Herman Balsters

Learnability with respect to fixed distributions

Benedek, G.M., and A. Itai, Learnability with respect to fixed distributions (Note), Theoretical Computer Science 86 (1991) 377-389. Valiant’s protocol for learning is extended to the case where the distribution of the examples is known to the learner. Namely, the notion of a concept class C being learnable with respect to distribution D is defined and the learnable pairs (C, D) of concept classes C and distributions D are characterized. Another notion is the existence of a finite cover for C with respect to D. The main result is that C is learnable with respect to D if and only if C is finitely coverable with respect to D. The size of the cover is then related to the Vapnik-Chervonenkis dimension. An additional property of the learning method is robustness, i.e., learning succeeds even if part of the input is erroneous. It is also shown that if D is discrete then every concept class is learnable with respect to D. The main concern of the paper is the number of examples sufficient to probabilistically identify (or approximate) a concept-not the time needed to compute it. Indeed, in some cases the function which associates a sample with a hypothesis is undecidable, and even if it is computable, the computation may be infeasible. The computational complexity of the algorithms used for learning are considered only for discrete distributions.

Modeling dynamic rules in ORM

This paper proposes an extension to the Object-Role Modeling approach to support formal declaration of dynamic rules Dynamic rules differ from static rules by pertaining to properties of state transitions, rather than to the states themselves In this paper, application of dynamic rules is restricted to so-called single-step transactions, with an old state (the input of the transaction) and a new state (the direct result of that transaction) Such restricted rules are easier to formulate (and enforce) than a constraint applying historically over all possible states In our approach, dynamic rules specify an elementary transaction type indicating which kind of object or fact is being added, deleted or updated, and (optionally) pre-conditions relevant to the transaction, followed by a condition stating the properties of the new state, including the relation between the new state and the old state These dynamic rules are formulated in a syntax designed to be easily validated by non-technical domain experts.

Automatic Verification of Transactions on an Object-Oriented Database

In the context of the object-oriented data model, a compiletime approach is given that provides for a significant reduction of the amount of run-time transaction overhead due to integrity constraint checking. The higher-order logic Isabelle theorem prover is used to automatically prove which constraints might, or might not be violated by a given transaction in a manner analogous to the one used by Sheard and Stemple (1989) for the relational data model. A prototype transaction verification tool has been implemented, which automates the semantic mappings and generates proof goals for Isabelle. Test results are discussed to illustrate the effectiveness of our approach.

Database Schema Evolution and Meta-Modeling

For adequately specifying and rapid-prototyping concurrent information systems, we proposed in [AS99] a new form of object oriented (OO) Petri nets. Referred to as Co-nets, this approach allows in particular to conceive such systems as complex autonomous yet cooperating components. Moreover, for coping with intrinsic dynamic evolution in such systems, we have straightforwardly extended this proposal by introducing notions of meta-places, non-instantiated transitions and a two-step evaluated inference rule [Aou00]. The purpose of this paper is to tackle with another crucial dimension characterizing real-world information systems, namely static and dynamic integrity constraints. For this aim, we propose to associate with each component a ‘constraints’ class. To enforce such constraints, we propose an appropriate ‘synchronization’ inference rule that semantically relates ‘constraints’ transitions with intrinsically dependent ones in the associated component. For a more flexible consistency management we enrich this first proposal by an adequate meta-level, where constraints may be dynamically created, modified or deleted. Finally, we show how this proposal covers a large number of constraint subclasses, including life-cycle based constraints and constraints based on complex derived information as view classes.

Formal Semantics of Dynamic Rules in ORM

This paper provides formal semantics for an extension of the Object-Role Modeling approach that supports declaration of dynamic rules. Dynamic rules differ from static rules by pertaining to properties of state transitions, rather than to the states themselves. In this paper we restrict application of dynamic rules to so-called single-step transactions, with an old state (the input of the transaction) and a new state (the direct result of that transaction). These dynamic rules further specify an elementary transaction type by indicating which kind of object or fact (being added, deleted or updated) is actually allowed. Dynamic rules may declare pre-conditions relevant to the transaction, and a condition stating the properties of the new state, including the relation between the new state and the old state. In this paper we provide such dynamic rules with a formal semantics based on sorted, first-order predicate logic. The key idea to our solution is the formalization of dynamic constraints as static constraints on the database transaction history.

