New Closure Operators and Lattice Representations for Multivalued Dependencies and Related Expressions

In Database Theory, Multivalued Dependencies are the main tool to define the Fourth Normal Form and, as such, their inference problem has been deeply studied; two related notions appearing in that study are a syntactical analog in propositional logic and a restriction that maintains to this logic the same relationship as Functional Dependencies do to Horn logic. We present semantic, lattice-theoretic characterizations of such multivalued dependencies that hold in a given relation, as well as similar results for the related notions just mentioned. Our characterizations explain better some previously known facts by providing a unifying framework that is also consistent with the studies of Functional Dependencies.Postprint (published version

Zero-one laws with respect to models of provability logic and two Grzegorczyk logics

It has been shown in the late 1960s that each formula of first-order logic without constants and function symbols obeys a zero-one law: As the number of elements of finite models increases, every formula holds either in almost all or in almost no models of that size. Therefore, many properties of models, such as having an even number of elements, cannot be expressed in the language of first-order logic. Halpern and Kapron proved zero-one laws for classes of models corresponding to the modal logics K, T, S4, and S5 and for frames corresponding to S4 and S5. In this paper, we prove zero-one laws for provability logic and its two siblings Grzegorczyk logic and weak Grzegorczyk logic, with respect to model validity. Moreover, we axiomatize validity in almost all relevant finite models, leading to three different axiom systems

DATA CONSTRUCTORS: ON THE INTEGRATION OF RULES AND RELATIONS

Although the goals and means of rule-based and data-based systems are too different to be fully integrated at the present time, it seems appropriate to investigate a closer integration of language constructs and a better cooperation of execution models for both kinds of approaches. In this paper, we propose a new language construct called constructor that â when applied to a base relation â causes relation membership to become true for all tuples constructable through the predicates provided by the constructor definition. The approach is shown to provide expressive power at least equivalent to PROLOG's declarative semantics while blending well both with a strongly typed modular programming language and with a relational calculus query formalism. A three-step compilation, optimization, and evaluation methodology for expressions with constructed relations is described that integrates constructors with the surrounding database programming environment. In particular, many recursive queries can be evaluated more efficiently within the set-construction framework of database systems than with proof-oriented methods typical for a rule-based approach.Information Systems Working Papers Serie

Similarity measures over refinement graphs

Similarity also plays a crucial role in support vector machines. Similarity assessment plays a key role in lazy learning methods such as k-nearest neighbor or case-based reasoning. In this paper we will show how refinement graphs, that were originally introduced for inductive learning, can be employed to assess and reason about similarity. We will define and analyze two similarity measures, S λ and S π, based on refinement graphs. The anti-unification-based similarity, S λ, assesses similarity by finding the anti-unification of two instances, which is a description capturing all the information common to these two instances. The property-based similarity, S π, is based on a process of disintegrating the instances into a set of properties, and then analyzing these property sets. Moreover these similarity measures are applicable to any representation language for which a refinement graph that satisfies the requirements we identify can be defined. Specifically, we present a refinement graph for feature terms, in which several languages of increasing expressiveness can be defined. The similarity measures are empirically evaluated on relational data sets belonging to languages of different expressiveness. © 2011 The Author(s).Support for this work came from the project Next-CBR TIN2009-13692-C03-01 (co-sponsored by EU FEDER funds)Peer Reviewe