. This short paper relates the conditional object-based and possibility theorybased approaches for reasoning with conditional statements pervaded with exceptions, to other methods in nonmonotonic reasoning which have been independently proposed: namely, Lehmann's preferential and rational closure entailments which obey normative postulates, the infinitesimal probability approach, and the conditional (modal) logics-based approach. All these methods are shown to be equivalent with respect to their capabilities for reasoning with conditional knowledge although they are based on different modeling frameworks. It thus provides a unified understanding of nonmonotonic consequence relations. More particularly, conditional objects, a purely qualitative counterpart to conditional probabilities, offer a very simple semantics, based on a 3-valued calculus, for the preferential entailment, while in the purely ordinal setting of possibility theory both the preferential and the rational closure entai...

In his well-known paper "How computer should think" ([Be77b]) Belnap argues that four valued semantics is a very suitable setting for computerized reasoning. In this paper we vindicate this thesis by showing that the logical role that the four-valued structure has among Ginsberg's well-known bilattices is similar to the role that the two-valued algebra has among Boolean algebras. Specifically, we provide several theorems that show that the most useful bilatticevalued logics can actually be characterized as four-valued inference relations. In addition, we compare the use of three-valued logics with the use of four-valued logics, and show that at least for the task of handling inconsistent or uncertain information, the comparison is in favor of the latter. Keyworkds: Bilattices, Paraconsistency, Multiple-valued systems, Preferential logics, Reasoning. 1 Introduction In [Be77a, Be77b] Belnap introduced a logic intended to deal in a useful way with inconsistent and incomplete information....

. At a workshop held in Toulouse, France in 1977, Gallaire, Minker and Nicolas stated that logic and databases was a field in its own right (see [131]). This was the first time that this designation was made. The impetus for this started approximately twenty years ago in 1976 when I visited Gallaire and Nicolas in Toulouse, France, which culminated in a workshop held in Toulouse, France in 1977. It is appropriate, then to provide an assessment as to what has been achieved in the twenty years since the field started as a distinct discipline. In this retrospective I shall review developments that have taken place in the field, assess the contributions that have been made, consider the status of implementations of deductive databases and discuss the future of work in this area. 1 Introduction As described in [234], the use of logic and deduction in databases started in the late 1960s. Prominent among the developments was the work by Levien and Maron [202, 203, 199, 200, 201] and Kuhns [1...

The links between Shoham's preference logic and possibilistic logic, a numerical logic of uncertainty based on Zadeh's possibility measures, are investigated. Starting from a fuzzy set of preferential interpretations of a propositional theory, we prove that the notion of preferential entailment is closely related to a previously introduced notion of conditional possibility. Conditional possibility is then shown to possess all properties (originally stated by Gabbay) of a well-behaved non-monotonic consequence relation. We obtain the possibilistic counterpart of Adams ' e-semantics of conditional probabilities which is the basis of the probabilistic model of non-monotonic logic proposed by Geffner and Pearl. Lastly we prove that our notion of possibilistic entailment is the one at work in possibilistic logic, a logic that handles uncertain propositional formulas, where uncertainty is modelled by degrees of necessity, and where partial inconsistency is allowed. Considering the formerly established close links between Gardenfors'epistemic entrenchment and necessity measures, what this paper proposes is a new way of relating belief revision and non-monotonic inference, namely via possibility theory. 1

We propose a model

This article proposes a framework, a so called information field, which allows information retrieval mechanisms to be compared inductively instead of experimentally. Such a comparison occurs as follows: Both retrieval mechanisms are first mapped to an associated information field. Within the field, the axioms that drive the retrieval process can be filtered out. In this way, the implicit assumptions governing an information retrieval mechanism can be brought to light. The retrieval mechanisms can then be compared according to which axioms they are governed by. Using this method it is shown that Boolean retrieval is more powerful than a strict form of coordinate retrieval. The salient point is not this result in itself, but how the result was achieved. 1 Introduction The logic based approach to information retrieval has been around for some time now. So far, a number of inference mechanisms, both strict and plausible, have been proposed for driving the retrieval process [15, 6, 4, 12]....

We present a new approach to deal with default information based on the theory of belief functions. Our semantic structures, inspired by Adams' epsilon semantics, are epsilon-belief assignments, where mass values are either close to 0 or close to 1. In the first part of this paper, we show that these structures can be used to give a uniform semantics to several popular non-monotonic systems, including Kraus, Lehmann and Magidor's system P, Pearl's system Z, Brewka's preferred sub-theories, Geffner's conditional entailment, Pinkas' penalty logic, possibilistic logic and the lexicographic approach. In the second part, we use epsilon-belief assignments to build a new system, called LCD, and show that this system correctly addresses the well-known problems of specificity, irrelevance, blocking of inheritance, ambiguity, and redundancy.

this paper we introduce Prohairetic Deontic Logic (PDL), a preference-based

Our aim in this article is to supplement the set of strong properties introduced in the preceding article ([Dix94]) with a set of weak principles in order to characterize semantics of logic programs. In [Dix94] we introduced our point of view: we observed that all semantics induce in a natural way a sceptical non-monotonic entailment relation SEM scept . We ask for the properties of these sceptical relations and use them to describe all possible semantics. We collect in this paper serious shortcomings of some semantics proposed recently. Their strange behaviour led us to formulate in a natural way certain principles to avoid these problems. We argue that any well-behaved semantics should satisfy these principles. The main results state that our list of weak principles is complete in the following sense: any well-behaved-semantics is an extension of the well-founded semantics WFS and coincides for stratified programs with Apt, Blair, and Walker's supported model M supp P . We also...

If a new piece of information contradicts our previously held beliefs, we have to revise our beliefs. This problem of belief revision arises in a number of areas in Computer Science and Artificial Intelligence, e.g., in updating logical database, in hypothetical reasoning, and in machine learning. Most of the research in this area is influenced by work in philosophical logic, in particular by Gardenfors and his colleagues, who developed the theory of belief revision. Here we will focus on the computational aspects of this theory, surveying results that address the issue of the computational complexity of belief revision.