this language allows straightforward representation of nondeterministic effects and indirect effects of (possibly concurrent) actions, as well as state constraints; therefore, the updates can be more general than elementary statements. The expressivity of this formalism allows us to study the update of an action domain description with a more general approach compared to related work. First of all, we consider the update of an action description with respect to further criteria, for instance, by ensuring that the updated description entails some observations, assertions, or general domain properties that constitute further constraints that are not expressible in an action description in general. Moreover, our framework allows us to discriminate amongst alternative updates of action domain descriptions and to single out a most preferable one, based on a given
The satisfiability problem is a basic core NP-complete problem. In recent years, a lot of heuristic algorithms have been developed to solve this problem, and many experiments have evaluated and compared the performance of different heuristic algorithms. However, rigorous theoretical analysis and comparison are rare. This paper analyzes and compares the expected runtime of three basic heuristic algorithms: RandomWalk, (1+1) EA, and hybrid algorithm. The runtime analysis of these heuristic algorithms on two 2-SAT instances shows that the expected runtime of these heuristic algorithms can be exponential time or polynomial time. Furthermore, these heuristic algorithms have their own advantages and disadvantages in solving different SAT instances. It also demonstrates that the expected runtime upper bound of RandomWalk on arbitrary k-SAT(k >/= 3) is O((k - 1)(n)), and presents a k-SAT instance that has Theta((k - 1)(n)) expected runtime bound.
In this paper we show that a corpus of a few thousand Wikipedia articles about concrete or visualizable concepts can be used to produce a low-dimensional semantic feature representation of those concepts. The purpose of such a representation is to serve as a model of the mental context of a subject during functional magnetic resonance imaging (fMRI) experiments. A recent study  showed that it was possible to predict fMRI data acquired while subjects thought about a concrete concept, given a representation of those concepts in terms of semantic features obtained with human supervision. We use topic models on our corpus to learn semantic features from text in an unsupervised manner, and show that those features can outperform those in  in demanding 12-way and 60-way classification tasks. We also show that these features can be used to uncover similarity relations in brain activation for different concepts which parallel those relations in behavioral data from human subjects.
Dropout is a recently introduced algorithm for training neural network by randomly dropping units during training to prevent their co-adaptation. A mathematical analysis of some of the static and dynamic properties of dropout is provided using Bernoulli gating variables, general enough to accommodate dropout on units or connections, and with variable rates. The framework allows a complete analysis of the ensemble averaging properties of dropout in linear networks, which is useful to understand the non-linear case. The ensemble averaging properties of dropout in non-linear logistic networks result from three fundamental equations: (1) the approximation of the expectations of logistic functions by normalized geometric means, for which bounds and estimates are derived; (2) the algebraic equality between normalized geometric means of logistic functions with the logistic of the means, which mathematically characterizes logistic functions; and (3) the linearity of the means with respect to sums, as well as products of independent variables. The results are also extended to other classes of transfer functions, including rectified linear functions. Approximation errors tend to cancel each other and do not accumulate. Dropout can also be connected to stochastic neurons and used to predict firing rates, and to backpropagation by viewing the backward propagation as ensemble averaging in a dropout linear network. Moreover, the convergence properties of dropout can be understood in terms of stochastic gradient descent. Finally, for the regularization properties of dropout, the expectation of the dropout gradient is the gradient of the corresponding approximation ensemble, regularized by an adaptive weight decay term with a propensity for self-consistent variance minimization and sparse representations.
Existing representations for multiattribute ceteris paribus preference statements have provided useful treatments and clear semantics for qualitative comparisons, but have not provided similarly clear representations or semantics for comparisons involving quantitative tradeoffs. We use directional derivatives and other concepts from elementary differential geometry to interpret conditional multiattribute ceteris paribus preference comparisons that state bounds on quantitative tradeoff ratios. This semantics extends the familiar economic notion of marginal rate of substitution to multiple continuous or discrete attributes. The same geometric concepts also provide means for interpreting statements about the relative importance of different attributes.
