Program of the Thirteenth Annual Conference of the Cognitive Science Society: 7-10 August 1991, Chicago, Illinois

Program of the Thirteenth Annual Conference of the Cognitive Science Society: 7-10 August 1991, Chicago, Illinois

Program of the Thirteenth Annual Conference of the Cognitive Science Society: 7-10 August 1991, Chicago, Illinois

Program of the Thirteenth Annual Conference of the Cognitive Science Society: 7-10 August 1991, Chicago, Illinois

Excerpt

This paper presents a method, generalization to interval, that can encode images into symbolic expressions. This method generalizes over instances of spatial patterns, and outputs a constraint program that can be used declaratively as a learned concept about spatial patterns, and procedurally as a method for reasoning about spatial relations. Thus our method transforms numeric spatial patterns to symbolic declarative/procedural representations. We have implemented generalization to interval with ACORN, a system that acquires knowledge about spatial relations by observing 2-D raster images. We have applied this system to some layout problems to demonstrate the ability of the system and the flexibility of constraint programs for knowledge representation.

1. Introduction

Representation of spatial knowledge is an important task for intelligent agents. This task can arise in many domains: visual scene understanding, problem solving, robot navigation and so on. One important aspect of spatial knowledge is the use of a set of symbolic predicates that define spatial relations among objects in a scene. Classic system such as STRIPS [Fikes 71] or GPS [Newell 63] use symbolic predicates for representing spatial knowledge. For example, in the blocks world domain, such systems usually use primitive predicates such as: on(block1, table), right-of(block1,block2), and top-of(block3). These primitives are an abstraction of the actual scene -- they give only approximate information about the location of objects -- but they are important abstractions for reasoning about objects in the environment.

However, in order to apply such system to real- world domains, one would need a perceptual system to provide the appropriate symbolic primitives for reasoning (see Figure 1a). Winston's ARCH system [Winston 75] and Connell's system [Connell 87] are designed in this fashion: a vision system translated images into a set of symbolic facts, which were then used by a concept learning system. This approach leads to some difficult questions for the perceptual system: the number of primitives is not known, nor methods for mapping continuous image information into symbolic primitives. Ideally, a perceptual system should be general-purpose, and not restricted to a particular set of symbolic predicates.

Figure 2 demonstrates one problem with using a priori primitives for concept learning. Suppose that a vision system has six primitives to represent the distance between two objects: very very near, very near, near, far, very far, very very far. Given two scenes of two objects A and B, their distances are 11 and 19, as examples for target concept. The vision system encodes these values to predicates: {very-near (A,B), near(A,B)} and { far(A,B) }. Some learning systems simply apply a kind of dropping condition rule to these predicates. This would mean that the system could not describe both examples with a single concept (all conditions would be dropped), even if this may be an appropriate decision.