Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not enjoy, i.e. monotonicity. We study here general patterns of nonmonotonic reasoning and try to isolate properties that could help us map the field of nonmonotonic reasoning by reference to positive properties. We concentrate on a number of families of nonmonotonic consequence relations, defined in the style of Gentzen [13]. Both proof-theoretic and semantic points of view are developed in parallel. The former point of view was pioneered by D. Gabbay in [10], while the latter has been advocated by Y. Shoham in [38]. Five such families are defined and characterized by representation theorems, relating the two points of view. One of the families of interest, that of preferential relations, turns out to have been studied by E. Adams in [2]. The pr...

This paper presents a logical approach to nonmonotonic reasoning based on the notion of a nonmonotonic consequence relation. A conditional knowledge base, consisting of a set of conditional assertions of the type if . . . then . . . , represents the explicit defeasible knowledge an agent has about the way the world generally behaves. We look for a plausible definition of the set of all conditional assertions entailed by a conditional knowledge base. In a previous paper [17], S. Kraus and the authors defined and studied preferential consequence relations. They noticed that not all preferential relations could be considered as reasonable inference procedures. This paper studies a more restricted class of consequence relations, rational relations. It is argued that any reasonable nonmonotonic inference procedure should define a rational relation. It is shown that the rational relations are exactly those that may be represented by a ranked preferential model, or by a (non-standard) probabilistic model.

Reasoning can lead not only to the adoption of beliefs, but also to the retraction of beliefs. In philosophy, this is described by saying that reasoning is defeasible. My ultimate objective is the construction of a general theory of reasoning and its implementation in an automated reasoner capable of both deductive and defeasible reasoning. The resulting system is named “OSCAR. ” This article addresses some of the theoretical underpinnings of OSCAR. This article extends my earlier theory in two directions. First, it addresses the question of what the criteria of adequacy should be for a defeasible reasoner. Second, it extends the theory to accommodate reasons of varying strengths.

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We propose a model

Conditional logics, introduced by Lewis and Stalnaker, have been utilized in artificial intelligence to capture a broad range of phenomena. In this paper we examine the complexity of several variants discussed in the literature. We show that, in general, deciding satisfiability is PSPACE-complete for formulas with arbitrary conditional nesting and NP-complete for formulas with bounded nesting of conditionals. However, we provide several exceptions to this rule. Of particular note are results showing that (a) when assuming uniformity (i.e., that all worlds agree on what worlds are possible), the decision problem becomes EXPTIME-complete even for formulas with bounded nesting, and (b) when assuming absoluteness (i.e., that all worlds agree on all conditional statements), the decision problem is NP-complete for formulas with arbitrary nesting. 1 INTRODUCTION The study of conditional statements of the form "If : : : then : : :" has a long history in philosophy [Sta68, Lew73, Che80, Vel8...

this paper, however, that the techniques of nonmonotonic logic may provide a better theoretical framework---at least for the formalization of commonsense normative reasoning---than the usual modal treatment. After reviewing some standard approaches to deontic logic, I focus on two areas in which nonmonotonic techniques promise improved understanding: reasoning in the presence of conflicting obligations, and reasoning with conditional obligations. 2 Modal techniques in deontic logic

The notion of minimality is widely used in three different areas of Artificial Intelligence: nonmonotonic reasoning, belief revision, and conditional reasoning. However, it is difficult for the readers of the literature in these areas to perceive the similarities clearly, because each formalization in those areas uses its own language sometimes without referring to other formalizations. We define ordered structures and families of ordered structures as the common ingredient of the semantics of all the works above. We also define the logics for ordered structures and families. We present a uniform view of how minimality is used in these three areas, and shed light on deep reciprocal relations among different approaches of the areas by using the ordered structures and the families of ordered structures. 1

We define an order independent version of default unification on typed feature structures. The operation is

How should what one knows about an individual affect default conclusions about that individual? This paper contrasts two views of "knowledge" in default reasoning systems. The first is the traditional view that one knows the logical consequences of one's knowledge base. It is shown how, under this interpretation, having to know an exception is too strong for default reasoning. It is argued that we need to distinguish "background" and "contingent" knowledge in order to be able to handle specificity, and that this is a natural distinction. The second view of knowledge is what is contingently known about the world under consideration. Using this view of knowledge, a notion of conditioning that seems like a minimal property of a default is defined. Finally, a qualitative version of the lottery paradox is given; if we want to be able to say that individuals that are typical in every respect do not exist, we should not expect to conclude the conjunction of our default conclusions. This paper...