Inductive properties of lattices

Abstract

This paper presents a family of algorithms able to produce effective constructions for representing and extracting new knowledge from a set of relevant examples or observed events of a given world. Representing a context by a pair (E, P) of examples and properties involved, we build the least lattice containing the ordering given by the dependencies of the properties. That is, we say that a property p is less or equal a propertyq whenever all occurrences of p are q instances. In this framework we can obtain inductive rules suggested by the examples. The rules are described in terms of lattices operations, and we develop an algorithm to compute the most convenient denotation of rules according to an economical optimization principle.

Keywords:

• Machine learning
• lattices
• order relations
• representations

C.R. Categories:

• 12.4
• 12.3