Toward a Theory of Representation Design
Abstract
This research is concerned with designing representations for analytical reasoning problems (of the sort found on the GRE and LSAT). These problems are intended to test the ability to draw logical conclusions from information presented and to synthesize that information in order to deduce interrelationships. A computer program was developed that takes as input a straightforward predicate calculus translation of a problem, requests additional information if necessary, decides what to represent and how, designs representations that capture the constraints of the problem, and finally, creates and executes a LISP program that uses those representations to produce a solution. Even though these problems are typically difficult for theorem provers to solve, the LISP program that uses the designed representations is very efficient. The representations designed by the system are powerful because they capture the constraints of a problem in two ways: 1) The structure of the representation resembles the structure of the thing represented. For example, consider representing married couples as sets of size two. The structure of this representation resembles the structure of married couples because both have exactly two individuals in them. 2) The structure enables efficient behaviors that enforce a problem's constraints by keeping them invariant in the structure. For example, as a set representing a married couple is manipulated, a behavior associated with it maintains its fixed size. This behavior efficiently enforces the size constraint on married couples. (kr)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1989
- Accession Number
- ADA210885
Entities
People
- Jeffrey Van Baalen
Organizations
- Massachusetts Institute of Technology