An optimal arc consistency algorithm AC-4 was given by R. Mohr and T.C. Henderson (1986). AC-4 has cost O ( ea <sup>2</sup>), and cost( na <sup>2</sup>) for scene labeling. Although their algorithm is indeed optimal, under certain conditions a constraint satisfaction problem can be transformed into a less complex problem. Conditions and mechanisms are presented for such transformations, and it is shown how to factor relations into more manageable components. A description is given of how factorization can reduce AC-4's cost to O ( ea ), and this result is applied to RETE match
The authors present techniques for recognizing instances of 3-D object classes from sets of 3-D feature observations. Recognition of a class instance is structured as a search of an interpretation tree in which geometric constraints on pairs of sensed features not only prune the tree, but are used to determine upper and lower bounds on the model parameter values of the instance. A real-valued constraint propagation network unifies the representations of the model parameters, model constraints and feature constraints, and provides a simple and effective mechanism for accessing and updating parameter values. Recognition of objects with multiple internal degrees of freedom, including non-uniform scaling and stretching, articulations, and subpart repetitions, is demonstrated for two different types of real range data: 3-D edge fragments from a stereo vision system, and position/surface normal data derived from planar patches extracted from a range image
Introduces a logic endowed with a two-place modal connective that
has the intended meaning of “if α, then normally
β”. On top of providing a well defined tool for analyzing
common default reasoning, such a logic allows nesting of the default
operator. We present a semantic framework in which many of the known
default proof systems can be naturally characterized, and prove
soundness and completeness theorems for several such proof systems. Our
semantics is a “neighborhood modal semantics”, and it allows
for subjective defaults, i.e. defaults may vary within different worlds
that belong to the same model. The semantics has an appealing intuitive
interpretation and may be viewed as a set theoretic generalization of
the probabilistic interpretations of default reasoning. We show that our
semantics is general in the sense that any modal semantics that is sound
for some basic axioms for default reasoning is a special case of our
semantics. Such a generality result may serve to provide a semantical
analysis of the relative strengths of different proof systems and to
show the nonexistence of semantics with certain properties
Prior works by the author have introduced the system QUAL (herein
Q) of qualified syllogisms. An example of such a syllogism is
“Most birds can fly; Tweety is a bird; therefore, it is likely
that Tweety can fly.” Q provides a formal language for expressing
such syllogisms, together with a semantics which validates them. Also
introduced in the prior works is the notion of a path logic.
Reformulating Q as a path logic allows for the expression of modifier
combination rules, such as “From likely P and unlikely P, infer
uncertain P.” The present work builds on this, showing how to
incorporate Q into a system for default reasoning. Here is introduced
the notion of a dynamic reasoning system (DRS), consisting of a path
logic, together with a semantic net, or more exactly, a taxonomic
hierarchy that allows for multiple inheritance. The taxonomic hierarchy
enables definition of a specificity relation, which can then be used in
default reasoning (more specific information takes priority over less
specific). Modifier combination rules prescribe what to do when defaults
are applied in the context of multiple inheritance. Propositions derived
in this manner all bear qualitative likelihood modifiers, representing
the extent to which the proposition is believed
A coherent way of interpolating 3-D data obtained by stereo, for
example, with a simplicial polyhedral surface is discussed. The method
is based on constrained Delaunay triangulation; the polyhedral surface
is obtained by using a simple visibility property to mark tetrahedra
likely to be empty. The method is intrinsically discontinuity-preserving
and yields both a surface representation of objects and a volume
representation of free space which may be useful in robotics. Algorithms
to implement the method are described and their complexity analyzed in
the worst case and average case situations where tools of probabilistic
geometry are used
We demonstrate how multiagent systems provide useful control techniques for modular self-reconfigurable (metamorphic) robots. Such robots consist of many modules that can move relative to each other, thereby changing the overall shape of the robot to suit different tasks. Multiagent control is particularly well-suited for tasks involving uncertain and changing environments. We illustrate this approach through simulation experiments of Proteo, a metamorphic robot system currently under development.
The PUPS theory and its ACT∗ predecessor are computational embodiments of psychology's effort to develop a theory of the origins of knowledge. The theories contain proposals for extraction of knowledge from the environment, a strength-based prioritization of knowledge, knowledge compilation mechanisms for forming use-specific versions of knowledge, and induction mechanisms for extending knowledge. PUPS differs from ACT∗ basically in its principles of induction which include analogy-based generalization, a discrimination mechanism, and principles of making causal inferences. The knowledge in these theories can be classified into the knowledge level, algorithm level, and implementation level. Knowledge at the knowledge level consists of information acquired from the environment and innate principles of induction and problem solving. Knowledge at the algorithm level consists of internal deductions, inductions, and compilation. Knowledge at the implementation level takes the form of setting strengths for the encoding of specific pieces of information
In his well-known paper “How computer should think” Belnap (1977) argues that four-valued semantics is a very suitable setting for computerized reasoning. In this paper we vindicate this thesis by showing that the logical role that the four-valued structure has among Ginsberg's bilattices is similar to the role that the two-valued algebra has among Boolean algebras. Specifically, we provide several theorems that show that the most useful bilattice-valued logics can actually be characterized as four-valued inference relations. In addition, we compare the use of three-valued logics with the use of four-valued logics, and show that at least for the task of handling inconsistent or uncertain information, the comparison is in favor of the latter.
