A coherence-based approach to default reasoning

Proceedings of the Sixth National Conference on Artificial Intelligence Volume 1, 1987

From: AAAI-87 Proceedings.

Synthese, 2005

This paper first provides a brief survey of a possibilistic handling of default rules. A set of default rules of the form,“generally, from α deduce β”, is viewed as the family of possibility distributions satisfying constraints expressing that the situation where α and β is true has a greater plausibility than the one where a and-β is true. When considering only the subset of linear possibility distributions, the well-known System P of postulates proposed by Kraus, Lehmann and Magidor, has been obtained. We also present two rational extensions: one ...

Artificial intelligence, 1997

We present an abstract framework for default reasoning, which includes Theorist, default logic, logic programming, autoepistemic logic, non-monotonic modal logics, and certain instances of circumscription as special cases. The framework can be understood as a generalisation of Theorist. The generalisation allows any theory formulated in a monotonic logic to be extended by a defeasible set of assumptions.

Synthese , 2025

This paper argues for the reasonableness of an inclusive conception of default reasoning. The inclusive conception allows untriggered default rules to influence beliefs: Since a default "from ϕ, infer ψ" is a defeasible inference rule, it by default warrants a belief in the material implication ϕ → ψ, even if ϕ is not believed. Such inferences are not allowed in standard default logic of the Reiter tradition, but are reasonable by analogy to the Deduction Theorem for classical logic. Our main contribution is a formal framework for inclusive default reasoning. The framework has a solid philosophical foundation, it draws conclusions non-trivially different from noninclusive frameworks, and it exhibits a host of benchmark properties deemed desirable in the literature-e.g., that extensions always exist and are consistent.

Annals of Mathematics and Artificial Intelligence, 2008

We provide a description of generalized default logic as a unified formalism for nonmonotonic reasoning. Special attention will be paid to the role of the monotonic logic underlying default reasoning, as well as to the representation opportunities created by the use of assumptions (justifications) in the heads of default rules. On the other hand, it will be shown that even the generalized default logic can be simplified to a formal system that involves only monotonic rules and default assumptions.

Annals of Mathematics and Artificial Intelligence, 2007

In nonmonotonic reasoning, a default conditional α → β has most often been informally interpreted as a defeasible version of a classical conditional, usually the material conditional. There is however an alternative interpretation, in which a default is regarded essentially as a rule, leading from premises to conclusion. In this paper, we present a family of logics, based on this alternative interpretation. A general semantic framework under this rule-based interpretation is developed, and associated proof theories for a family of weak conditional logics is specified. Nonmonotonic inference is easily defined in these logics. Interestingly, the logics presented here are weaker than the commonly-accepted base conditional approach for defeasible reasoning. However, this approach resolves problems that have been associated with previous approaches.

Computational Intelligence, 1997

This is a position paper concerning the role of empirical studies of human default reasoning in the formalization of AI theories of default reasoning. We note that AI motivates its theoretical enterprise by reference to human skill at default reasoning, but that the actual research does not make any use of this sort of information and instead relies on intuitions of individual investigators. We discuss two reasons theorists might not consider human performance relevant to formalizing default reasoning: (a) that intuitions are sufficient to describe a model, and (b) that human performance in this arena is irrelevant to a competence model of the phenomenon. We provide arguments against both these reasons. We then bring forward three further considerations against the use of intuitions in this arena: (a) it leads to an unawareness of predicate ambiguity, (b) it presumes an understanding of ordinary language statements of typicality, and (c) it is similar to discredited views in other fields. We advocate empirical investigation of the range of human phenomena that intuitively embody default reasoning. Gathering such information would provide data with which to generate formal default theories and against which to test the claims of proposed theories. Our position is that such data are the very phenomena that default theories are supposed to explain. obvious and well-appreciated. By the same token, we expect that there may be less acceptance of our prescription to ground formalizing default reasoning in human default reasoning. We give due consideration to some of these arguments concerning such a prescription in the final sections of this article.

Artificial Intelligence, 1994

Reiter's default logic has proven to be an enduring and versatile approach to nonmonotonic reasoning. Subsequent work in default logic has concentrated in two major areas. First, modifications have been developed to extend and augment the approach. Second, there has been ongoing interest in semantic foundations for default logic. In this paper, a number of variants of default logic are developed to address differing intuitions arising from the original and subsequent formulations. First, we modify the manner in which consistency is used in the definition of a default extension. The idea is that a global rather than local notion of consistency is employed in the formation of a default extension. Second, we argue that in some situations the requirement of proving the antecedent of a default is too strong. A second variant of default logic is developed where this requirement is dropped; subsequently these approaches are combined, leading to a final variant. These variants then lead to default systems which conform to alternative intuitions regarding default reasoning. For all of these approaches, a fixed-point and a pseudo-iterative definition are given; as well a semantic characterisation of these approaches is provided. In the combined approach we argue also that one can now reason about a set of defaults and can determine, for example, if a particular default in a set is redundant. We show the relation of this work to that of Lukaszewicz and Brewka, and to the Theorist system.

In Proceedings of the International Conference on the Principles of Knowledge Representation and Reasoning (KR 2004), 2004

This article provides an experimental analysis of the possibilistic handling of default rules. Three different nonmonotonic consequence relations are considered: minimum specificity inference (MSP), lexicographical closure (LC), and epsilon-belief functions (LCD). The latter was initially proposed within the belief function framework; it is rephrased here within a possibility theory framework. These three consequence relations share some properties but differ on others, which allows for an experimental test of their psychological ...

1995

In this paper performance of a lately proposed decision procedure for Reiter's default logic is evaluated. Recent complexity results indicate that there are two orthogonal sources of complexity in default reasoning: classical (first-order) reasoning and conflict resolution (i.e. choosing an appropriate set of applicable non-conflicting default rules). For classical reasoning well-known techniques exist and conflict resolution presents the new computational