The Developement of A Lattice Structured Database

In this project we have investigated the possibilities to make a system based on the concept algebra described in [3], [4] and [5]. The concept algebra is used for ontology specification and knowledge representation. It is a distributive lattice extended with attribution operations. One of the main ideas in this work is to use Birkhoff's representation theorem, so we represent distributive lattices using its dual representation: the partial order of join irreducibles. We show how to construct a concept algebra satisfying a given set of equations. The universal/initial algebra is usually too big to be useful even in its dual representation, so it is important to use a smaller one from the set of possible solutions. Here the most important contribution seems to be the idea of inserting terms in the lattice. For this to make sense we introduced the concept of the most disjoint lattice with respect to a given set of inserted terms, that is the smallest lattice where the inserted terms preserve their value compared to the value in the initial algebra/lattice. The database is the dual representation of this most disjoint lattice. We develop algorithms to construct and make queries to the database.