Specificity and Inheritance in Default Reasoning

When specificity considerations are incorporated in default reasoning systems, it is hard lo ensure that exceptional subclasses inherit all legitimate features of their parent classes To reconcile these two requirements specificitv and inheritance, this paper proposes the addi­ tion of a new rule called coherence rule, to the desiderata for default inference The coherence rule captures the intuition that formulae which are more compatible with the defaults in the database are more believable We offer a for­ mal definition of this extended desiderata and analyze the behavior of its associated closure relation which we call coherence closure We provide a concrete embodiment of a system sat­ isfying the extended desiderata by taking the coherence closure of system Z A procedure for computing the (unique) most compact, be lief ranking in the coherence closure of svstem Z is also described 1 Introduction It has been proposed [Makinson, ] 989 hrauh et al, ] 990] that default reasoning systems be analyzed in terms of their (default) consequence relations A number of in ference rules (or axioms) have generally been accepted [Pearl, 1991 Makinson, 1989] as a reasonable set of desiderata for a commonsense consequence relation De spite (lie general acceptance of these detiderata, they fail to reconcile two accepted lines of reasoning widely known as "inheritance" and 'specificity' These can be illustrated by the classical Tweety example as fol­ lows Consider the database (Figure 1) containing four defaults, "penguins are birds', 'penguins do not fly', birds fly' and'birds have wings' "Specificity' tells us. that lf Tweety is a penguin, then Tweety does not fly because penguin is a more specific classification of Tweety than bird "Inheritance", on the other hand, does equip Tweety with wings by virtue of being a bird albeit an exceptional bird with respect to flying ability " The inheritance and specificity lines of reasoning de­ pend on the interactions among the defaults in the database An inspection of the rules proposed in past desiderata reveals that, invariably, each rule refers to the defaults database as one unit no reference is made to specific subsets of defaults, the interaction among which produces the tension between inheritance and specificity In this paper we propose a new rule, called coherence, that resolves this tension Intuitively, the coherence rule prefers formulas that are more compatible with the de­ faults database We will formalize the requirements of inheritance and specificitv, and show that …