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13
Principles of Programming with Complex Objects and Collection Types
 Theoretical Computer Science
, 1995
"... We present a new principle for the development of database query languages that the primitive operations should be organized around types. Viewing a relational database as consisting of sets of records, this principle dictates that we should investigate separately operations for records and sets. Th ..."
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Cited by 130 (28 self)
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We present a new principle for the development of database query languages that the primitive operations should be organized around types. Viewing a relational database as consisting of sets of records, this principle dictates that we should investigate separately operations for records and sets. There are two immediate advantages of this approach, which is partly inspired by basic ideas from category theory. First, it provides a language for structures in which record and set types may be freely combined: nested relations or complex objects. Second, the fundamental operations for sets are closely related to those for other "collection types" such as bags or lists, and this suggests how database languages may be uniformly extended to these new types. The most general operation on sets, that of structural recursion, is one in which not all programs are welldefined. In looking for limited forms of this operation that always give rise to welldefined operations, we find a number of close ...
An Extended Algebra for Constraint Databases
 IEEE Transactions on Knowledge and Data Engineering
, 1999
"... Constraint relational databases use constraints to both model and query data. A constraint relation contains a finite set of generalized tuples. Each generalized tuple is represented by a conjunction of constraints on a given logical theory and, depending on the logical theory and the specific conju ..."
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Cited by 20 (3 self)
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Constraint relational databases use constraints to both model and query data. A constraint relation contains a finite set of generalized tuples. Each generalized tuple is represented by a conjunction of constraints on a given logical theory and, depending on the logical theory and the specific conjunction of constraints, it may possibly represent an infinite set of relational tuples. For their characteristics, constraint databases are well suited to model multidimensional and structured data, like spatial and temporal data. The definition of an algebra for constraint relational databases is important in order to make constraint databases a practical technology. In this paper, we extend the previously defined constraint algebra (called generalized relational algebra). First, we show that the relational model is not the only possible semantic reference model for constraint relational databases and we show how constraint relations can be interpreted under the nested relational model. Then...
Constructibility and Decidability versus Domain Independence and Absoluteness
"... We develop a unified framework for dealing with constructibility and absoluteness in set theory, decidability of relations in effective structures (like the natural numbers), and domain independence of queries in database theory. Our framework and results suggest that domainindependence and absolut ..."
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Cited by 4 (2 self)
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We develop a unified framework for dealing with constructibility and absoluteness in set theory, decidability of relations in effective structures (like the natural numbers), and domain independence of queries in database theory. Our framework and results suggest that domainindependence and absoluteness might be the key notions in a general theory of constructibility, predicativity, and computability. 1
Safety Signatures for Firstorder Languages and Their Applications
 In FirstOrder Logic Revisited (Hendricks et all,, eds.), 3758, Logos Verlag
, 2004
"... ..."
Safety and Domain Independence in Relational and Web Query Languages, and in Set Theory
"... We show that there have been common ideas concerning important properties of formulas which were independently developed in the research on query languages and in the mathematical discipline of set theory: safety versus limitation of size, domainindependent versus absoluteness. For each of these pa ..."
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We show that there have been common ideas concerning important properties of formulas which were independently developed in the research on query languages and in the mathematical discipline of set theory: safety versus limitation of size, domainindependent versus absoluteness. For each of these pairs we provide common generalizations and show that they are useful for both theories. In the database case they provide obvious improvements of usual syntactically characterized classes of reasonable queries. Apart from significantly enlarging those classes, they provide a firm theoretical foundation for using in queries complex terms as well as relations which do not belong to the database scheme, or relations that are not completely given, but only partially accessible through links (like in the world wide web). On the other hand a completely new understanding of the axioms of the axiomatic set theory ZF is gained by looking at ZF from the perspective of relational databases.
Institute for Research in Cognitive Science Parallel Programming Languages for Collections Ph.D. Dissertation
, 1995
"... by ..."