We present an abstract framework for default reasoning, which includes Theorist, default logic, logic programming, autoepistemic logic, non-monotonic modal logics, and certain instances of circumscription as special cases. The framework can be understood as a generalisation of Theorist. The generalisation allows any theory formulated in a monotonic logic to be extended by a defeasible set of assumptions.An assumption can be defeated (or “attacked”) if its “contrary” can be proved, possibly with the aid of other conflicting assumptions. We show that, given such a framework, the standard semantics of most logics for default reasoning can be understood as sanctioning a set of assumptions, as an extension of a given theory, if and only if the set of assumptions is conflict-free (in the sense that it does not attack itself) and it attacks every assumption not in the set.We propose a more liberal, argumentation-theoretic semantics, based upon the notion of admissible extension in logic programming. We regard a set of assumptions, in general, as admissible if and only if it is conflict-free and defends itself (by attacking) every set of assumptions which attacks it. We identify conditions for the existence of extensions and for the equivalence of different semantics.
This paper addresses the problem of computing posterior probabilities in a discrete Bayesian network where the conditional distributions of the model belong to convex sets. The computation on a general Bayesian network with convex sets of conditional distributions is formalized as a global optimization problem. It is shown that such a problem can be reduced to a combinatorial problem, suitable to exact algorithmic solutions. An exact propagation algorithm for the updating of a polytree with binary variables is derived. The overall complexity is linear to the size of the network, when the maximum number of parents is fixed.
The main statistics used in rough set data analysis, the approximation quality, is of limited value when there is a choice of competing models for predicting a decision variable. In keeping within the rough set philosophy of non-invasive data analysis, we present three model selection criteria, using information theoretic entropy in the spirit of the minimum description length principle. Our main procedure is based on the principle of indifference combined with the maximum entropy principle, thus keeping external model assumptions to a minimum. The applicability of the proposed method is demonstrated by a comparison of its error rates with results of C4.5, using 14 published data sets.
The complexities of various search algorithms are considered in terms of time, space, and cost of solution path. It is known that breadth-first search requires too much space and depth-first search can use too much time and doesn't always find a cheapest path. A depth-first iterative-deepening algorithm is shown to be asymptotically optimal along all three dimensions for exponential tree searches. The algorithm has been used successfully in chess programs, has been effectively combined with bi-directional search, and has been applied to best-first heuristic search as well. This heuristic depth-first iterative-deepening algorithm is the only known algorithm that is capable of finding optimal solutions to randomly generated instances of the Fifteen Puzzle within practical resource limits.
One of the original motivations for research in qualitative physics was the development of intelligent tutoring systems and learning environments for physical domains and complex systems. This article demonstrates how a synergistic combination of qualitative reasoning and other AI techniques can be used to create an intelligent learning environment for students learning to analyze and design thermodynamic cycles. Pedagogically this problem is important because thermodynamic cycles express the key properties of systems which interconvert work and heat, such as power plants, propulsion systems, refrigerators, and heat pumps, and the study of thermodynamic cycles occupies a major portion of an engineering student's training in thermodynamics. This article describes CyclePad, a fully implemented articulate virtual laboratory that captures a substantial fraction of the knowledge in an introductory thermodynamics textbook and provides explanations of calculations and coaching support for students who are learning the principles of such cycles. CyclePad employs a distributed coaching model, where a combination of on-board facilities and a server-based coach accessed via email provide help for students, using a combination of teleological and case-based reasoning. CyclePad is a fielded system, in routine use in classrooms scattered all over the world. We analyze the combination of ideas that made CyclePad possible and comment on some lessons learned about the utility of various AI techniques based on our experience in fielding CyclePad.
Today's Web sites are intricate but not intelligent; while Web navigation is dynamic and idiosyncratic, all too often Web sites are fossils cast in HTML. In response, this paper investigates adaptive Web sites: sites that automatically improve their organization and presentation by learning from visitor access patterns. Adaptive Web sites mine the data buried in Web server logs to produce more easily navigable Web sites.To demonstrate the feasibility of adaptive Web sites, the paper considers the problem of index page synthesis and sketches a solution that relies on novel clustering and conceptual clustering techniques. Our preliminary experiments show that high-quality candidate index pages can be generated automatically, and that our techniques outperform existing methods (including the Apriori algorithm, K-means clustering, hierarchical agglomerative clustering, and COBWEB) in this domain.
Representing and reasoning with priorities are important in commonsense reasoning. This paper introduces a framework of prioritized logic programming (PLP), which has a mechanism of explicit representation of priority information in a program. When a program contains incomplete or indefinite information, PLP is useful for specifying preference to reduce non-determinism in logic programming. Moreover, PLP can realize various forms of commonsense reasoning in AI such as abduction, default reasoning, circumscription, and their prioritized variants. The proposed framework increases the expressive power of logic programming and exploits new applications in knowledge representation.
