Partial orders and lattices

Abstract

Abstract Presently we shall want to examine the relationships between the various Hmodels of a definite program. The usual framework in which we investigate such matters is the theory of lattices, which are just particular kinds of partial order. A (weak) partial order over a set S is any subset’(‘ of SxS having these properties: The relation ( is termed ‘weak’ owing to its reflexivity, in contrast to a ‘strict’ partial order ‘<‘ which has to be irreflexive, asymmetric and transitive. Clausalform definitions of these basic properties of order relations can be found in the answers to Question 1 of Exercises 41.