The purpose of this paper is to study the fundamental mechanism humans use in argumentation and its role in different major approaches to commonsense reasoning in AI and logic programming. We present three novel results: We develop a theory for argumentation in which the acceptability of arguments is precisely defined. We show that logic programming and nonmonotonic reasoning in AI are different forms of argumentation. We show that argumentation can be viewed as a special form of logic programming with negation as failure. This result introduces a general method for generating metainterpreters for argumentation systems. 1.

this paper allows any defaults to be overridden by defaults which are associated with more specific types: thus priority ordering reflects the type hierarchy ordering. (In 6.2, we will mention other possibilities for imposing a priority order on defaults.) Barring criterion 6, all of the above properties are necessary for making default unification behave as much like normal unification as possible, save that (default) information can be overridden. These criteria ensure that the default unification operation has properties familiar from monotonic unification, such as determinacy, the way information is accumulated, the conditions when unification fails, and order independence. Since this guarantees that default unification shares many of the properties of normal unification, a `seamless transition' is possible between the monotonic approach to linguistic analysis supplied by normal unification, and the extension to these analyses provided by supplying default constraints and default unification operating over them. We will justify these assumptions with respect to particular linguistic examples in 4

In many situations humans have to reason with inconsistent knowledge. These inconsistencies may occur due to not fully reliable sources of information. In order to reason with inconsistent knowledge, it is not possible to view a set of premisses as absolute truths as is done in predicate logic. Viewing the set of premisses as a set of assumptions, however, it is possible to deduce useful conclusions from an inconsistent set of premisses. In this paper a logic for reasoning with inconsistent knowledge is described. This logic is a generalization of the work of N. Rescher [12]. In the logic a reliability relation is used to choose between incompatible assumptions. These choices are only made when a contradiction is derived. As long as no contradiction is derived, the knowledge is assumed to be consistent. This makes it possible to define an executable deduction process for the preference logic. For the logic a semantics based on the ideas of Y. Shoham [14, 15], is defined. It turns out t...

The main claim of this paper is that reasoning with rules, especially rules of law, is different from reasoning with statements that are true or false. This difference is, amongst others, reflected in the defeasibility of arguments in which rules play a role. Reason-Based Logic is a logic that has special facilities for dealing with rules and with reasons based on rules. In particular it allows arguments in which conclusions are derived by 'weighing' the reasons that plead for and against them. In this article we illustrate some characteristics of reasoning with rules, and show how Reason-Based Logic deals with these characteristics. The article is concluded with some general considerations concerning Reason-Based Logic, and a comparison with some other logics for defeasible reasoning. 1.1. INTRODUCTION Rules are different from statements, and a logic that deals with rules should take this difference seriously. This is maybe the most important message that this article contains. The ...

In this paper we consider constrained and rational default logics. We provide two characterizations of constrained extensions. One of them is used to derive complexity results for decision problems involving constrained extensions. In particular, we show that the problem of membership of a formula in at least one (in all) constrained extension(s) of a default theory is \Sigma P 2 -complete (\Pi P 2 -complete). We establish the relationship between constrained and rational default logics. We prove that rational extensions determine constrained extensions and that for seminormal default theories there is a one-to-one correspondence between these objects. We also show that the definition of a constrained extension can be extended to cover the case of default theories which may contain justification-free defaults.

This paper derives a new and surprisingly low complexity result for inference in a new form of Reiter's propositional default logic [18]. The problem studied here is the default inference problem whose fundamental importance was pointed out by Kraus, Lehmann, and Magidor [12]. We prove that "normal" default inference, in propositional logic, is a problem complete for co-NP(3), the third level of the Boolean hierarchy [4]. Our result (by changing the underlying semantics) contrasts favorably with a similar result of Gottlob [7], who proves that standard default inference is \Pi P 2 -complete. Our inference relation also obeys all of the laws for preferential consequence relations set forth by Kraus, Lehmann, and Magidor. In particular, we get the property of being able to reason by cases and the law of cautious monotony. Both of these laws fail for standard propositional default logic. The key technique for our results is the use of Scott's domain theory to integrate defaults into pa...

We present a development of the theory of default information structures, combining ideas from domain theory with ideas from non-monotonic logic. Conceptually, our treatment is distinguished from standard default logic in that we view default structures as generating models rather than theories. Reiter's default rules are viewed as non-deterministic algorithms for generating preferred partial models. Using domain-theoretical notions, we improve the standard definition of extensions in default logic, by introducing the notion of dilation. We prove the existence of such dilations for a new, natural class of default information structures, properly including the so-called semi-normal ones. This class, called the class of rational structures, is a robust generalization of the usual kind of default rule system.

. Default logic is one of the most widely used formalisms to formalize commonsense reasoning. In this paper we analyze the complexity of deciding whether a propositional interpretation is a model of a default theory for some of the variants of default logic presented in the literature. We prove that all the analyzed variants have the same complexity and that this problem is in general # p 2 complete, while it is coNP complete under some restrictions on the form of the defaults. 1 INTRODUCTION Among all the formalisms proposed to model commonsense reasoning, default logic [15] is one of the most successful ones. Many aspects of default logic have been analyzed in the literature: semantics, algorithms, complexity, relationship with other formalisms, and so on. In this paper we focus on a specific usage of default logic, that is, on using it as a tool to represent information in the form of sets of models. Any knowledge representation formalism is a formal tool to represent informatio...

. In this paper, we contribute to the proof-theory of Reiter's Default Logic by introducing a sequent calculus for skeptical reasoning. The main features of this calculus are simplicity and regularity, and the fact that proofs can be surprisingly concise and, in many cases, involve only a small part of the default theory. 1 Introduction Non-monotonic logics play a fundamental role in knowledge representation and commonsense reasoning, as well as in the theory of programming languages. 1 The semantic and algorithmic aspects of non-monotonic reasoning have been extensively investigated (e.g. see [22, 26, 13, 17, 18, 9, 29, 33, 25] and [30, 27, 3, 4, 7, 35, 1, 2, 31, 36]). On the other hand, the proof-theoretic aspects are not yet completely understood. The fundamental papers by Gabbay [14] , Makinson [24] and Kraus, Lehmann and Magidor [19] , focus their attention on general properties of non-monotonic inference, rather than on specific formalisms. In particular, they do not axio...

We present a new priority-based approach to reasoning with specificity which subsumes inheritance reasoning. The new approach differs from other priority-based approaches in the literature in the way priority between defaults is handled. Here, it is conditional rather than unconditional as in other approaches. We show that