An expert system has been developed to aid in the analysis of carbon-13 nuclear magnetic resonance (13C nmr) spectra of complex organic molecules. This system uses a knowledge base of rules relating substructural and spectral features: these rules are derived automatically from data for known structures. Such rules have a number of current, practical applications relating to spectrum prediction. They also constitute the basis of a method for the structural interpretation of 13C spectral data of unknown compounds. This method, which is basically a constraint refinement search, provides for a much more complete analysis of such data than any approach currently utilized.
In this paper we propose a methodology to derive a qualitative description of the behavior of a system from an incompletely known nonlinear dynamical model. The model is written as an algebraic structure with unknown parameters and/or functions. Under some hypotheses, we obtain a graph describing the possible transitions between regions, defined by the trends of the state variables and their relative positions. A qualitative simulation of the model can be compared with on-line data for fault detection purpose. We give the example of a nonlinear biological model (in dimension three) for the growth of cells in a bioreactor.
To represent an engineer's knowledge will require domain theories that are orders of magnitude larger than today's theories, describe phenomena at several levels of granularity, and incorporate multiple perspectives. To build and use such theories effectively requires strategies for organizing domain models and techniques for determining which subset of knowledge to apply for a given task. This paper describes compositional modeling, a technique that addresses these issues. Compositional modeling uses explicit modeling assumptions to decompose domain knowledge into semi-independent model fragments, each describing various aspects of objects and physical processes. We describe an implemented algorithm for model composition. That is, given a general domain theory, a structural description of a specific system, and a query about the system's behavior, the algorithm composes a model which suffices to answer the query while minimizing extraneous detail. We illustrate the utility of compositional modeling by outlining the organization of a large-scale, multi-grain, multi-perspective model we have built for engineering thermodynamics, and showing how the model composition algorithm can be used to automatically select the appropriate knowledge to answer questions in a tutorial setting.
The phase transition in binary constraint satisfaction problems, i.e. the transition from a region in which almost all problems have many solutions to a region in which almost all problems have no solutions, as the constraints become tighter, is investigated by examining the behaviour of samples of randomly-generated problems. In contrast to theoretical work, which is concerned with the asymptotic behaviour of problems as the number of variables becomes larger, this paper is concerned with the location of the phase transition in finite problems. The accuracy of a prediction based on the expected number of solutions is discussed; it is shown that the variance of the number of solutions can be used to set bounds on the phase transition and to indicate the accuracy of the prediction. A class of sparse problems, for which the prediction is known to be inaccurate, is considered in detail; it is shown that, for these problems, the phase transition depends on the topology of the constraint graph as well as on the tightness of the constraints.
J.F. Allen's theory of time and action is examined and found to be unsuitable for representing facts about continuous change. A series of revisions to Allen's theory is proposed in order to accommodate this possibility. The principal revision is a diversification of the temporal ontology to include instants on the same footing as intervals; a distinction is also made between two kinds of property, called states of position and states of motion, with respect to the logic of their temporal incidence. As a consequence of these revisions, it is also found necessary to diversify the range of predicates specifying temporal location. Finally, it is argued that Allen's category of processes is superfluous, since it can be assimilated with the category of properties. The implications of this assimilation for the representation of sentences containing verbs in the progressive aspect are discussed.
In this paper we show how tree decomposition can be applied to reasoning with first-order and propositional logic theories. Our motivation is two-fold. First, we are concerned with how to reason effectively with multiple knowledge bases that have overlap in content. Second, we are concerned with improving the efficiency of reasoning over a set of logical axioms by partitioning the set with respect to some detectable structure, and reasoning over individual partitions either locally or in a distributed fashion. To this end, we provide algorithms for partitioning and reasoning with related logical axioms in propositional and first-order logic.Many of the reasoning algorithms we present are based on the idea of passing messages between partitions. We present algorithms for both forward (data-driven) and backward (query-driven) message passing. Different partitions may have different associated reasoning procedures. We characterize a class of reasoning procedures that ensures completeness and soundness of our message-passing algorithms. We further provide a specialized algorithm for propositional satisfiability checking with partitions. Craig's interpolation theorem serves as a key to proving soundness and completeness of all of these algorithms. An analysis of these algorithms emphasizes parameters of the partitionings that influence the efficiency of computation. We provide a greedy algorithm that automatically decomposes a set of logical axioms into partitions, following this analysis.
