Jan M. Zytkow

A Theory of Historical Discovery: The Construction of Componential Models

One of the major goals of 18th century chemistry was to determine the components of substances. In this paper we describe STAHL, a system that models significant portions of 18th century reasoning about compositional models. The system includes a number of heuristics for generating componential models from reactions, as well as error recovery mechanisms for dealing with inconsistent results. STAHL processes chemical reactions incrementally, and is therefore capable of reconstructing extended historic episodes, such as the century-long development of the phlogiston theory. We evaluate STAHL’s heuristics in the light of historical data, and conclude that the same reasoning mechanisms account for a variety of historical achievements, including Black’s models of mild alkali and Lavoisier’s oxygen theory. STAHL explains the generation of competing accounts of the same reactions, since the system’s reasoning chain depends on knowledge it has accumulated at earlier stages.

Data-driven approaches to empirical discovery

Abstract In this paper we track the development of research in empirical discovery. We focus on four machine discovery systems that share a number of features: the use of data-driven heuristics to constrain the search for numeric laws; a reliance on theoretical terms; and the recursive application of a few general discovery methods. We examine each system in light of the innovations it introduced over its predecessors, providing some insight into the conceptual progress that has occurred in machine discovery. Finally, we reexamine this research from the perspectives of the history and philosophy of science.

Combining many searches in the FAHRENHEIT discovery system

Abstract Modeling scientific discovery requires combining a large variety of searches into one complex system. This causes conceptual difficulty and slows development of discovery systems. This paper discusses a version of the discovery system FAHRENHEIT which uses search templates to represent a number of different searches in a homogeneous way and a search interpreter to run the system. Search interpreter generates search instances and executes them, and takes care of interaction between searches. Practice shows that the clarity of control increases and that the changes to each search are much easier in the implementation that uses search templates and search interpreter.

Experimenting and theorizing in theory formation

The BACON system, developed by Langley, Simon and Bradshaw, has shown the utility of a data driven discovery system. A new system, called FAHRENHEIT, has been built which extends BACON, making it more robust and allowing it perform a wider range of discovery activity. The new system extends BACON in several ways: 1) It determines the scope of a law by making simulated experiments, and by searching for regularities that describe the scope boundaries. 2) The world model in which the experiments are performed is more sophisticated. 3) The order in which the data are considered is placed under the control of FAHRENHEIT so that the system continues the discovery process even if no regularity is found for a particular variable.

Normative systems of discovery and logic of search

New computer systems of discovery create a research program for logic and philosophy of science. These systems consist of inference rules and control knowledge that guide the discovery process. Their paths of discovery are influenced by the available data and the discovery steps coincide with the justification of results. The discovery process can be described in terms of fundamental concepts of artificial intelligence such as heuristic search, and can also be interpreted in terms of logic. The traditional distinction that places studies of scientific discovery outside the philosophy of science, in psychology, sociology, or history, is no longer valid in view of the existence of computer systems of discovery. It becomes both reasonable and attractive to study the schemes of discovery in the same way as the criteria of justification were studied: empirically as facts, and logically as norms.

Unified Algorithm for Undirected Discovery of Execption Rules

This paper presents an algorithm that seeks every possible exception rule which violates a common sense rule and satisfies several assumptions of simplicity. Exception rules, which represent systematic deviation from common sense rules, are often found interesting. Discovery of pairs that consist of a common sense rule and an exception rule, resulting from undirected search for unexpected exception rules, was successful in various domains. In the past, however, an exception rule represented a change of conclusion caused by adding an extra condition to the premise of a common sense rule. That approach formalized only one type of exceptions, and failed to represent other types. In order to provide a systematic treatment of exceptions, we categorize exception rules into eleven categories, and we propose a unified algorithm for discovering all of them. Preliminary results on fifteen real-world data sets provide an empirical proof of effectiveness of our algorithm in discovering interesting knowledge. The empirical results also match our theoretical analysis of exceptions, showing that the eleven types can be partitioned in three classes according to the frequency with which they occur in data.

Automated Discovery of Empirical Equations from Data

We describe a machine discovery system for automated finding regularities in numerical data. It can detect a broad range of empirical equations useful in different sciences, and can be easily expanded by addition of new variable transformations. Our system treats experimental error and evaluation of equations in a systematic and statistically sound manner in contradistinction to systems such as BACON, ABACUS, which include error-related parameters, but disregard problems of error analysis and propagation, leading to paradoxical results. Our system propagates error to the transformed variables and assigns error to parameters in equations. Furthermore, it uses errors in weighted least squares fitting, in the evaluation of equations, including their acceptance, rejection and ranking, and uses parameter error to eliminate spurious parameters. In the last part of our paper we analyse the evaluation of equation finding systems. We introduce two convergence tests and we analyze the performance of our system on those tests.

Automated Discovery Of Empirical Laws

We define the problem of empirical search for knowledge by interaction with a setup experiment, and we present a solution implemented in the FAHRENHEIT discovery system. FAHRENHEIT autonomously explores multi-dimensional empirical spaces of numerical parameters, making experiments, generalizing them into empirical equations, finding the scope of applications for each equation, and setting new discovery goals, until it reaches the empirically complete theory. It turns out that a small number of generic goals and a small number of data structures, when combined recursively, can lead to complex discovery processes and to the discovery of complex theories. We present FAHRENHEITs knowledge representation and the ways in which the discovery mechanism interacts with the emerging knowledge. Brief descriptions of several real-world applications demonstrate the systems discovery potential.

Automatic Theorem Generation in Plane Geometry

We introduce a conceptual framework for discovery of theorems in geometry and a mechanism which systematically discovers such theorems. Our mechanism incrementally generates geometrical situations, makes conjectures about them, uses a geometry theorem prover to determine the consistency of situations, and keeps valid conjectures as theorems. We define geometry situations, situation descriptions, theorems, and their relationships important to understand our discovery task. An exhaustive generator of situation descriptions has enormous combinatorial complexity. We analyze various ways to reduce that complexity. Ideally, the generator should create a single description of each situation, should generate more general situations before more specific ones, and should use the previously discovered theorems to constrain its generation mechanism. We describe our generator which possesses most of these properties, and we outline further improvements. Our theorem prover is based on Wus algebraic method for proving geometry theorems. We discuss the interface between our situation generator and theorem prover and the limitations of our discovery system. Examples of theorems discovered by our system are also presented.

Utilizing Experience for Improving the Tactical Manager

Abstract We describe a mechanism for simulation-based learning for a tactical manager expert system working in real-time. The learning is based on utilizing past experiences when attempting similar goals. The tactical manager, a prototype of an automated pilot, is the performance element in our system. The learning system accumulates experience about the functioning of the tactical manager in a large number of simulations. Then, search in the space of experimental results leads to the improved performance. The improvement is evaluated experimentally by confronting the performance of the initial system and the system that utilizes results of learning. As a simple example, we consider the task of learning how an airplane can evade a missile.