A family of Non-Monotonic Inference Systems based on Conditional Logics

A large number of common sense assertions such as prototypical properties, obligation, possibility, nonmonotonic rules, can be expressed using conditional logics. They are precisely under the lights because of their great representation power for common sense notions. But representation is only the half of the work: reasoning is also needed. Furthermore, non-monotonic reasoning necessites both powerful representation and powerful reasoning. For this last point it is well known that the deduction relations of conditional logics are powerless ~ . In this article we propose to use conditional logics to represent defensible rules and we present different ways, based on semantics, to increase their deductive power. This leads to different non-monotonic systems, the less powerful being equivalent to Pearl’s system Z. A tableau like theorem proving method is proposed to implement all of these formalisms.