37804897
Directions for Qualitative Reasoning
Sacks & Doyle provide an excellent overview of the fundamental limitations of the SPQR representations for reasoning about the qualitative properties of dynamic systems. We take this opportunity to outline some new directions for qualitative reasoning. In this paper, we provide a rigorous mathematical characterization for the term “qualitative property” in the context of static and dynamic systems. Based on these characterizations, we show that interval representations are well suited for reasoning about the qualitative properties of static systems such as qualitative comparative statics and qualitative stability. Moreover, we also show that symbolic computations help in the derivation of useful global properties of dynamic systems which can be used to guide numerical sampling of differential equations. The integration of symbolic and numeric methods provides a powerful approach for automating the qualitative analysis of differential equations.
21852626
Search and Reasoning in Problem Solving
In the course of the extensive research that has been done on problem solving in AI , several rather distinct ways have emerged for representing and thinking about problem solving tasks. One way to view problem solving is as search. We postulate some kind of space in which treasures are hidden. We build symbol structures (nodes) that model this space, and 'move ' operators that alter these symbol structures, taking us from one node to another. In this metaphor, solving a problem consists in searching the model of the space (selectively), moving from one node to another along links that connect them until a treasure is encountered. A second way of viewing problem solving is as reasoning. We postulate a system of logic that allows us to deduce new statements from axioms and previously deduced statements. We represent a problem by a set of axioms in the formal language of our logic. In this metaphor, solving the problem consists in accumulating more and more information (more and more statements) by inference until the answer to the problem has been found. A third way of viewing problem solving is as constraint satisfaction. We postulate a set of objects and various subsets defined by the constraints they satisfy. In this metaphor, solving a problem consists in narrowing down the original set to a subset or unique object that satisfies all of the constraints. In no sense are the metaphors mutually exclusive; metaphors seldom are. The same problem-solving algorithm can be viewed, now as search, now as reasoning, now as constraint satisfaction. Consider, for example, a simple theorem-proving program that works forward from a set of axioms, applying its rules of inference to these to obtain new expressions that can be added to the
6846387
Causality and Model Abstraction
Abstract Much of science and engineering is concerned with characterizing processes by equations describing the relations that hold among parameters of objects and govern their behavior over time. In formal descriptions of processes in terms of parameters and equations, the notion of causality is rarely made explicit. Formal treatments of the foundations of sciences have avoided discussions of causation and spoken only of functional relations among variables. Nevertheless, the notion of causality plays an important role in our understanding of phenomena. Even when we describe the behavior of a system formally in terms of acausal, mathematical relations, we often give an informal, intuitive explanation of why the system behaves the way it does in terms of cause-effect relations. In this paper, we will present an operational definition of causal ordering. The definition allows us to extract causal dependency relations among variables implicit in a model of a system, when a model is represented as a set of acausal, mathematical relations. Our approach is based on the theory of causal ordering first presented by Simon [22]. The paper shows how to use the theory and its extension in reasoning about physical systems. Further, the paper studies the relation of the theory to the problems of model aggregation.
14801431
Causality in Bayesian Belief Networks
We address the problem of causal interpretation of the graphical structure of Bayesian belief networks (BBNs). We review the concept of causality explicated in the domain of structural equations models and show that it is applicable to BBNs. In this view, which we call mechanism-based, causality is defined within models and causal asymmetries arise when mechanisms are placed in the context of a system. We lay the link between structural equations models and BBNs models and formulate the conditions under which the latter can be given causal interpretation.
29911339
Artificial Intelligence: An Empirical Science
My initial tasks in this paper are, first, to delimit the boundaries of artificial intelligence, then, to justify calling it a science: is AI science, or is it engineering, or some combination of these? After arguing that it is (at least) a science, I will consider how it is best pursued: in particular, the respective roles for experiment and theory in developing AI. I will rely more on history than on speculation, for our actual experience in advancing the field has much to tell us about how we can continue and accelerate that advance. Many of my examples will be drawn from work with which I have been associated, for I can speak with greater confidence about what motivated that work and its methods (and about its defects) than I can about the work of others. My goal, however, is not to give you a trip through history, but to make definite proposals for our future priorities, using history, where relevant, as evidence for my views.
