Accession Number : ADA133630

Title :   Symmetric Set Theory, a General Theory of Isomorphism, Abstraction, and Representation.

Descriptive Note : Memorandum rept.,

Corporate Author : MASSACHUSETTS INST OF TECH CAMBRIDGE ARTIFICIAL INTELLIGENCE LAB

Personal Author(s) : McAllester,David Allen ; Poggio,T ; Rosser,B L

PDF Url : ADA133630

Report Date : Aug 1983

Pagination or Media Count : 31

Abstract : It is possible to represent a finite set of points (atoms) by a finite sequence of points. However a finite set of points has no distinguished member and therefore it is impossible to define a function which takes a finite set of points and returns a first point in that set. Thus it is impossible to represent a finite sequence of points by a finite set of points. The theory of symmetric sets provides a framework in which this observation about sets and sequences can be proven. The theory of symmetric sets is similar to classical (Zermello-Fraenkel) set theory with the exception that the universe of symmetric sets includes points (ur-elements). Points provide a basis for general notions of isomorphism and symmetry. The general notions of isomorphism and symmetry in turn provide a basis for natural, simple, and universal defintions of abstractness, essential properties and functions, canonicality, and representations. It is expected that these notions will play an important role in the theory of data structures and in the construction of general techniques for reasoning about data structures. (Author)

Descriptors :   *Set theory, *Symmetry, Metamathematics, Points(Mathematics), Sequences(Mathematics), Reasoning, Observation, Data bases

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE