A logic is defined that allows to express information about statistical probabilities and about degrees of belief in specific propositions. By interpreting the two types of probabilities in one common probability space, the semantics given are well suited to model the in uence of statistical information on the formation of subjective beliefs. Cross entropy minimization is a key element in these semantics, the use of which is justified by showing that the resulting logic exhibits some very reasonable properties.

Irrelevance reasoning refers to the process in which a system reasons about which parts of its knowledge are relevant (or irrelevant) to a specific query. Aside from its importance in speeding up inferences from large knowledge bases, relevance reasoning is crucial in advanced applications such as modeling complex physical devices and information gathering in distributed heterogeneous systems. This article presents a novel framework for studying the various kinds of irrelevance that arise in inference and efficient algorithms for relevance reasoning. We present a

Motivated by problems that arise in computing degrees of belief, we consider the problem of computing asymptotic conditional probabilities for first-order sentences. Given first-order sentences ' and `, we consider the structures with domain f1; : : : ; Ng that satisfy `, and compute the fraction of them in which ' is true. We then consider what happens to this fraction as N gets large. This extends the work on 0-1 laws that considers the limiting probability of first-order sentences, by considering asymptotic conditional probabilities. As shown by Liogon'kii [Lio69], if there is a non-unary predicate symbol in the vocabulary, asymptotic conditional probabilities do not always exist. We extend this result to show that asymptotic conditional probabilities do not always exist for any reasonable notion of limit. Liogon'kii also showed that the problem of deciding whether the limit exists is undecidable. We analyze the complexity of three problems with respect to this limit: deciding whether it is well-defined, whether it exists, and whether it lies in some nontrivial interval. Matching upper and lower bounds are given for all three problems, showing them to be highly undecidable.

At present, the search for specific information on the World Wide Web is faced with several problems, which arise on the one hand from the vast number of information sources available, and on the other hand from their intrinsic heterogeneity, since standards are missing. A promising approach for solving the complex problems emerging in this context is the use of multi-agent systems of information agents, which cooperatively solve advanced information-retrieval problems. This requires advanced capabilities to address complex tasks, such as search and assessment of information sources, query planning, information merging and fusion, dealing with incomplete information, and handling of inconsistency. In this paper, our interest lies in the role which some methods from the field of declarative logic programming can play in the realization of reasoning capabilities for information agents. In particular, we are interested to see in how they can be used, extended, and further developed for the specific needs of this application domain. We review some existing systems and current projects, which typically address information-integration problems. We then focus on declarative knowledge-representation methods, and review and evaluate approaches and methods from logic programming and nonmonotonic reasoning for information agents. We discuss advantages and drawbacks, and point out the possible extensions and open issues. 1

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Many applications of knowledge discovery and data mining such as rule discovery for semantic query optimization, database integration and decision support, require the knowledge to be consistent with data. However, databases usually change over time and makemachine-discovered knowledge inconsistent. Useful knowledge should be robust against database changessothatitisunlikely to become inconsistentafter database changes. This paper defines this notion of robustness in the context of relational databases that contain multiple relations and describes how robustness of first-order Horn-clause rules can be estimated and applied in knowledge discovery.Our experiments show that the estimation approach can accurately predict the robustness of a rule.

We consider a reinterpretation of the rules of default logic. We make Reiter's default rules into a constructive method of building models, not theories. To allow reasoning in first order systems, we equip standard first-order logic with a (new) Kleene 3-valued partial model semantics. Then, using our methodology, we add defaults to this semantic system. The result is that our logic is an ordinary monotonic one, but its semantics is now nonmonotonic. Reiter's extensions now appear in the semantics, not in the syntax. As an application, we show that this semantics gives a partial solution to the conceptual problems with open defaults pointed out by Lifschitz [16], and Baader and Hollunder [2]. The solution is not complete, chiefly because in making the defaults model-theoretic, we can only add conjunctive information to our models. This is in contrast to default theories, where extensions can contain disjunctive formulas, and therefore disjunctive information. Our proposal to treat ...

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Abstract. We present a powerful quasi-probabilistic default formalism for graded defaults based on a well-motivated canonical ranking construction procedure, System JLZ. It implements the minimal construction paradigm and verifies the major inference principles and inheritance desiderata, including rational monotony for propositions and structured cumulativity for default conditionals. With help from a structured ranking semantics for defaults, it also avoids some drawbacks of semi-qualitative entropy maximization and other competing accounts. 1

Abstract. Statistical Default Logic (SDL) is an expansion of classical (i.e., Reiter) default logic that allows us to model common inference patterns found in standard inferential statistics, e.g., hypothesis testing and the estimation of a population‘s mean, variance and proportions. This paper presents an embedding of an important subset of SDL theories, called literal statistical default theories, into stable model semantics. The embedding is designed to compute the signature set of literals that uniquely distinguishes each extension on a statistical default theory at a pre-assigned error-bound probability. 1