8839735
Internal representation and rule development in object-oriented design
This article proposes a cognitive framework describing the software development process in object-oriented design (OOD) as building internal representations and developing rules. Rule development (method construction) is performed in two problem spaces: a rule space and an instance space. Rules are generated, refined, and evaluated in the rule space by using three main cognitive operations: Infer, Derive, and Evoke. Cognitive activities in the instance space are called mental simulations and are used in conjunction with the Infer operation in the rule space. In an empirical study with college students, we induced different representations to the same problem by using problem isomorphs. Initially, subjects built a representation based on the problem description. As rule development proceeded, the initial internal representation and designed objects were refined, or changed if necessary, to correspond to knowledge gained during rule development. Differences in rule development processes among groups created final designs that are radically different in terms of their level of abstraction and potential reusability. The article concludes by discussing the implications of these results for object-oriented design.
17561186
Situated Action: A Symbolic Interpretation
The congeries of theoretical views collectively referred to as “situated action” (SA) claim that humans and their interactions with the world cannot be understood using symbol-system models and methodology, but only by observing them within real-world contexts or building nonsymbolic models of them. SA claims also that rapid, real-time interaction with a dynamically changing environment is not amenable to symbolic interpretation of the sort espoused by the cognitive science of recent decades. Planning and representation, central to symbolic theories, are claimed to be irrelevant in everyday human activity. 
 
We will contest these claims, as well as their proponents' characterizations of the symbol-system viewpoint. We will show that a number of existing symbolic systems perform well in temporally demanding tasks embedded in complex environments, whereas the systems usually regarded as exemplifying SA are thoroughly symbolic (and representational), and, to the extent that they are limited in these respects, have doubtful prospects for extension to complex tasks. As our title suggests, we propose that the goals set forth by the proponents of SA can be attained only within the framework of symbolic systems. The main body of empirical evidence supporting our view resides in the numerous symbol systems constructed in the past 35 years that have successfully simulated broad areas of human cognition.
7797628
Bayesian Networks and Inner Product Spaces
In connection with two-label classification tasks over the Boolean domain, we consider the possibility to combine the key advantages of Bayesian networks and of kernel-based learning systems. This leads us to the basic question whether the class of decision functions induced by a given Bayesian network can be represented within a low-dimensional inner product space. For Bayesian networks with an explicitly given (full or reduced) parameter collection, we show that the “natural” inner product space has the smallest possible dimension up to factor 2 (even up to an additive term 1 in many cases). For a slight modification of the so-called logistic autoregressive Bayesian network with n nodes, we show that every sufficiently expressive inner product space has dimension at least 2 n/4. The main technical contribution of our work consists in uncovering combinatorial and algebraic structures within Bayesian networks such that known techniques for proving lower bounds on the dimension of inner product spaces can be brought into play.
36481911
Retrospective on "Causality in Device Behavior"
I first encountered causality in the late 1940s, while seeking to formalize the concept of political power (causation of the behavior of one person by another). This concept turned out to be closely related to the concept of identification in simultaneous equation models, then being investigated by the Cowles Commission for Research in Economics. I published in 1952-54 several papers [ 13,14 ] introducing a definition of causal ordering and exploring both the mathematical properties and the underlying semantics of the formalism. When, years later, I read the early papers on qualitative reasoning in AI, it seemed to me that causal ordering, and related ideas for applying the method of comparative statics (with which I had also had experience in my work in economics) provided a more powerful method than those being proposed.
1494125
Gordon Bell prize lectures
No abstract available
30978174
Whether software engineering needs to be artificially intelligent
The author discusses the roles that humans now play versus the roles that could be taken over by artificial intelligence in developing computer systems. Also discussed is how the intelligent part of the automatic system can communicate effectively with humans. Topics covered include an artificial intelligence overview; weak methods; the heuristic search; the problem space; the knowledge base; expert systems; and conclusions drawn from a description of the general artificial intelligence paradigm.