ABSTRACT
Substructural logics are rich and complex: they allow us to draw many distinctions which are collapsed in classical logic. This richness necessitates some degree of complexity in semantics. The simple two-valued semantics of classical logic will not do. We have already seen one way to enrich two-valued semantics - you can inflate the number of values for a sentence to take. The algebras of Part II provide us with semantic values for sentences with enough richness to model all sorts of behaviour manifest in substructural systems. But this multiplicity of semantic values is not the only way to model substructural logics. It is also possible to keep the simple two-valued scheme - sentences are either true or they fail to be true - and to enrich the scheme instead by providing more places at which sentences are evaluated.
