Roland Ducournau

Proposal for a monotonic multiple inheritance linearization

Previous studies concerning multiple inheritance convinced us that a better analysis of conflict resolution mechanisms was necessary. In [DHHM92], we stated properties that a sound mechanism has to respect. Among them, a monotonicity principle plays a critical role, ensuring that the inheritance mechanism behaves “naturally” relative to the incremental design of the inheritance hierarchy. We focus here on linearizations and present an intrinsically monotonic linearization, whereas currently used linearizations are not. This paper describes the algorithm in detail, explains the design choices, and compares it to other linearizations, with LOOPS and CLOS taken as references. In particular, this new linearization extends CLOS and LOOPS linearizations, producing the same results when these linearizations are sound.

On some algorithms for multiple inheritance in object-oriented programming

We study here some problems yielded by multiple inheritance in object-oriented languages. We give an interpretation and a formalism of heritance mechanisms within the framework of partially ordered sets theory. An inheritance mechanism can be regarded as a traversing algorithm of the inheritance graph, and we prove that those which yields linear extension (total order) play a central role.We discuss some operational semantic aspects of multiple inheritance, with the introduction of a concept named by multiplicity. After a presentation of some well-known inheritance algorithms we propose two new algorithms based upon depth-first search techniques and some particular classes of linear extensions, recently studied.We end by applying these results in the case of inheritance with exceptions and by setting a few problems. All these results are implemented in the frame-based language YAFOOL.

On Stein's paper: resolving ambiguity in nonmonotonic inheritance hierarchies

Abstract Inheritance hierarchies provide a simple encoding of common sense knowledge. Though attracted by the simplicity of hierarchies, the artificial intelligence community does not agree on how to deal with the ambiguities caused by the nonmonotonicity of these hierarchies. Stein (1992) presents a theory of multiple defeasible inheritance which is different from the theory of Touretzky et al. (1990, 1991, 1994). We show here that her way of defining an extension with respect to a focus node and as a subgraph of the inheritance graph is very attractive and compatible with Touretzky et al.s theoretic framework, but that her definition of admissibility is not intuitively satisfactory. Nevertheless, her polynomial algorithm for computing the ideally skeptical conclusion set according to this definition of admissibility provides an interesting heuristic to compute a really skeptical conclusion set, i.e. a subset of the ideally skeptical one. In Touretzky et al.s theory, ideal skepticism is NP-hard.