Binary relations, matrices and inference developments

摘要

The relationships among binary relations, directed graphs and boolean matrices are discussed. The development of new relations from given relations is described in terms of boolean matrix operations.The development of new relations from given relations is equivalent to inferring new relationships from the given facts and the operations on these facts. Given a directed graph, one can infer all the facts possible by completing the graph. An alternative method is to store the given facts and upon being queried, one derives the results required.Two algorithms are described which employ matrix operations to make explicit new relationships that are implicit as a result of the given facts and general rules which map sets of relations into new relations. The two algorithms are analyzed in terms of space and time requirements. Comments are made concerning the practicality of the approach.