A novel approach to default reasoning for MAS

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.

An approach to nonmonotonic inference, based on preference orderings between possible worlds or states of affairs, is presented. We begin with an extant weak theory of default conditionals; using this theory, or- derings on worlds are derived. The idea is that if a conditional such as "birds fly" is true then, all other things being equal, worlds in which birds fly are pre- ferred over those where they don't. In this case, a red bird would fly by virtue of red-bird-worlds being among the least exceptional worlds in which birds fly. In this approach, irrelevant properties are correctly handled, as is specificity, reasoning within exceptional circumstances, and inheritance reasoning. A sound proof-theoretic characterisation is also given. Lastly, the approach is shown to subsume that of conditional entailment.

Electronic Proceedings in Theoretical Computer Science, 2019

Often, we assume that an action is permitted simply because it is not explicitly forbidden; or, similarly, that an action is forbidden simply because it is not explicitly permitted. This kind of assumptions appear, e.g., in autonomous computing systems where decisions must be taken in the presence of an incomplete set of norms regulating a particular scenario. Combining default and deontic reasoning over actions allows us to formally reason about such assumptions. With this in mind, we propose a logical formalism for default reasoning over a deontic action logic. The novelty of our approach is twofold. First, our formalism for default reasoning deals with actions and action operators, and it is based on the deontic action logic originally proposed by Segerberg in [27]. Second, inspired by Segerberg's approach, we use tools coming from the theory of Boolean Algebra. These tools allow us to extend Segerberg's algebraic completeness result to the setting of Default Logics.

Computational Intelligence, 2004

We present a general approach for representing and reasoning with sets of defaults in default logic, focussing on reasoning about preferences among sets of defaults. First, we consider how to control the application of a set of defaults so that either all apply (if possible) or none do (if not). From this, an approach to dealing with preferences among sets of default rules is developed. We begin with an ordered default theory, consisting of a standard default theory, but with possible preferences on sets of rules. This theory is transformed into a second, standard default theory wherein the preferences are respected. The approach differs from other work, in that we obtain standard default theories and do not rely on prioritised versions of default logic. In practical terms this means we can immediately use existing default logic theorem provers for an implementation. As well, we directly generate just those extensions containing the most preferred applied rules; in contrast, most previous approaches generate all extensions, then select the most preferred. In a major application of the approach, we show how semi-monotonic default theories can be encoded so that reasoning can be carried out at the object level. With this, we can reason about default extensions from within the framework of standard default logic. Hence one can encode notions such as skeptical and credulous conclusions, and can reason about such conclusions within a single extension.

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

From: AAAI-87 Proceedings.

Lecture Notes in Computer Science, 1998

The purpose of this paper is to investigate the methodology of reasoning with prioritized defaults in the language of logic programs under the answer set semantics. We present a domain independent system of axioms, written as an extended logic program, which defines reasoning with prioritized defaults. These axioms are used in conjunction with a description of a particular domain encoded in a simple language allowing representation of defaults and their priorities. Such domain descriptions are of course domain dependent and should be specified by the users. We give sufficient conditions for consistency of domain descriptions and illustrate the use of our system by formalizing various examples from the literature. Unlike many other approaches to formalizing reasoning with priorities ours does not require development of the new semantics of the language. Instead, the meaning of statements in the domain description is given by the system of (domain independent) axioms. We believe that in many cases this leads to simpler and more intuitive formalization of reasoning examples. We also present some discussion of differences between various formalizations.

Artificial Intelligence, 2000

Conditional knowledge bases have been proposed as belief bases that include defeasible rules (also called defaults) of the form "¢ ¤ £ ¦ ¥ ", which informally read as "generally, if ¢ then ¥ ." Such rules may have exceptions, which can be handled in different ways. A number of entailment semantics for conditional knowledge bases have been proposed in the literature. However, while the semantic properties and interrelationships of these formalisms are quite well understood, about their computational properties only partial results are known so far. In this paper, we fill these gaps and first draw a precise picture of the complexity of default reasoning from conditional knowledge bases: Given a conditional knowledge base § © and a default ¢ £ ¥ , does § entail ¢ £ ¥ ? We classify the complexity of this problem for a number of well-known approaches (including Goldszmidt et al.'s maximum entropy approach and Geffner's conditional entailment), where we consider the general propositional case as well as natural syntactic restrictions (in particular, to Horn and literal-Horn conditional knowledge bases). As we show, the more sophisticated semantics for conditional knowledge bases are plagued with intractability in all these fragments. We thus explore cases in which these semantics are tractable, and find that most of them enjoy this property on feedback-free Horn conditional knowledge bases, which constitute a new, meaningful class of conditional knowledge bases. Furthermore, we generalize previous tractability results from Horn to q-Horn conditional knowledge bases, which allow for a limited use of disjunction. Our results complement and extend previous results, and contribute in refining the tractability/intractability frontier of default reasoning from conditional knowledge bases. They provide useful insight for developing efficient implementations.

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

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.

This paper superimposes an assumption generation mechanism (AGM) and a lower bound propagation mechanism (LBM) on default reasoning. AGM generates minimal probabilistic assumptions which are needed to derive default conclusions safely, and LBM supplies (approximately) tight lower probability bounds of the conclusions. Together both mechanisms make default reasoning probabilistically reliable. The underlying logical framework is an extension of Adams' probability logic P by irrelevance and contraposition assumptions, called the system P DP. There is an exact correspondence between Poole-extensions and P DP-extensions. The procedure for P DPentailment is comparable in complexity with Poole's procedure.