On Structured Argumentation with Conditional Preferences

We study defeasible knowledge bases with conditional preferences (DKB). A DKB consists of a set of undisputed facts and a rule-based system that contains different types of rules: strict, defeasible, and preference. A major challenge in defining the semantics of DKB lies in determining how conditional preferences interact with the attack relations represented by rebuts and undercuts, between arguments. We introduce the notions of preference attack relations as sets of attacks between preference arguments and the rebuts or undercuts among arguments as well as of preference attack relation assignments which map knowledge bases to preference attack relations. We present five rational properties (referred to as regular properties), the inconsistency-resolving, effective rebuts, context-independence, attack monotonicity and link-orientation properties generalizing the properties of the same names for the case of unconditional preferences. Preference attack relation assignment are defined as regular if they satisfy all regular properties. We show that the set of regular assignments forms a complete lower semilattice whose least element is referred to as the canonical preference attack relation assignment. Canonical attack relation assignment represents the semantics of preferences in defeasible knowledge bases as intuitively, it could be viewed as being uniquely identified by the regular properties together with the principle of minimal removal of undesired attacks. We also present the normal preference attack relation assignment as an approximation of the canonical attack relation assignment.