10043574
Scientific Model-Building as Search in Matrix Spaces
Many reported discovery systems build discrete models of hidden structure, properties, or processes in the diverse fields of biology, chemistry, and physics. We show that the search spaces underlying many well-known systems are remarkably similar when re-interpreted as search in matrix spaces. A small number of matrix types are used to represent the input data and output models. Most of the constraints can be represented as matrix constraints; most notably, conservation laws and their analogues can be represented as matrix equations. Typically, one or more matrix dimensions grow as these systems consider more complex models after simpler models fail, and we introduce a notation to express this. The novel framework of matrix-space search serves to unify previous systems and suggests how at least two of them can be integrated. Our analysis constitutes an advance toward a generalized account of model-building in science.
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.
16243913
Experiments with a Heuristic Compiler
This report describes some experiments in constructing a compiler that makes use of heuristic problem~solving techniques such as those incorporated in the General Problem Solver (GPS) [1]. The experiments were aimed at the dual objectives of throwing light on some of the problems of constructing more powerful programming languages and compilers, and of testing whether the task of writing a computer program can be regarded as a "problem" in the sense in which that term is used in GPS. The present paper is concerned primarily with the second objective--with analyzing some of the problem-solving processes that are involved in writing computer programs. At the present stage of their development, no claims will be made for the heuristic programming procedures described here as practical approaches to the construction of compilers. Their interest lies in what they teach us about the nature of the programming task.
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.
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.
5581562
Computer science as empirical inquiry: symbols and search
Computer science is the study of the phenomena surrounding computers. The founders of this society understood this very well when they called themselves the Association for Computing Machinery. The machine—not just the hardware, but the programmed, living machine—is the organism we study.
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.
17442679
Inner Product Spaces for Bayesian Networks
Bayesian networks have become one of the major models used for statistical inference. We study the question whether the decisions computed by a Bayesian network can be represented within a low-dimensional inner product space. We focus on two-label classification tasks over the Boolean domain. As main results we establish upper and lower bounds on the dimension of the inner product space for Bayesian networks with an explicitly given (full or reduced) parameter collection. In particular, these bounds are tight up to a factor of 2. For some nontrivial cases of Bayesian networks we even determine the exact values of this dimension. We further consider logistic autoregressive Bayesian networks and show that every sufficiently expressive inner product space must have dimension at least Ω(n2), where n is the number of network nodes. We also derive the bound 2Ω(n) for an artificial variant of this network, thereby demonstrating the limits of our approach and raising an interesting open question. As a major technical contribution, this work reveals combinatorial and algebraic structures within Bayesian networks such that known methods for the derivation of lower bounds on the dimension of inner product spaces can be brought into play.
31930258
How Many Missing Answers Can Be Tolerated by Query Learners?
We consider the model of exact learning using an equivalence oracle and an incomplete membership oracle. In this model, a random subset of the learners membership queries is left unanswered. Our results are as follows. First, we analyze the obvious method for coping with missing answers: search exhaustively through all possible "answer patterns" associated with the unanswered queries. Thereafter, we present two specific concept classes that are efficiently learnable using an equivalence oracle and a (completely reliable) membership oracle, but are provably not polynomially learnable if the membership oracle becomes slightly incomplete. The first class will demonstrate that the aforementioned method of exhaustively searching through all possible answer patterns cannot be substantially improved in general (despite its apparent simplicity). The second class will demonstrate that the incomplete membership oracle can be rendered useless even if it leaves only a fraction 1/poly(n) of all queries unanswered. Finally, we present a learning algorithm for monotone DNF formulas that can cope with a relatively large fraction of missing answers (more than sixty percent), but is as efficient (in terms of run-time and number of queries) as the classical algorithm whose questions are always answered reliably.
16971158
Laboratory Replication of Scientific Discovery Processes
Fourteen subjects were tape-recorded while they undertook to find a law to summarize numerical doto they were given. The source of the data was not identified, nor were the variables lobeled semantically. Unknown to the subjects. the data were measurements of the distances of the planets from the sun and the periods of their revolutions obout it-equivalent to the doto used by Johonnes Kepler to discover his third low of planetary motion. Four of the 14 subjects discovered the some low as Kepler did (the period varies OS the 3/2 power of the distance), and a fifth come very close to the answer. The subiects’ protocols provide a detatled picture of the problem-solving searches they engoged in, which were mainly, but not exclusively, in the space of possible functions for fitting the data. and provide explanations OS to why some succeeded and the others foiled. The scorch heuristics used by the subjects ore similar to those embodied in the BACON program, a computer simulation of certain scientific discovery processes. The experiment demonstrates the feasibility of examining some of the processes of scientific discovery by recreating, in the laboratory, discovery situations of substontiol historical relevance. It demonstrates also. that under conditions rather similar to those of the originol discoverer, a low can be rediscovered by persons of ordinory intelligence (i.e., the intelligence needed for academic success in a good university). The data for the successful subjects reveal no “creative” processes in this kind of o discovery situation different from those that are regulorly observed in all kinds of problem-solving settings.
9115069
Causality in Device Behavior
Abstract This paper shows how formal characterizations of causality and of the method of comparative statics, long used in econometrics, thermodynamics and other domains, can be applied to clarify and make rigorous the qualitative causal calculus recently proposed by de Kleer and Brown [2]. The formalization shows exactly what assumptions are required to carry out causal analysis of a system of interdependent variables in equilibrium and to propagate disturbances through such a system. The intuitive concepts of causality captured by de Kleer and Brown provide a rough approximation to the standard analytic techniques that are used in the treatment of simultaneous algebraic and differential equations.