Approximate Theory Formation: An Explanation-Based Approach

Existing machine learning techniques have only limited capabilities of handling computationally intractable domains. This research extends explanation-based learning techniques in order to overcome such limitations. It is based on a strategy of sacrificing theory accuracy in order to gain tractability. Intractable theories are approximated by incorporating simplifying assumptions. Explanations of teacher-provided examples are used to guide a search for accurate approximate theories. The paper begins with an overview of this learning technique. Then a typology of simplifying assumptions is presented along with a technique for representing such assumptions in terms of generic functions. Methods for generating and searching a space of approximate theories are discussed. Empirical results from a testbed domain are presented. Finally, some implications of this research for the field of explanation-based learning are also discussed

Mechanical Generation of Heuristics for Intractable Theories

A domain independent mechanism for generating heuristics for intractable theories has been implemented in the POLLYANNA program. Heuristics are generated by a process of systematically applying generic simplifying assumptions to an initial intractable theory. Such assumptions sacrifice the accuracy of an intractable theory to gain efficiency in return. Truth preserving reformulations are also used to enhance the power of generic simplifying assumptions. This paper describes a framework for generating heuristics using these basic types of knowledge. Examples and representations of each are presented along with an architecture within which they interact to generate heuristic theories. Results from testing this technique in the hearts card domain are presented as well. This work is pan of a system combining analytic and empirical methods for learning heuristics. In the analytic phase, a set of candidate heuristics is generated from an intractable theory. In the empirical phase, heuristic theories are evaluated against teacher-provided training examples. This paper concentrates on the analytic process of generating heuristics

The Classification, Detection and Handling of Imperfect Theory Problems

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryOffice of Naval Research / N00014-86-K-030

Model simplification by asymptotic order of magnitude reasoning

AbstractOne of the hardest problems in reasoning about a physical system is finding an approximate model that is mathematically tractable and yet captures the essence of the problem. This paper describes an implemented program AOM which automates a powerful simplification method. AOM is based on two domain-independent ideas: self-consistent approximations and asymptotic order of magnitude reasoning. The basic operation of AOM consists of five steps: (1) assign order of magnitude estimates to terms in the equations, (2) find maximal terms of each equation, i.e., terms that are not dominated by any other terms in the same equation, (3) consider all possible n-term dominant balance assumptions, (4) propagate the effects of the balance assumptions, and (5) remove partial models based on inconsistent balance assumptions. AOM also exploits constraints among equations and submodels. We demonstrate its power by showing how the program simplifies difficult fluid models described by coupled nonlinear partial differential equations with several parameters. We believe the derivation given by AOM is more systematic and easily understandable than those given in published papers

Predicting the approximate functional behaviour of physical systems

This dissertation addresses the problem of the computer prediction of the approximate behaviour of physical systems describable by ordinary differential equations.Previous approaches to behavioural prediction have either focused on an exact mathematical description or on a qualitative account. We advocate a middle ground: a representation more coarse than an exact mathematical solution yet more specific than a qualitative one. What is required is a mathematical expression, simpler than the exact solution, whose qualitative features mirror those of the actual solution and whose functional form captures the principal parameter relationships underlying the behaviour of the real system. We term such a representation an approximate functional solution.Approximate functional solutions are superior to qualitative descriptions because they reveal specific functional relationships, restore a quantitative time scale to a process and support more sophisticated comparative analysis queries. Moreover, they can be superior to exact mathematical solutions by emphasizing comprehensibility, adequacy and practical utility over precision.Two strategies for constructing approximate functional solutions are proposed. The first abstracts the original equation, predicts behaviour in the abstraction space and maps this back to the approximate functional level. Specifically, analytic abduction exploits qualitative simulation to predict the qualitative properties of the solution and uses this knowledge to guide the selection of a parameterized trial function which is then tuned with respect to the differential equation. In order to limit the complexity of a proposed approximate functional solution, and hence maintain its comprehensibility, back-of-the-envelope reasoning is used to simplify overly complex expressions in a magnitude extreme. If no function is recognised which matches the predicted behaviour, segment calculus is called upon to find a composite function built from known primitives and a set of operators. At the very least, segment calculus identifies a plausible structure for the form of the solution (e.g. that it is a composition of two unknown functions). Equation parsing capitalizes on this partial information to look for a set of termwise interactions which, when interpreted, expose a particular solution of the equation.The second, and more direct, strategy for constructing an approximate functional solution is embodied in the closed form approximation technique. This extends approximation methods to equations which lack a closed form solution. This involves solving the differential equation exactly, as an infinite series, and obtaining an approximate functional solution by constructing a closed form function whose Taylor series is close to that of the exact solutionThe above techniques dovetail together to achieve a style of reasoning closer to that of an engineer or physicist rather than a mathematician. The key difference being to sacrifice the goal of finding the correct solution of the differential equation in favour of finding an approximation which is adequate for the purpose to which the knowledge will be put. Applications to Intelligent Tutoring and Design Support Systems are suggested

System Concepts and Formal Modelling Methods for Business Processes

The major quality breakthrough of the 1980s was the realisation by management that business and manufacturing processes are the key to customer service and organisational performance. This thesis is concerned with the overall problem of modelling of business processes. Of special interest is the study of business processes through an interdisciplinary approach that cuts across the boundaries of management and information technology. The overall effort is placed on being able to move from a purely conceptual level of describing a business process to a more formal one, enabling decision making, and driving the analysis away from experience, intuition, and informal debate. The extended review and presentation of the various modelling methodologies given here, serve as a guide to their basic concepts and capabilities. A particular case study - the management of the human resources in a consulting company - has been used in this thesis to enable the evaluation of the modelling techniques. Hence, models have been produced, as well as simulation results to indicate the limitations, the advantages and the information gained. Through this application, the understanding of requirements for modelling analysis and decision making of business processes was acquired. Particularly, two very important techniques were investigated. System Dynamics and Petri nets provide the answers when process models are geared to deliver not only qualitative but also quantitative results. However, Petri nets provide the mathematical notation and the plethora of analysis tools needed for the validation, verification, and performance analysis of the model. Additionally, two different simulation software packages were used, based on these methodologies; Ithink®, which is based on System Dynamics, and Alpha/Sim®, based on Petri nets theory. The model produced in the case study depicts perfectly the capabilities of the two techniques. Petri nets is not the total business modelling solution, it can be complemented by other methods, such as System Dynamics and discrete-time modelling as shown in Chapter 6. The feasibility of all these modelling techniques lies entirely on the analyst, who should use them alternately to satisfy the requirements of the problem

Approximation in Mathematical Domains

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryNational Science Foundation / NSF IST 83-17889Ope

Approximation in Mathematical Domains

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryNational Science Foundation / NSF IST 83-17889Ope