Evaluation of counterfactual queries (e.g., "If A were true, would C have been true?") is important to fault diagnosis, planning, and determination of liability. We present a formalism that uses probabilistic causal networks to evaluate one's belief that the counterfactual consequent, C, would have been true if the antecedent, A, were true. The antecedent of the query is interpreted as an external action that forces the proposition A to be true, which is consistent with Lewis' Miraculous Analysis. This formalism offers a concrete embodiment of the "closest world" approach which (1) properly reflects common understanding of causal influences, (2) deals with the uncertainties inherent in the world, and (3) is amenable to machine representation. Introduction A counterfactual sentence has the form If A were true, then C would have been true where A, the counterfactual antecedent, specifies an event that is contrary to one's real-world observations, and C, the counterfactual consequen...

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In this paper we examine ten concrete propositional update operations of the literature. We start by completely characterizing their relative strength and their computational complexity. Then we evaluate the competing update operations w.r.t. the postulates proposed by Katsuno and Mendelzon. It turns out that the majority violates most of the postulates. We argue that all violated postulates are undesirable except one. After that we evaluate the update operations w.r.t. another property which has been investigated extensively in the literature, viz. that disjunctive updates should not be identified with the exclusive disjunction. We argue that this is desirable, and show that the argument gives further support to the rejection of two of the postulates. Finally we study how the different approaches accommodate general laws governing the world, alias integrity constraints. Summing up our results, we conclude that only two of the update operations are satisfactory. Key words: Belief chan...

The use of logic to model the information retrieval process has become an established research area. Nevertheless, many people in the information retrieval community do not yet appreciate the work performed in this area, mainly because they do not understand logical formalisms, and hence cannot see the connection between logic and information retrieval. This paper aims at resolving the problem. It introduces the formalisms used in logical models for information retrieval, shows the use of logic to build the models, and presents a brief overview of some of the current logical models in information retrieval. 2 1 INTRODUCTION It has been argued that current information retrieval (IR) models offer only simplistic and specific representations of information (Chiaramella and Chevallet, 1992, Nie, 1990, van Rijsbergen, 1989). There is, therefore, a need for the development of a new formalism able to model IR systems in a more generic manner, hence capturing information as it appear...

Abstract: Semantic-based approaches to Information Retrieval make a query evaluation similar to an inference process based on semantic relations. semantic-based approaches find out hidden semantic relationships between a document and a query, but quantitative estimation of the correspondence between them is often empiric. On the other hand, probabilistic approaches usually consider only statistical relationships between terms. It is expected that improvement may be brought by integrating these two approaches. This paper demonstrates, using some particular probabilistic models which are strongly related to modal logic, that such an integration is feasible and natural. A new model is developed on the basis of an extended modal logic. It has the advantages of (1) augmenting a semantic-based approach with a probabilistic measurement, and (2) augmenting a probabilistic approach with finer semantic relations than just statistical ones. It is shown that this model verifies most of the conditions for an absolute probabiliyfinction. 1.

In this paper we present a labelled proof method for computing nonmonotonic consequence relations in a conditional logic setting. The method exploits the strong connection between these deductive relations and conditional logics, and it is based on the usual possible world semantics devised for the latter. The label formalism KEM, introduced to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logic by simply indexing labels with formulas. The basic inference rules are provided by the propositional system KE ---a tableau-like analytic proof system devised to be used both as a refutation method and a direct method of proof--- that is the classical core of KEM which is thus enlarged with suitable elimination rules for the conditional connective. The resulting algorithmic framework is able to compute cumulative consequence relations in so far as they can be expressed as conditional implications.

We study how a logic C+J conbining classical logic C and intuitionistic logic J can be defined. We show that its Hilbert axiomatization cannot be attained by simply extending the union of the axiomatizations of C and J by so called interaction axioms. Such a logic would collapse into classical logic.

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. We point out a simple but hitherto ignored link between the theory of updates and counterfactuals and classical modal logic: update is a classical existential modality, counterfactual is a classical universal modality, and the accessibility relations corresponding to these modalities are inverses. The Ramsey Rule (often thought esoteric) is simply an axiomatisation of this inverse relationship. We use this fact to translate between postulates for updates and postulates for counterfactuals. Thus, Katsuno/Mendelzon's postulates U1--U8 are translated into counterfactual postulates C1--C8 (table VII), and many of the familiar counterfactual postulates are translated into postulates for updates (table VIII). Our conclusions are summarised in table V. We also present a syntactic condition which is sufficient to guarantee that a translation from update to counterfactual (or vice versa) is possible. 1. Introduction Background. An intuitive connection between theory change and counterfactuals...

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