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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 132 (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 ...
Stable Models and NonDeterminism in Logic Programs with Negation
, 1990
"... Previous researchers have proposed generalizations of Horn clause logic to support negation and nondeterminism as two seperate extensions. In this paper, we show that the stable model semantics for logic programs provides a unified basis for the treatment of both concepts. First, we introduce the c ..."
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Cited by 131 (31 self)
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Previous researchers have proposed generalizations of Horn clause logic to support negation and nondeterminism as two seperate extensions. In this paper, we show that the stable model semantics for logic programs provides a unified basis for the treatment of both concepts. First, we introduce the concepts of partial models, stable modds, strongly founded models and deterministic models and other interesting classes of partial models and study their relationships. We show that the maximal deterministic model of a program is a subset of the intersection of all its stable models and that the wellfounded model of a program is a subset of its maximal deterministic model. Then, we show that the use of stable models subsumes the use of the nondeterministic choice construct in LDL and provides an alternative definition of the semantics of this construct. Finally, we provide a constructive definition for stable models with the introduction of a procedure, called backtracking fixpoint, that noneteterminisfically constructs a total stable model, if such a model exists.
NonDeterminism in Deductive Databases
 In Proc. 2nd Int. Conf. on Deductive and ObjectOriented Databases
, 1991
"... This paper examines the problem of adding nondeterministic constructs to a declarative database language based on Horn Clause Logic. We revise a previously proposed approach, the choice construct introduced by Krishnamurthy and Naqvi, from the viewpoints of amenability to efficient implementation a ..."
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Cited by 42 (22 self)
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This paper examines the problem of adding nondeterministic constructs to a declarative database language based on Horn Clause Logic. We revise a previously proposed approach, the choice construct introduced by Krishnamurthy and Naqvi, from the viewpoints of amenability to efficient implementation and expressive power.
Fixpoint Logics, Relational Machines, and Computational Complexity
 In Structure and Complexity
, 1993
"... We establish a general connection between fixpoint logic and complexity. On one side, we have fixpoint logic, parameterized by the choices of 1storder operators (inflationary or noninflationary) and iteration constructs (deterministic, nondeterministic, or alternating). On the other side, we have t ..."
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Cited by 38 (5 self)
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We establish a general connection between fixpoint logic and complexity. On one side, we have fixpoint logic, parameterized by the choices of 1storder operators (inflationary or noninflationary) and iteration constructs (deterministic, nondeterministic, or alternating). On the other side, we have the complexity classes between P and EXPTIME. Our parameterized fixpoint logics capture the complexity classes P, NP, PSPACE, and EXPTIME, but equality is achieved only over ordered structures. There is, however, an inherent mismatch between complexity and logic  while computational devices work on encodings of problems, logic is applied directly to the underlying mathematical structures. To overcome this mismatch, we develop a theory of relational complexity, which bridges tha gap between standard complexity and fixpoint logic. On one hand, we show that questions about containments among standard complexity classes can be translated to questions about containments among relational complex...
A NestedGraph Model for the Representation and Manipulation of Complex Objects
 ACM Transactions on Information Systems
, 1994
"... this paper we report upon a graphbased approach to such an integration. Our use of graphs has two key advantages : firstly, graphs are formally defined, wellunderstood structures; secondly, it is widely accepted that graphbased formalisms considerably enhance the usability of complex systems [19] ..."
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Cited by 37 (4 self)
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this paper we report upon a graphbased approach to such an integration. Our use of graphs has two key advantages : firstly, graphs are formally defined, wellunderstood structures; secondly, it is widely accepted that graphbased formalisms considerably enhance the usability of complex systems [19]. Graphs have been used in conjunction with a number of conventional data models, for example the hierarchical and network models [35], the entityrelationship model [9] and a recent extension thereof for complex objects [27], and various semantic data models [16, 20, 31]. Graphs or hypergraphs [6] have also been used more recently in [12, 17, 23, 25, 33, 36] as a data modelling tool in their own right. We give a comparison between this recent work and our own approach in Section 4 of the paper. Directed graphs have also been the foundation of Hypertext databases [11, 33]. Such databases are graphs consisting of nodes which refer to units of stored information (typically text) and of named links. Each link connects two nodes, the "source" and the "destination". Links are traversed either forwards (from source to destination) or backwards (from destination to source). The process of traversing named links and examining the text associated with nodes is called
Bounded Fixpoints for Complex Objects
, 1997
"... We study a query language for complexobject databases, which is designed to (1) express only tractable queries, and (2) be as expressive over flat relations as firstorder logic with fixpoints. The language is obtained by extending the nested relational algebra, NRA, with a "bounded fixpoint&q ..."
