7 - Theories of Entailment

Summary

This chapter generalizes the ideas given in the previous chapter. It sets out the notion of a model based on a set of theories. One of these theories is the logic itself. It is, so to speak, the correct theory of theories. It correctly states the principles under which all the theories (including itself) are closed. But each theory has associated with it a closure operator. Some of these operators get the principles of theory closure quite wrong in the sense that they do not apply correctly to every theory in the model. The interaction between these closure operators can be altered in various ways, giving rise to different logical systems. The resulting formal semantics can be represented in the manner of Kit Fine’s “Models for Entailment”.