Given a single picture which is a projection of a three-dimensional scene onto the two-dimensional picture plane, we usually have definite ideas about the 3-D shapes of objects. To do this we need to use assumptions about the world and the image formation process, since there exist a large number of shapes which can produce the same picture.The purpose of this paper is to identify some of these assumptions—mostly geometrical ones—by demonstrating how the theory and techniques which exploit such assumptions can provide a systematic shape-recovery method. The method consists of two parts. The first is the application of the Origami theory which models the world as a collection of plane surfaces and recovers the possible shapes qualitatively. The second is the technique of mapping image regularities into shape constraints for recovering the probable shapes quantitatively.Actual shape recovery from a single view is demonstrated for the scenes of an object such as a box and a chair. Given a single image, the method recovers the 3-D shapes of an object in it, and generates images of the same object as we would see it from other directions.
The embodied and situated approach to artificial intelligence (AI) has matured and become a viable alternative to traditional computationalist approaches with respect to the practical goal of building artificial agents, which can behave in a robust and flexible manner under changing real-world conditions. Nevertheless, some concerns have recently been raised with regard to the sufficiency of current embodied AI for advancing our scientific understanding of intentional agency. While from an engineering or computer science perspective this limitation might not be relevant, it is of course highly relevant for AI researchers striving to build accurate models of natural cognition. We argue that the biological foundations of enactive cognitive science can provide the conceptual tools that are needed to diagnose more clearly the shortcomings of current embodied AI. In particular, taking an enactive perspective points to the need for AI to take seriously the organismic roots of autonomous agency and sense-making. We identify two necessary systemic requirements, namely constitutive autonomy and adaptivity, which lead us to introduce two design principles of enactive AI. It is argued that the development of such enactive AI poses a significant challenge to current methodologies. However, it also provides a promising way of eventually overcoming the current limitations of embodied AI, especially in terms of providing fuller models of natural embodied cognition. Finally, some practical implications and examples of the two design principles of enactive AI are also discussed.
Using the language of dynamical systems theory, a general theoretical framework for the synthesis and analysis of autonomous agents is sketched. In this framework, an agent and its environment are modeled as two coupled dynamical systems whose mutual interaction is in general jointly responsible for the agent's behavior. In addition, the adaptive fit between an agent and its environment is characterized in terms of the satisfaction of a given constraint on the trajectories of the coupled agent-environment system. The utility of this framework is demonstrated by using it to first synthesize and then analyze a walking behavior for a legged agent.
This book, the first volume in a JAI Press series entitled Advances in Human and Machine Cognition, is a collection of fifteen papers edited by Kenneth M. Ford and Patrick J. Hayes. These papers were originally presented at The First International Workshop on Human & Machine Cognition, Pensacola, Florida, May 11–13, 1989. The workshop is a biannual affair which at each meeting addresses a core interdisciplinary topic in artificial intelligence (AI) and cognitive science. The special topic for the conference, and book, is the frame problem. The papers in the book incorporate an interdisciplinary approach drawing from AI, cognitive science, psychology and philosophy. The book is quite formal and some chapters require a background in logic, computer science and AI principles—although a few will appeal to the general reader. There is a six-page introduction by the editors that provides a brief synopsis of the frame problem and related problems as well as a brief organization and summaries of the papers presented in the book.
Reiter and de Kleer have independently developed a theory of diagnosis from first principles. Reiter's approach to computing all diagnoses for a given faulty system is based upon the computation of all minimal hitting sets for the collection of conflict sets for (sd,components,obs). Unfortunately, his theory does not include a theory of measurement. De Kleer and Williams have developed GDE—general diagnostic engine. Their procedure computes all minimal conflict sets resulting from a measurement before discriminating the candidate space. However, they do not provide a formal justification for their theory.We propose a general theory of measurement in diagnosis and provide a formal justification for our theory. Several novel contributions make up the central focus of this paper. First, this work provides an efficient incremental method for computing new diagnoses given a new measurement, based on the previous diagnoses predicting the opposite. Second, this work defines the concepts of conflict set resulting from a measurement, equivalence classes and homogeneous diagnoses as the basis of the method. Finally, this work leads to a procedure for computing all diagnoses and discriminating among competing diagnoses resulting from a measurement.
The sceptical inference relation associated with a Poole system without constraints is known to have a simple semantic representation by means of a smooth order directly defined on the set of interpretations associated with the underlying language. Conversely, we prove in this paper that, on a finite prepositional language, any preferential inference relation defined by such a model is induced by a Poole system without constraints. In the particular case of rational relations, the associated set of defaults may be chosen to be minimal; it then consists of a set of formulae, totally ordered through classical implication, with cardinality equal to the height of the given relation. This result can be applied to knowledge representation theory and corresponds, in revision theory, to Grove's family of spheres. In the framework of conditional knowledge bases and default extensions, it implies that any rational inference relation may be considered as the rational closure of a minimal knowledge base. An immediate consequence of this is the possibility of replacing any conditional knowledge base by a minimal one that provides the same amount of information.