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Cited by 33 (9 self)
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We study a query language for complexobject databases, which is designed to (1) express only tractable queries, and (2) be as expressive over flat relations as firstorder logic with fixpoints. The language is obtained by extending the nested relational algebra, NRA, with a "bounded fixpoint" operator. Similar to results for flat relations, all tractable queries over ordered databases are expressible in this language. The main result consists in proving that this language is a conservative extension of the firstorder logic with fixpoints, or of the whilequeries (depending on the interpretation of the bounded fixpoint: inflationary or partial). That is, a query from flat relations to flat relations is expressible in our language if and only if it is expressible in firstorder logic with fixpoints, or in the whilequeries respectively. The proof technique for this theorem uses indexes to encode complex objects into flat relations. It can serve as basis for an implementation method of ...
The Expressiveness of a Family of Finite Set Languages
 IN PROCEEDINGS OF 10TH ACM SYMPOSIUM ON PRINCIPLES OF DATABASE SYSTEMS
, 1991
"... In this paper we characterise exactly the complexity of a set based database language called SRL, which presents a unified framework for queries and updates. By imposing simple syntactic restrictions on it, we are able to express exactly the classes, P and LOGSPACE. We also discuss the role of orde ..."
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Cited by 28 (3 self)
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In this paper we characterise exactly the complexity of a set based database language called SRL, which presents a unified framework for queries and updates. By imposing simple syntactic restrictions on it, we are able to express exactly the classes, P and LOGSPACE. We also discuss the role of ordering in database query languages and show that the hom operator of Machiavelli language in [OBB89] does not capture all the orderindependent properties.
Tractable Query Languages for Complex Object Databases
, 1995
"... The expressiveness and complexity of several calculusbased query languages for complex objects is considered. Unlike previous investigations, we are concerned with the complexity of queries on databases of complex objects, rather than flat databases. This raises new issues specific to complex objec ..."
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Cited by 24 (4 self)
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The expressiveness and complexity of several calculusbased query languages for complex objects is considered. Unlike previous investigations, we are concerned with the complexity of queries on databases of complex objects, rather than flat databases. This raises new issues specific to complex objects. For instance, it is shown that the way the database makes use of its higherorder types has direct impact on query complexity. The use of fixpoint operators is shown to yield languages wellbehaved with respect to complexity and expressiveness. In particular, an extension of the fixpoint queries to complex objects is shown to express precisely the PTIME queries, under the assumption that the database makes "full" use of all its types. Similar results involve rangerestricted queries. 1 Introduction Complex objects are increasingly part of advanced database systems. They provide the structural core of objectoriented databases. Several query languages for complex objects have been propo...
Local Normal Forms for FirstOrder Logic with Applications to Games and Automata
 DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 1998
"... ..."
Higher Order Logic
 In Handbook of Logic in Artificial Intelligence and Logic Programming
, 1994
"... Contents 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2 The expressive power of second order Logic : : : : : : : : : : : 3 2.1 The language of second order logic : : : : : : : : : : : : : 3 2.2 Expressing size : : : : : : : : : : : : : : : : : : : : : : : : 4 2.3 Definin ..."
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Cited by 19 (0 self)
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Contents 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2 The expressive power of second order Logic : : : : : : : : : : : 3 2.1 The language of second order logic : : : : : : : : : : : : : 3 2.2 Expressing size : : : : : : : : : : : : : : : : : : : : : : : : 4 2.3 Defining data types : : : : : : : : : : : : : : : : : : : : : 6 2.4 Describing processes : : : : : : : : : : : : : : : : : : : : : 8 2.5 Expressing convergence using second order validity : : : : : : : : : : : : : : : : : : : : : : : : : 9 2.6 Truth definitions: the analytical hierarchy : : : : : : : : 10 2.7 Inductive definitions : : : : : : : : : : : : : : : : : : : : : 13 3 Canonical semantics of higher order logic : : : : : : : : : : : : 15 3.1 Tarskian semantics of second order logic : : : : : : : : : 15 3.2 Function and re