Handling exceptions in a knowledge-based system has been considered as an important issue in many domains of applications, such as medical domain. In this paper, we propose several preferential semantics for plausible subsumption to deal with exceptions in description logic-based knowledge bases. Our preferential semantics are defined in the framework of possibility theory, which is an uncertainty theory devoted to the handling of incomplete information. We consider the properties of these semantics and their relationships. Entailment of these plausible subsumption relative to a knowledge base is also considered. We show the close relationship between two of our semantics and the mutually dual preferential semantics given by Britz, Heidema and Meyer. Finally, we show that our semantics for plausible subsumption can be reduced to standard semantics of an expressive description logic. Thus, the problem of plausible subsumption checking under our semantics can be reduced to the problem of subsumption checking under the classical semantics.

We provide two approaches for explaining inconsistency in multi-context systems, where decentralized and heterogeneous system parts interact via nonmonotonic bridge rules. Inconsistencies arise easily in such scenarios, and nonmonotonicity calls for specific methods of inconsistency analysis. Both our approaches characterize inconsistency in terms of involved bridge rules: either by pointing out rules which need to be altered for restoring consistency, or by finding combinations of rules which cause inconsistency. We show duality and modularity properties, give precise complexity characterizations, and provide algorithms for computation using HEX-programs. Our results form a basis for inconsistency management in heterogeneous knowledge integration systems.

This paper introduces a new methodology of revising general KBs in DL-Lite. Two specific revision operators are defined, their properties are investigated and algorithms for computing revisions are developed.

Measuring the inconsistency degree of a knowledge base can help us to deal with inconsistencies. Several inconsistency measures have been given under different multi-valued semantics, including 4-valued semantics, 3-valued semantics, LPm and Quasi Classical semantics. In this paper, we first carefully analyze the relationship between these inconsistency measures by showing that the inconsistency degrees under 4-valued semantics, 3-value semantics, LPm are the same, but different from the one based on Quasi Classical semantics. We then consider the computation of these inconsistency measures and show that computing inconsistency measurement under multi-valued semantics is usually intractable. To tackle this problem, we propose two novel algorithms that respectively encode the problems of computing inconsistency degrees under 4-valued semantics (3-valued semantics, LPm) and under Quasi Classical semantics into the partial Max-SAT problems. We implement these algorithms and do experiments on some benchmark data sets. The preliminary but encouraging experimental results show that our approach is efficient to handle large knowledge bases.

The satisfiability problem for monadic infinite-valued Gödel logic is known to be undecidable. We identify a fragment of this logic extended with strong negation whose satisfiability is not only decidable but it is decidable within classical logic. We use this fragment to formalize the rules of CADIAG-2, a well performing fuzzy expert system assisting in the differential diagnosis in internal medicine. A (classical) satisfiability check of the resulting formulas allowed the detection of some errors in the rules of the system.

We consider positive rules in which the conclusion may contain existentially quantified variables, which makes reasoning tasks (such as Deduction) undecidable. These rules, called "ForallExists-rules," have the same logical form as TGD (tuple-generating dependencies) in databases and as conceptual graph rules. The aim of this paper is to provide a clearer picture of the frontier between decidability and non-decidability of reasoning with these rules. We show that Deduction remains undecidable with a single rule; then we show that none of the known abstract decidable classes is recognizable. Turning our attention to concrete decidable classes, we provide new classes and classify all known classes by inclusion. Finally, we study, in a systematic way, the question "given two decidable sets of rules, is their union decidable?" and provide an answer for all known decidable cases except one.

A lot of mathematical knowledge has been formalized and stored in repositories by now: different mathematical theorems and theories have been taken into consideration and included in mathematical repositories. Applications more distant from pure mathematics, however --- though based on these theories --- often need more detailed knowledge about the underlying theories. In this paper we present an example Mizar formalization from the area of electrical engineering focusing on stability theory which is based on complex analysis. We discuss what kind of special knowledge is necessary here and which amount of this knowledge is included in existing repositories.

Greedy search is commonly used in an attempt to generate solutions quickly at the expense of completeness and optimality. In this work, we consider learning sets of weighted action-selection rules for guiding greedy search with application to automated planning. We make two primary contributions over prior work on learning for greedy search. First, we introduce weighted sets of action-selection rules as a new form of control knowledge for greedy search. Prior work has shown the utility of action-selection rules for greedy search, but has treated the rules as hard constraints, resulting in brittleness. Our weighted rule sets allow multiple rules to vote, helping to improve robustness to noisy rules. Second, we give a new iterative learning algorithm for learning weighted rule sets based on RankBoost, an efficient boosting algorithm for ranking. Each iteration considers the actual performance of the current rule set and directs learning based on the observed search errors. This is in contrast to most prior approaches, which learn control knowledge independently of the search process. Our empirical results have shown significant promise for this approach in a number of domains.

We present in this paper an evolution of a tool from a user interface for a concrete Computer Algebra system for Algebraic Topology (the Kenzo system), to a front-end allowing the interoperability among different sources for computation and deduction. The architecture allows the system not only to interface several systems, but also to make them cooperate in shared calculations.

This paper presents a variation of Apriori algorithm that includes the role of domain expert to guide and speed up the overall knowledge discovery task. Usually, the user is interested in finding relationships between certain attributes instead of the whole dataset. Moreover, he can help the mining algorithm to select the target database which in turn takes less time to find the desired association rules. Variants of the standard Apriori and Interactive Apriori algorithms have been run on artificial datasets. The results show that incorporating user's preference in selection of target attribute helps to search the association rules efficiently both in terms of space and time.