From Children's Arithmetic To Medical Problem Solving An Extension of the Kintch-Greeno Model

It has been found that expert physicians use forward reasoning in diagnostic explanations of clinical cases. This paper shows that the Kintsch-Greeno model for solving arithmetic word problems, which assumes a forward chaining process, can be extended to explain this phenomena. The basic approach is to modify the lexicon and the schema structure of the existing simulation program while retaining the basic control structure. The principle modifications are in the structure of the schemata which make use of three slots: indicator,abnormality and consequence. As with the Kintsch-Greeno theory,the model proceeds by using these schemata to build super-schemata from the propositional representation of the problem text

An Overview of Schema Theory

The purpose of this paper is to give an introduction to the field of Schema Theory written by a mathematician and for mathematicians. In particular, we endeavor to to highlight areas of the field which might be of interest to a mathematician, to point out some related open problems, and to suggest some large-scale projects. Schema theory seeks to give a theoretical justification for the efficacy of the field of genetic algorithms, so readers who have studied genetic algorithms stand to gain the most from this paper. However, nothing beyond basic probability theory is assumed of the reader, and for this reason we write in a fairly informal style. Because the mathematics behind the theorems in schema theory is relatively elementary, we focus more on the motivation and philosophy. Many of these results have been proven elsewhere, so this paper is designed to serve a primarily expository role. We attempt to cast known results in a new light, which makes the suggested future directions natural. This involves devoting a substantial amount of time to the history of the field. We hope that this exposition will entice some mathematicians to do research in this area, that it will serve as a road map for researchers new to the field, and that it will help explain how schema theory developed. Furthermore, we hope that the results collected in this document will serve as a useful reference. Finally, as far as the author knows, the questions raised in the final section are new.Comment: 27 pages. Originally written in 2009 and hosted on my website, I've decided to put it on the arXiv as a more permanent home. The paper is primarily expository, so I don't really know where to submit it, but perhaps one day I will find an appropriate journa

Integrating explanation-based and empirical learning methods in OCCAM

This paper discusses an approach to integrating empirical and explanation based learning techniques. The paper focuses on OCCAM, a program that has the capability to acquire via empirical means the knowledge needed for analytical learning. Two examples of this capability are discussed:The ability to use empirical techniques to acquire a domain theory for explanation based learning.The ability to use empirical learning techniques to find common patterns for causal relationships. These patterns encode a theory of causality (i.e., a set of general principles for recognizing causal relationships). Once acquired, a theory of causality can facilitate later learning by focusing on hypotheses which are consistent with the theory

Automation and schema acquisition in learning elementary computer programming: Implications for the design of practice

Two complementary processes may be distinguished in learning a complex cognitive skill such as computer programming. First, automation offers task-specific procedures that may directly control programming behavior, second, schema acquisition offers cognitive structures that provide analogies in new problem situations. The goal of this paper is to explore what the nature of these processes can teach us for a more effective design of practice. The authors argue that conventional training strategies in elementary programming provide little guidance to the learner and offer little opportunities for mindful abstraction, which results in suboptimal automation and schema acquisition. Practice is considered to be most beneficial to learning outcomes and transfer under strict conditions, in particular, a heavy emphasis on the use of worked examples during practice and the assignment of programming tasks that demand mindful abstraction from these examples

Elements of latent learning in a maze environment

A general purpose learning program is described which demonstrates a latent learning ability by operating at two separate goal pursuit levels. At one level are the constant, implicit goals associated with the system's memory management mechanisms. At the higher level are the dynamic, explicit behavioral goals which the implicit goals enable by manipulating memory representations to conform to the external surroundings. The program is shown to negotiate a simulated maze environment by the step-wise refinement of its latently learned experiences

The Semantics of Graph Programs

GP (for Graph Programs) is a rule-based, nondeterministic programming language for solving graph problems at a high level of abstraction, freeing programmers from handling low-level data structures. The core of GP consists of four constructs: single-step application of a set of conditional graph-transformation rules, sequential composition, branching and iteration. We present a formal semantics for GP in the style of structural operational semantics. A special feature of our semantics is the use of finitely failing programs to define GP's powerful branching and iteration commands