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Published online by Cambridge University Press: 05 June 2012
Introduction
10.1.1 In this chapter we look at logics in the family of main stream relevant logics. These are obtained by employing a ternary relation to formulate the truth conditions of →. In the most basic logic, there are no constraints on the relation. Stronger logics are obtained by adding constraints.
10.1.2 We also see how these semantics can be combined with the semantics of conditional logics of chapter 5 to give an account of ceteris paribus enthymemes.
The Logic B
10.2.1 N4 and N* are relevant logics, but, as relevant logics go, they are relatively weak. Many proponents of relevant logic have thought that the relevant logics of the last chapter are too weak, on the ground that there are intuitively correct principles concerning the conditional that they do not validate. A way to accommodate such principles within a possible-world semantics is to use a relation on worlds to give the truth conditions of conditionals at non-normal worlds. Unlike the binary relation of modal logic, xRy, though, this relation is a ternary, that is, three-place, relation, Rxyz.
10.2.2 Intuitively, the ternary relation Rxyz means something like: for all A and B, if A → B is true at x, and A is true at y, then B is true at z. What philosophical sense to make of this, we will come back to later.
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