More Notes on "A Clash of Intuitions"

A path-based inheritance logic is proposed for handling nonmonotonic inheritance structures. The formalism is called exceptional inheritance logic (EIL). Exceptional information which is nevertheless inheritable is encapsulated in a class, called an exceptional class. EIL also takes into account a difference between acquired and inheritable properties. The paper describes ways in which exceptional classes are identified and subsequently located in inheritance struc­ tures. The on-path versus off-path debate is reassessed using EIL. 1 Introduction A major problem for network representations of defea­ sible and default knowledge (called 'nonmonotonic in­ heritance structures') concerns the use of 'redundant' links. Whilst the use of shortest-path algorithms for de­ riving network conclusions returns the (intuitively) cor­ rect result in many cases, in many other cases it does not [Touretzky, 1984]. One obvious answer is to as­ sert 'redundant' links explicitly into the network rep­ resentation so that shortest-path algorithms continue to work correctly. Such links represent binary assertions which explicitly relate by one link two nodes which pre­ viously were related by two or more intervening links. But the introduction of such 'redundant links' can make previously non-problematic network structures problem­ atic: unambiguous structures can become ambiguous, and there may be side-effects in other parts of the net­ work not involved with the redundant link. Touretzky [1986] describes a formal mechanism called on-path preemption which comes into play when a re­ dundant link causes such problems. The general idea is that where there is a redundant link, another path can override paths containing the redundant link (as will be described later). The effect is to implement formally the basic requirement that, despite the presence of redun­ dant links, more general information should be overrid­ den by more specific, i.e. that information from more specific superclasses should take precedence over infor­ mation from more general superclasses in cases of con­ flict. However, Sandewall [1986] notes that Touretzky's definitions do not take into account cases where the re­ dundant link is itself interrupted by another node (i.e. where a redundant link contains two or more sublinks). In such cases (exemplified by the so-called Clyde— African.elephant structure) counterintuitive results are sometimes returned. Sandewall proposes off-path pre-emption , where the idea that more explicit informa­ tion should win in cases of conflict. Touretzky, Horty and Thomason [1987] present a structure, called the 'George-marine' example, in which off-path preemption also returns counterintuitive results. Unfortunately, in the 'George-marine' example chosen …