We propose a novel formalism, called Frame Logic (abbr., F-logic), that accounts in a clean and declarative fashion for most of the structural aspects of object-oriented and frame-based languages. These features include object identity, complex objects, inheritance, polymorphic types, query methods, encapsulation, and others. In a sense, F-logic stands in the same relationship to the objectoriented paradigm as classical predicate calculus stands to relational programming. F-logic has a model-theoretic semantics and a sound and complete resolution-based proof theory. A small number of fundamental concepts that come from object-oriented programming have direct representation in F-logic; other, secondary aspects of this paradigm are easily modeled as well. The paper also discusses semantic issues pertaining to programming with a deductive object-oriented language based on a subset of F-logic.

We describe a novel logic, called HiLog, and show that it provides a more suitable basis for logic programming than does traditional predicate logic. HiLog has a higher-order syntax and allows arbitrary terms to appear in places where predicates, functions and atomic formulas occur in predicate calculus. But its semantics is first-order and admits a sound and complete proof procedure. Applications of HiLog are discussed, including DCG grammars, higher-order and modular logic programming, and deductive databases.

We propose a database logic which accounts in a clean declarative fashion for most of the “object-oriented” features such as object identity, complex objects, inheritance, methods, etc. Furthermore, database schema is part of the object language, which allows the user to browse schema and data using the same declarative formalism. The proposed logic has a formal semantics and a sound and complete resolution-based proof procedure, which makes it also computationally attractive.

Various models and languages for describing and manipulating hierarchically structured data have been proposed. Algebraic, calculus-based and logic-programming oriented languages have all been considered. This paper presents a general model for complex objects, and languages for it based on the three paradigms. The algebraic language generalizes those presented in the literature; it is shown to be related to the functional style of programming advocated by Backus. The notion of domain independence familiar from relational databases is defined, and syntactic restrictions (referred to as safety conditions) on calculus queries are formulated, that guarantee domain independence. The main results are: The domain-independent calculus, the safe calculus, the algebra, and the logic-programming oriented language have equivalent expressive power. In particular, recursive queries, such as the transitive closure, can be expressed in each of the languages. For this result, the algebra needs the pow...

yosikawaQkyoto-su.ac.jp Abstract: This paper introduces ILOG ( a declarative language in the style of (stratified) datalog ( which can be used for querying, schema translation, and schema augmentation in the context of object-based data models. The semantics of ILOG is based on the use of Skolem functors, and is closely related to semantics for object-based data manipulation languages which provide mechanisms for explicit creation of object identifiers (OIDs). A normal form is presented for ILOG ’ programs not involving recursion through OID creation, which identifies a precise correspondence between OIDs created in the target, and values and OIDs in the source. The expressive power of various sublanguages of ILOG ’ is shown to range from a natural generalization of the conjunctive queries to the object-based context, to a language which can specify all computable database translat.ions (up to duplicate copies). The issue of testing vuliilityof ILOG programs translat.ing one semantic schema to another is studied: cases are presented for which several-validity issues (e.g., functional and/or subset relationships in the

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A language for databases with sets, tuples, lists, object identity and structural inheritance is proposed. The core language is logic-based with a fixpoint semantics. Methods with overloading and methods evaluated externally providing extensibility of the language are considered. Other important issues such as updates and the introduction of explicit control are discussed. 1 INTRODUCTION The success of the relational database model [19, 38, 27] is certainly due to technological advances such as fast query processing or reliable concurrency control. However, we believe that a major factor in that success has been the existence of simple-to-use languages allowing the definition and manipulation of data. This has to be remembered while considering future generations of database systems. Object-oriented database systems are now being developed, e.g., [15, 12, 22, 39, 36]. An object-oriented approach [24] is used to answer the needs of a much wider variety of applications. Most of th...

Bags, i.e. sets with duplicates, are often used to implement relations in database systems. In this paper, we study the expressive power of algebras for manipulating bags. The algebra we present is a simple extension of the nested relation algebra. Our aim is to investigate how the use of bags in the language extends its expressive power, and increases its complexity. We consider two main issues, namely (i) the impact of the depth of bag nesting on the expressive power, and (ii) the complexity and the expressive power induced by the algebraic operations. We show that the bag algebra is more expressive than the nested relation algebra (at all levels of nesting), and that the difference may be subtle. We establish a hierarchy based on the structure of algebra expressions. This hierarchy is shown to be highly related to the properties of the powerset operator. Invited to a special issue of the Journal of Computer and System Sciences selected from ACM Princ. of Database Systems,...

Abstract. Various models and languages for describing and manipulating hierar-chically structured data have been proposed. Algebraic, calculus-based, and logic-programming oriented languages have all been considered. This article presents a general model for complex values (i.e., values with hierarchical structures), and languages for it based on the three paradigms. The algebraic language generalizes those presented in the literature; it is shown to be related to the functional style of programming advocated by Backus (1978). The notion of domain independence (from relational databases) is defined, and syntactic restrictions (referred to as safety conditions) on calculus queries are formulated to guarantee domain inde-pendence. The main results are: The domain-independent calculus, the safe cal-culus, the algebra, and the logic-programming oriented language have equivalent expressive power. In particular, recursive queries, such as the transitive closure, can be expressed in each of the languages. For this result, the algebra needs the powerset operation. A more restricted version of safety is presented, such that the restricted safe calculus is equivalent to the algebra without the powerset. The results are extended to the case where arbitrary functions and predicates are used in the languages. Key Words. Database, query language, complex value, complex object, database model.

The set-height of a complex object type is defined to be its level of nesting of the set construct. In a query of the complex object calculus which maps a database D to an output type T,anintermediate type is a type which is used by some variable of the query, but which is not present in D or T.Foreachk, i ≥ 0 we define CALCk,i to be the family of calculus queries mapping from and to types with set-height ≤ k and using intermediate types with set-height ≤ i. In particular, CALC0,0 is the classical relational calculus, and CALC0,1 is equivalent to the family of secondorder (relational) queries. Several results concerning these families of languages are obtained. A primary focus is on the families CALC0,i, which map relations to relations. Upper and lower bounds in terms of hyper-exponential time and space on the complexity of these families are provided. The CALC0,i hierarchy does not collapse with respect to expressive power. The union ∪0≤iCALC0,i is exactly the family of elementary queries, i.e., queries with hyper-exponential complexity. The expressive power of queries from the complex object calculus interpreted using semantics based on the use of arbitrarily large finite or infinite set of invented values is studied. Under these semantics, the expressive power of the relational calculus is not increased, and the CALC0,i hierarchy collapses at CALC0,1. In general, queries with these semantics may not be computable. We also consider an alternative semantics which yields a family of queries equivalent to the computable queries. 1