Class Algebra

D.J. Buehrer (Taiwan)


Class algebra, object-oriented IS-A class hierarchy, SDNF


This paper describes class algebra, which is a Boolean algebra < /2, /2, ~/1> with the addition of a pseudo complement operator -/1 and a dot operator ./2 for binary relations. Rather than working with the objects of the Boolean algebra, class algebra is an algebra of the consequents of its own Sorted Disjunctive Normal Form (SDNF) formulas. Such an algebra of formulas is a Lindenbaum algebra. The provable entailments between the equivalence classes of formulas form an IS-A hierarchy of object-oriented programming. We will show how class algebra can serve as a typing and query mechanism for Web-based persistent data. The number of objects in each class can be used as a fuzzy measure, and those predicates which divide a class into approximately equal-sized subclasses can be used to identify the “interesting” subclasses within the lattice. The fuzzy measures can also be used to optimize the SDNF programs, thus producing a universal learning algorithm.

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