Information Flow and Relevant Logics

2 Routley-Meyer Frames Relevant logics are interesting things. One motivating principle for these logics is the requirement that if a conditional of the form ! is to be true, there must be a connection between and . The antecedent must somehow be relevant to the consequent . This is simple to chart prooftheoretically, and for years, this was how relevant logics were studied. (A great deal of that work is charted in Anderson and Belnap 1975.) It was quite a deal harder to give relevant logics a semantics like the possible-worlds semantics for modal logics. There is a good reason for this. In possible worlds talk, a conditional ! is true at a world w (say w j= ! ) if and only if for each world v accessible from w (say wRv) if is true at v then is also true at v. In other words, a conditional is true at a world if and only if it is truth preserving at all accessible worlds.