admin%cogsci.Berkeley.EDU@UCBVAX.BERKELEY.EDU (Cognitive Science Program) (11/18/86)
BERKELEY COGNITIVE SCIENCE PROGRAM
Cognitive Science Seminar - IDS 237A
Tuesday, November 25, 11:00 - 12:30
2515 Tolman Hall
Discussion: 12:30 - 1:30
2515 Tolman Hall
``Analogical and Deductive Reasoning"
Stuart Russell
Computer Science
UC Berkeley
The first problem I will discuss is that of analogical reason-
ing, the inference of further similarities from known similari-
ties. Analogy has been widely advertised as a method for apply-
ing past experience in new situations, but the traditional
approach based on similarity metrics has proved difficult to
operationalize. The reason for this seems to be that it
neglects the importance of relevance between known and inferred
similarities. The need for a logical semantics for relevance
motivates the definition of determinations, first-order expres-
sions capturing the idea of relevance between generalized pro-
perties. Determinations are shown to justify analogical infer-
ences and single-instance generalizations, and to express an
apparently common form of knowledge hitherto neglected in
knowledge-based systems. Essentially, the ability to acquire
and use determinations increases the set of inferences a system
can make from given data. When specific determinations are
unavailable, a simple statistical argument can relate similar-
ity to the probability that an analogical solution is correct,
in a manner closely connected to Shepard's stimulus generaliza-
tion results. The second problem, suggested by and subsuming
the first, is to identify the ways in which existing knowledge
can be used to help a system to learn from experience. I
describe a simple method for enumerating the types of knowledge
(of which determinations are but one) that contribute to learn-
ing, so that the monolithic notion of confirmation can be
teased apart. The results find strong echoes in Goodman's work
on induction. The application of a logical, knowledge-based
approach to the problems of analogy and induction indicates the
need for a system to be able to detect as many forms of regu-
larity as possible in order to maximize its inferential capa-
bility. The possibility that important aspects of common sense
are captured by complex, abstract regularities suggests further
empirical research to identify this knowledge.