Order and lattices
Cleave John P. · 1991
Abstract As in algebraic systems, the subsystems (closed sets) of logic are ordered by the relation of inclusion and in Chapter 3, §3.10, this relation was represented by ‘lattice diagrams’. This itself is sufficient reason for developing a theory about this ordering. But, more importantly, the logical consequence of a logic itself defines an order relation, implication (Definition 3.8), which has familiar properties (Example 3.4(ii)). The notion of logical equivalence is defined in terms of this relation.