Founded by Benjamin Franklin in 1740
, 1995
"... We investigate queries in the presence of external functions with arbitrary inputs and outputs (atomic values, sets, nested sets etc). We propose a new notion of domain independence for queries with external functions which, in contrast to previous work, can also be applied to query languages with x ..."
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We investigate queries in the presence of external functions with arbitrary inputs and outputs (atomic values, sets, nested sets etc). We propose a new notion of domain independence for queries with external functions which, in contrast to previous work, can also be applied to query languages with xpoints or other kinds of iterators. Next, we de ne two new notions of computable queries with external functions, and prove that they are equivalent, under the assumption that the external functions are total. Thus, our de nition of computable queries with external functions is robust. Finally, based on the equivalence result, we giveexamples of complete query languages with external functions. A byproduct of the equivalence result is the fact that Relational Machines are complete for complex objects: it was known that they are not complete over at relations. 1
Modeling and Language Support for the Management of
 in: Proceedings of the 16th International Conference on Scientific and Statistical Database Management (SSDBM’04), IEEE Computer Society
, 2004
"... In our days knowledge extraction methods are able to produce artifacts (also called patterns) that concisely represent data. Patterns are usually quite heterogeneous and require adhoc processing techniques. So far, little emphasis has been posed on developing an overall integrated environment for u ..."
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In our days knowledge extraction methods are able to produce artifacts (also called patterns) that concisely represent data. Patterns are usually quite heterogeneous and require adhoc processing techniques. So far, little emphasis has been posed on developing an overall integrated environment for uniformly representing and querying different types of patterns. Within the larger context of modelling, storing, and querying patterns, in this paper, we: (a) formally define the logical foundations for the global setting of pattern management through a model that covers data, patterns and their intermediate mappings; (b) present a pattern specification language for pattern management along with safety restrictions; and (c) introduce queries and query operators and identify interesting query classes.
Modeling and Language Support for the Management of PatternBases ⋆
"... Information overloading is today a serious concern that may hinder the potential of modern webbased information systems. A promising approach to deal with this problem is represented by knowledge extraction methods able to produce artifacts (also called patterns) that concisely represent data. Patt ..."
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Information overloading is today a serious concern that may hinder the potential of modern webbased information systems. A promising approach to deal with this problem is represented by knowledge extraction methods able to produce artifacts (also called patterns) that concisely represent data. Patterns are usually quite heterogeneous and voluminous. So far, little emphasis has been posed on developing an overall integrated environment for uniformly representing and querying different types of patterns. In this paper we consider the larger problem of modelling, storing, and querying patterns, in a databaselike setting and use a PatternBase Management System (PBMS) for this purpose. Specifically, (a) we formally define the logical foundations for the global setting of pattern management through a model that covers data, patterns, and their intermediate mappings; (b) we present a formalism for pattern specification along with safety restrictions; and (c) we introduce predicates for comparing patterns and query operators.
Safety of Formulas in Query Languages, in Arithmetics, and in Set Theory
"... We show that there have been common ideas concerning important properties of formulas which were independently developed in the research on query languages and in some basic mathematical theories, like set theory and formal number theory: finiteness versus limitation of size, effectiveness versus sa ..."
Abstract
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We show that there have been common ideas concerning important properties of formulas which were independently developed in the research on query languages and in some basic mathematical theories, like set theory and formal number theory: finiteness versus limitation of size, effectiveness versus safety, domainindependence versus absoluteness. We provide common generalizations in each case, and show that they are useful for both disciplines. In the database case they provide obvious improvements of usual syntactically characterized classes of reasonable queries. Apart from significantly enlarging those classes, they provide a firm theoretical basis for using in queries relations that are not completely given, but only partially accessible through links (like in the world wide web). In formal number theory our concepts lead to a new, simple characterization of the class of primitive recursive formulas. In set theory we show that the various comprehension axioms of ZF can be replaced by a single comprehension principle, which only allows the use of the syntactically defined class of "safe" formulas.