Psychological evidence for assumptions of path-based inheritance reasoning

The psychological validity of inheritance reasoners is clarified. Elio and Pelletier (1993) presented the first pilot experiment exploring some of these issues. We investigate other foundational assumptions of inheritance reasoning with defaults: transitivity, blocking of transitivity by negative defaults, pre-emption in terms of structurally defined specificity and structurally defined redundancy of information. Responses were in accord with the assumption of at least limited transitivity, however, reasoning with negative information and structurally defined specificity conditions did not support the predictions of the literature. 'Preemptive' links were found to provide additional information leading to indeterminacy, rather than providing completely overriding information as the literature predicts. On the other hand, results support the structural identification of certain links as redundant. Other findings suggest that inheritance proof-theory might be excessively guided by its syntax

Reformulating Non-Monotonic Theories for Inference and Updating

We aim to help build programs that do large-scale, expressive non-monotonic reasoning (NMR): especially, 'learning agents' that store, and revise, a body of conclusions while continually acquiring new, possibly defeasible, premise beliefs. Currently available procedures for forward inference and belief revision are exhaustive, and thus impractical: they compute the entire non-monotonic theory, then re-compute from scratch upon updating with new axioms. These methods are thus badly intractable. In most theories of interest, even backward reasoning is combinatoric (at least NP-hard). Here, we give theoretical results for prioritized circumscription that show how to reformulate default theories so as to make forward inference be selective, as well as concurrent; and to restrict belief revision to a part of the theory. We elaborate a detailed divide-and-conquer strategy. We develop concepts of structure in NM theories, by showing how to reformulate them in a particular fashion: to be conjunctively decomposed into a collection of smaller 'part' theories. We identify two well-behaved special cases that are easily recognized in terms of syntactic properties: disjoint appearances of predicates, and disjoint appearances of individuals (terms). As part of this, we also definitionally reformulate the global axioms, one by one, in addition to applying decomposition. We identify a broad class of prioritized default theories, generalizing default inheritance, for which our results especially bear fruit. For this asocially monadic class, decomposition permits reasoning to be localized to individuals (ground terms), and reduced to propositional. Our reformulation methods are implementable in polynomial time, and apply to several other NM formalisms beyond circumscription

Remarks on Inheritance Systems

We try a conceptual analysis of inheritance diagrams, first in abstract terms, and then compare to "normality" and the "small/big sets" of preferential and related reasoning. The main ideas are about nodes as truth values and information sources, truth comparison by paths, accessibility or relevance of information by paths, relative normality, and prototypical reasoning

Defeasible inheritance systems and reactive diagrams

We give an analysis of defeasible inheritance diagrams, also from the perspective of reactive diagrams

Logical tools for handling change in agent-based systems

We give a unified approach to various results and problems of nonclassical logic

Proceedings of the Workshop on Change of Representation and Problem Reformulation

The proceedings of the third Workshop on Change of representation and Problem Reformulation is presented. In contrast to the first two workshops, this workshop was focused on analytic or knowledge-based approaches, as opposed to statistical or empirical approaches called 'constructive induction'. The organizing committee believes that there is a potential for combining analytic and inductive approaches at a future date. However, it became apparent at the previous two workshops that the communities pursuing these different approaches are currently interested in largely non-overlapping issues. The constructive induction community has been holding its own workshops, principally in conjunction with the machine learning conference. While this workshop is more focused on analytic approaches, the organizing committee has made an effort to include more application domains. We have greatly expanded from the origins in the machine learning community. Participants in this workshop come from the full spectrum of AI application domains including planning, qualitative physics, software engineering, knowledge representation, and machine learning

The Tractability of Path-Based Inheritance

Touretzky (1984) proposed a formalism for nonmonotonic multiple inheritance reasoning which is sound in the presence of ambiguities and redundant links. We show that Touretzky's inheritance notion is NP-hard, and thus, provided P#NP, computationally intractable. This result holds even when one only considers unambiguous, totally acyclic inheritance networks. A direct consequence of this result is that the conditioning strategy proposed by Touretzky to allow for fast parallel inference is also intractable. Therefore, it follows that nonmonotonic multiple inheritance hierarchies, although compact representations, may not allow for efficient retrieval of information as has been suggested in attempts to use such hierarchies, e.g., in NETL (Fahlman 1979). We also analyze the influence of various design choices made by Touretzky. We show that all versions of downward (coupled) inheritance, i.e., on-path or off-path preemption and skeptical or credulous reasoning, are intractable. However, tractability can be achieved when using upward (decoupled) inheritance.