This paper echoes, from a philosophical standpoint, the claim of McCarthy and Hayes that Philosophy and Artificial Intelligence have important relations. Philosophical problems about the use of “intuition” in reasoning are related, via a concept of anlogical representation, to problems in the simulation of perception, problem-solving and the generation of useful sets of possibilities in considering how to act. The requirements for intelligent decision-making proposed by McCarthy and Hayes are criticised as too narrow, and more general requirements are suggested instead.
Autonomous robots must be able to learn and maintain models of their environments. Research on mobile robot navigation has produced two major paradigms for mapping indoor environments: grid-based and topological. While grid-based methods produce accurate metric maps, their complexity often prohibits efficient planning and problem solving in large-scale indoor environments. Topological maps, on the other hand, can be used much more efficiently, yet accurate and consistent topological maps are often difficult to learn and maintain in large-scale environments, particularly if momentary sensor data is highly ambiguous. This paper describes an approach that integrates both paradigms: grid-based and topological. Grid-based maps are learned using artificial neural networks and naive Bayesian integration. Topological maps are generated on top of the grid-based maps, by partitioning the latter into coherent regions. By combining both paradigms, the approach presented here gains advantages from both worlds: accuracy/consistency and efficiency. The paper gives results for autonomous exploration, mapping and operation of a mobile robot in populated multi-room environments.
Belief networks are directed acyclic graphs in which the nodes represent propositions (or variables), the arcs signify direct dependencies between the linked propositions, and the strengths of these dependencies are quantified by conditional probabilities. A network of this sort can be used to represent the generic knowledge of a domain expert, and it turns into a computational architecture if the links are used not merely for storing factual knowledge but also for directing and activating the data flow in the computations which manipulate this knowledge.The first part of the paper deals with the task of fusing and propagating the impacts of new information through the networks in such a way that, when equilibrium is reached, each proposition will be assigned a measure of belief consistent with the axioms of probability theory. It is shown that if the network is singly connected (e.g. tree-structured), then probabilities can be updated by local propagation in an isomorphic network of parallel and autonomous processors and that the impact of new information can be imparted to all propositions in time proportional to the longest path in the network.The second part of the paper deals with the problem of finding a tree-structured representation for a collection of probabilistically coupled propositions using auxiliary (dummy) variables, colloquially called “hidden causes.” It is shown that if such a tree-structured representation exists, then it is possible to uniquely uncover the topology of the tree by observing pairwise dependencies among the available propositions (i.e., the leaves of the tree). The entire tree structure, including the strengths of all internal relationships, can be reconstructed in time proportional to n log n, where n is the number of leaves.
This short paper relates the conditional object-based and possibility theory-based approaches for reasoning with conditional statements pervaded with exceptions, to other methods in nonmonotonic reasoning which have been independently proposed: namely, Lehmann's preferential and rational closure entailments which obey normative postulates, the infinitesimal probability approach, and the conditional (modal) logics-based approach. All these methods are shown to be equivalent with respect to their capabilities for reasoning with conditional knowledge although they are based on different modeling frameworks. It thus provides a unified understanding of nonmonotonic consequence relations. More particularly, conditional objects, a purely qualitative counterpart to conditional probabilities, offer a very simple semantics, based on a 3-valued calculus, for the preferential entailment, while in the purely ordinal setting of possibility theory both the preferential and the rational closure entailments can be represented.
Constraint satisfaction networks have been shown to be a very useful tool for knowledge representation in Artificial Intelligence applications. These networks often utilize local constraint propagation techniques to achieve local consistency (consistent labeling in vision). Such methods have been used extensively in the context of image understanding and interpretation, as well as planning, natural language analysis and truth maintenance systems. In this paper we study the parallel complexity of discrete relaxation, one of the most commonly used constraint propagation techniques. Since the constraint propagation procedures such as discrete relaxation appear to operate locally, it has been previously believed that the relaxation approach for achieving local consistency has a natural parallel solution. Our analysis suggests that a parallel solution is unlikely to improve the known sequential solutions by much. Specifically, we prove that the problem solved by discrete relaxation (arc consistency) is log-space complete for P (the class of polynomial-time deterministic sequential algorithms). Intuitively, this implies that discrete relaxation is inherently sequential and it is unlikely that we can solve the polynomial-time version of the consistent labeling problem in logarithmic time by using only a polynomial number of processors. Some practical implications of our result are discussed. We also provide a two-way transformation between AND/OR graphs, propositional Horn satisfiability and local consistency in constraint networks that allows us to develop optimal linear-time algorithms for local consistency in constraint networks.
