Guibert.pa@PARC-MAXC.ARPA (03/06/84)
[Forwarded from the CSLI bboard by Laws@SRI-AI.]
Title: "MATHEMATICAL ONTOLOGY"
Speaker: David McAllester (M.I.T.)
When: Monday March 12th at 11:00am
Where: Xerox PARC Twin Conference Room, Room 1500
AI techniques are often divided into "weak" and "strong" methods. A
strong method exploits the structure of some domain while a weak method
is more general and therefore has less structure to exploit. But it may
be possible to exploit UNIVERSAL structure and thus to find STRONG
GENERAL METHODS. Mathematical ontology is the study of the general
nature of mathematical objects. The goal is to uncover UNIVERSAL
RELATIONS, UNIVERSAL FUNCTIONS, and UNIVERSAL LEMMAS which can be
exploited in general inference techniques. For example there seems to
be a natural notion of isomorphism and a standard notion of essential
property which are universal (they can be meaningfully applied to ALL
mathematical objects). These universal relations are completely ignored
in current first order formulations of mathematics. A particular theory
of mathematical ontology will be discussed in which many natural
universal relations can be precisely defined. Some particular strong
general inference techniques will also be discussed.