A Deductive and Typed Object-Oriented Language

In this paper we introduce a logical query language extended with object-oriented typing facilities. This language, called DTL (from DataTypeLog), can be seen as an extension of Datalog equipped with complex objects, object identities, and multiple inheritance based on Cardelli type theory. The language also incorporates a very general notion of sets as first-class objects. The paper offers a formal description of DTL, as well as a denotational semantics for DTL programs.

Integration of integrity constraints in federated schemata based on tight constraining

A database federation provides for tight coupling of a collection of heterogeneous legacy databases into a global integrated system. A large problem regarding information quality in database federations concerns achieving and maintaining consistency of the data on the global level of the federation. Integrity constraints are an essential part of any database schema and are aimed at maintaining data consistency in an arbitrary database state. Data inconsistency problems in database federations resulting from the integration of integrity constraints can basically occur in two situations. The first situation pertains to the integration of existing local integrity constraints occurring within component legacy databases into a single global federated schema, whereas the second situation pertains to the introduction of newly-defined additional integrity constraints on the global level of the federation. These situations gives rise to problems in so-called global and local understandability of updates in database federations. We shall describe a semantic framework for specification of federated database schemas based on the UML/OCL data model; UML/OCL will be shown to provide a high-level, coherent, and precise framework in which to specify and analyze integrity constraints in database federations. This paper will tackle the problem of global and local understandability by introducing a new algorithm describing the integration of integrity constraints occurring in local databases. Our algorithm is based on the principle of tight constraining; i.e., integration of local integrity constraints into a single global federated schema takes place without any loss of constraint information. Our algorithm will improve existing algorithms in three aspects: it offers a considerable reduction in complexity; it applies to a larger category of local integrity constraints; and it will result in a global federated schema with a clear maintenance strategy for update operations.

Modeling data federations in ORM

Two major problems in constructing data federations (for example, data warehouses and database federations) concern achieving and maintaining consistency and a uniform representation of the data on the global level of the federation. The first step in creating uniform representations of data is known as data extraction, whereas data reconciliation is concerned with resolving data inconsistencies. Our approach to constructing a global conceptual schema as the result of integrating a collection of (semantically) heterogeneous component schemas is based on the concept of exact views. We show that a global schema constructed in terms of exact views integrates component schemas in such a way that the global schema is populated by exactly those instances allowed by the local schemas (and in special cases, also the other way around). In this sense, the global schema is equivalent to the set of component schemas from which the global schema is derived. This paper describes a modeling framework for data federations based on the Object-Role Modeling (ORM) approach. In particular, we show that we can represent exact views within ORM, providing the means to resolve in a combined setting data extraction and reconciliation problems on the global level of the federation.

An ORM-Driven Implementation Framework for Database Federations

Database federations are employed more and more in situations involving virtual and integrated information on demand, e.g., real-time integration of two databases. Heterogeneity in hardware and software platforms, as well heterogeneity in underlying semantics of participating local databases, makes it a hard challenge to design a consistent and well-performing global database federation. The ORM modeling framework allows not only for precise modeling of a data federation, but also hosts tools for reverse engineering, enabling local databases to recapture their intended meanings on a linguistic basis. We will demonstrate how ORM models together with reverse engineering techniques can be used in combination with actual, industrial-strength implementation platforms to develop semantically consistent and high performance database federations.

An object-oriented framework for reconciliation and extraction in heterogeneous data federations

Two major problems in constructing database federations concern achieving and maintaining consistency and a uniform representation of the data on the global level of the federation. The process of creation of uniform representations of data is known as data extraction, whereas data reconciliation is concerned with resolving data inconsistencies. Our approach to constructing a global, integrated system from a collection of (semantically) heterogeneous component databases is based on the concept of exact view. We will show that a global database constructed by exact views integrates component schemas without loss of constraint information. We shall describe a semantic framework for specification of database federations based on the UML/OCL data model. In particular, we will show that we can represent exact views by so-called derived classes in UML/OCL, providing the means to resolve in a combined setting data extraction and reconciliation problems on the global level of the federation.