Motivation analysis in story comprehension requires matching an action mentioned in the story against actions which might be predicted by possible explanatory motivations. This requires matching constants from the story against Skolem functions in the possible motivations (assuming a normal first-order representation of stories, plans, etc.). We will show that extending unification to allow for unifying two things if they are nonmonotonically equal does exactly what is needed in such cases. We also show that such a procedure allows for a clean method of noun-phrase reference determination. The work described here has all been implemented.
A common basis is suggested for the optical flow estimation approaches of Nagel (1983), Haralick and Lee (1983) and Tretiak and Pastor (1984). Based on a discussion of these approaches, an exact solution for the system of partial differential equations proposed by Horn and Schunck (1981) is given at gray value corners and extrema. The insight gained by this solution results in a modification of the “oriented smoothness” approach of Nagel (1983) which thereby becomes considerably simpler. In addition, the optical flow estimation approach of Hildreth (1983, 1984) can be shown to represent a kind of special case of this modified “oriented smoothness” approach in a more direct manner than discussed in Nagel (1984).
We report results about the redundancy of formulae in 2CNF form. In particular, we give a slight improvement over the trivial redundancy algorithm and give some complexity results about some problems related to finding Irredundant Equivalent Subsets (i.e.s.) of 2CNF formulae. The problems of checking whether a 2CNF formula has a unique i.e.s. and checking whether a clause in is all its i.e.s.'s are polynomial. Checking whether a 2CNF formula has an i.e.s. of a given size and checking whether a clause is in some i.e.s.'s of a 2CNF formula are polynomial or NP-complete depending on whether the formula is cyclic. Some results about Horn formulae are also reported.
In Tarski's formalisation, the universe of a relation algebra (RA) consists of a set of binary relations. A first contribution of this work is the introduction of RAs whose universe is a set of ternary relations: these support rotation as an operation in addition to those present in Tarski's formalisation. Then we propose two particular RAs: a binary RA, , whose universe is a set of (binary) relations on 2D orientations; and a ternary RA, , whose universe is a set of (ternary) relations on 2D orientations. The RA , more expressive than , constitutes a new approach to cyclic ordering of 2D orientations. An atom of expresses for triples of orientations whether each of the three orientations is equal to, to the left of, opposite to, or to the right of each of the other two orientations. has 24 atoms and the elements of its universe consist of all possible 224 subsets of the set of all atoms. Amongst other results, 1.we provide for a constraint propagation procedure computing the closure of a problem under the different operations, and show that the procedure is polynomial, and complete for a subset including all atoms;2.we prove that another subset, expressing only information on parallel orientations, is NP-complete;3.we show that provided that a subset of includes two specific elements, deciding consistency for a problem expressed in the closure of can be polynomially reduced to deciding consistency for a problem expressed in ; and4.we derive from the previous result that for both RAs we “jump” from tractability to intractability if we add the universal relation to the set of all atoms.
A comparison to the most closely related work in the literature indicates that the approach is promising.
A computer vision system has been implemented that can recognize three-dimensional objects from unknown viewpoints in single gray-scale images. Unlike most other approaches, the recognition is accomplished without any attempt to reconstruct depth information bottom-up from the visual input. Instead, three other mechanisms are used that can bridge the gap between the two-dimensional image and knowledge of three-dimensional objects. First, a process of perceptual organization is used to form groupings and structures in the image that are likely to be invariant over a wide range of viewpoints. Second, a probabilistic ranking method is used to reduce the size of the search space during model-based matching. Finally, a process of spatial correspondence brings the projections of three-dimensional models into direct correspondence with the image by solving for unknown viewpoint and model parameters. A high level of robustness in the presence of occlusion and missing data can be achieved through full application of a viewpoint consistency constraint. It is argued that similar mechanisms and constraints form the basis for recognition in human vision.
This paper describes a new approach to inheritance reasoning in semantic networks allowing for multiple inheritance with exceptions. The approach leads to an analysis of defeasible inheritance which is both well-defined and intuitively attractive: it yields unambiguous results applied to any acyclic semantic network, and the results conform to our intuitions in those cases in which the intuitions themselves are firm and unambiguous. Since the definition provided here is based on an alternative, skeptical view of inheritance reasoning, however, it does not always agree with previous definitions when it is applied to nets about which our intuitions are unsettled, or in which different reasoning strategies could naturally be expected to yield distinct results. After exploring certain features of the definition presented here, we describe also a hybrid (parallel-serial) algorithm that implements the definition in a parallel marker-passing architecture.
