5,645 research outputs found
Reason Maintenance - State of the Art
This paper describes state of the art in reason maintenance with a focus on its future usage in the KiWi project. To give a bigger picture of the field, it also mentions closely related issues such as non-monotonic logic and paraconsistency. The paper is organized as follows: first, two motivating scenarios referring to semantic wikis are presented which are then used to introduce the different reason maintenance techniques
A Calculus for Generating Ground Explanations
Full Paper: Applications II: Mathematical Structures, Explanation Generation, SecurityInternational audienceWe present a modification of the superposition calculus that is meant to generate explanations why a set of clauses is satisfiable. This process is related to abductive reasoning, and the explanations generated are clauses constructed over so-called abductive constants. We prove the correctness and completeness of the calculus in the presence of redundancy elimination rules, and develop a sufficient condition guaranteeing its termination; this sufficient condition is then used to prove that all possible explanations can be generated in finite time for several classes of clause sets, including many of interest to the SMT community. We propose a procedure that generates a set of explanations that should be useful to a human user and conclude by suggesting several extensions to this novel approach
Unique key Horn functions
Given a relational database, a key is a set of attributes such that a value
assignment to this set uniquely determines the values of all other attributes.
The database uniquely defines a pure Horn function , representing the
functional dependencies. If the knowledge of the attribute values in set
determines the value for attribute , then is an implicate
of . If is a key of the database, then is an implicate
of for all attributes .
Keys of small sizes play a crucial role in various problems. We present
structural and complexity results on the set of minimal keys of pure Horn
functions. We characterize Sperner hypergraphs for which there is a unique pure
Horn function with the given hypergraph as the set of minimal keys.
Furthermore, we show that recognizing such hypergraphs is co-NP-complete
already when every hyperedge has size two. On the positive side, we identify
several classes of graphs for which the recognition problem can be decided in
polynomial time.
We also present an algorithm that generates the minimal keys of a pure Horn
function with polynomial delay. By establishing a connection between keys and
target sets, our approach can be used to generate all minimal target sets with
polynomial delay when the thresholds are bounded by a constant. As a byproduct,
our proof shows that the Minimum Key problem is at least as hard as the Minimum
Target Set Selection problem with bounded thresholds.Comment: 12 pages, 5 figure
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