A nonmonotonic conditional logic for belief revision. Part 1: Semantics and logic of simple conditionals

Using Gardenfors's notion of epistemic entrenchment, we develop the semantics of a logic which accounts for the following points. It explains why we may generally infer If ⌍A then B if all we know is A∨B while must not generally infer If ⌍A then B if all we know is {A∨B,A}. More generally, it explains the nonmonotonic nature of the consequence relation governing languages which contain conditionals, and it explains how we can deduce conditionals from premise sets without conditionals. Depending on the language at hand, our logic provides different ways of keeping the Ramsey test and getting round the Gardenfors triviality theorem. We indicate that consistent additions of new items of belief are not to be performed by transitions to logical expansions.