The theory of evidence has become a widely used method for handling uncertainty in intelligent systems. The method has, however, an efficiency problem. To solve this problem there is a need for approximations. In this paper an approximation method in the theory of evidence is presented. Further, it is compared experimentally with Bayesian and consonant approximation methods with regard to the error they make. Depending on parameters and the nature of evidence the experiments show that the new method gives comparatively good results. Properties of the approximation methods for presentation purposes are also discussed.
The current research presents a system that learns to understand object names, spatial relation terms and event descriptions from observing narrated action sequences. The system extracts meaning from observed visual scenes by exploiting perceptual primitives related to motion and contact in order to represent events and spatial relations as predicate-argument structures. Learning the mapping between sentences and the predicate-argument representations of the situations they describe results in the development of a small lexicon, and a structured set of sentence form-to-meaning mappings, or simplified grammatical constructions. The acquired grammatical construction knowledge generalizes, allowing the system to correctly understand new sentences not used in training. In the context of discourse, the grammatical constructions are used in the inverse sense to generate sentences from meanings, allowing the system to describe visual scenes that it perceives. In question and answer dialogs with naïve users the system exploits pragmatic cues in order to select grammatical constructions that are most relevant in the discourse structure. While the system embodies a number of limitations that are discussed, this research demonstrates how concepts borrowed from the construction grammar framework can aid in taking initial steps towards building systems that can acquire and produce event language through interaction with the world.
Default logic is a formal means of reasoning about defaults: what normally is the case, in the absence of contradicting information. Autoepistemic logic, on the other hand, is meant to describe the consequences of reasoning about ignorance: what must be true if a certain fact is not known. Although the motivation and formal character of these two systems are different, a closer analysis shows that they share a common trait, which is the indexical nature of certain elements in the theory. In this paper we compare the expressive power of the two systems. First, we give an effective translation of default logic into autoepistemic logic; default theories can thus be embedded into autoepistemic logic. We also present a more surprising result: the reverse translation is also possible, so that every set of sentences in autoepistemic logic can be effectively rewritten as a default theory. The formal equivalence of these two differing systems is thus established. This analysis gives an interpretive semantics to default logic, and yields insight into the nature of defaults in autoepistemic reasoning.
The 3D Mosaic system is a vision system that incrementally reconstructs complex 3D scenes from a sequence of images obtained from multiple viewpoints. The system encompasses several levels of the vision process, starting with images and ending with symbolic scene descriptions. This paper describes the various components of the system, including stereo analysis, monocular analysis, and constructing and updating the scene model. In addition, the representation of the scene model is described. This model is intended for tasks such as matching, display generation, planning paths through the scene, and making other decisions about the scene environment. Examples showing how the system is used to interpret complex aerial photographs of urban scenes are presented.
We present a novel approach to model-based pattern recognition where structural information and spatial relationships have a most important role. It is illustrated in the domain of 3D brain structure recognition using an anatomical atlas. Our approach performs segmentation and recognition of the scene simultaneously. The solution of the recognition task is progressive, processing successively different objects, and using different pieces of knowledge about the object and about relationships between objects. Therefore, the core of the approach is the knowledge representation part, and constitutes the main contribution of this paper. We make use of a spatial representation of each piece of information, as a spatial fuzzy set representing a constraint to be satisfied by the searched object, thanks in particular to fuzzy mathematical morphology operations. Fusion of these constraints allows us to select, segment and recognize the desired object.
Inferring the 3D structures of nonrigidly moving objects from images is a difficult yet basic problem in computational vision. Our approach makes use of dynamic, elastically deformable object models that offer the geometric flexibility to satisfy a diversity of real-world visual constraints. We specialize these models to include intrinsic forces inducing a preference for axisymmetry. Image-based constraints are applied as extrinsic forces that mold the symmetry-seeking model into shapes consistent with image data. We describe an extrinsic force that applies constraints derived from profiles of monocularly viewed objects. We generalize this constraint force to incorporate profile information from multiple views and use it to exploit binocular image data. For time-varying images, the force becomes dynamic and the model is able to infer not only depth, but nonrigid motion as well. We demonstrate the recovery of 3D shape and nonrigid motion from natural imagery.
There are many applications for a vision system which derives a three-dimensional model of a scene from one or more images and stores the model for easy retrieval and matching. The derivation of a 3D model of a scene involves transformations between four levels of representation: images, 2D features, 3D structures, and 3D geometric models. Geometric reasoning is used to perform these transformations, as well as for the eventual model matching. Since the image formation process is many-to-one, the problem of deriving 3D features from 2D features is ill-constrained. Additional constraints may be derived from knowledge of the domain from which the images were taken. The 3D MOSAIC system has successfully used domain specific knowledge to drive the geometric reasoning necessary to acquire 3D models for complex real-world urban scenes. To generalize this approach, a framework for the representation and use of domain knowledge for geometric reasoning for vision is proposed.