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: Katsuno and Mendelzon divide theory change, the problem of adding new information to a logical theory, into two types: revision and update. We propose a third type of theory change: arbitration. The key idea is the following: the new information is considered neither better nor worse than the old information represented by the logical theory. The new information is simply one voice against a set of others already incorporated into the logical theory. From this follows that arbitration should be commutative. First we define arbitration by a set of postulates and then describe a model-theoretic characterization of arbitration for the case of propositional logical theories. We also study weighted arbitration where different models of a theory can have different weights. 1 Introduction The problem of updating logical theories is a common fundamental concern to databases, to Artificial Intelligence [McC68, Rei92], and to belief revision [Mak85, Gar88]. It is well-known that giving semant...

This paper describes a new object-oriented model and query algebra that will be used as an input language for the query optimizers that are being built as a part of the EREQ project. The model adopts a uniform view of objects and values and separates syntactic, semantic, and implementation concerns. The algebra addresses issues of type-defined equality and duplicate elimination as well as extensions to bulk types other than sets. 1 Introduction Recently, a great deal of work has been done on the topic of object-oriented query algebras [27, 22, 11] and the modeling of bulk types [4, 25, 19]. These proposals as well as those of other researchers on the topic have explored some of the fundamental issues and provided the starting point for the work reported here. AQUA (A QUery Algebra) is the result of a joint effort among researchers who have participated in the design of previous algebras [26, 30, 31]. AQUA has been designed to address a number of detailed modeling issues that we beli...

We establish a general connection between fixpoint logic and complexity. On one side, we have fixpoint logic, parameterized by the choices of 1st-order 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...

Stable models have been first introduced in the domain of total interpretations (T- stable models), where the existence of multiple T-stable models for the same program provides a powerful mechanism to express non-determinism. Stable models have been later extended to the domain of partial interpretations (P-stable models). In this paper, we show that the presence of multiple P-stable models need not be a direct manifestation of non-determinism, for it can be instead an expression of assorted degrees of undefinedness. To separate the two factors, non-determinism and undefinedness, this paper introduces the notion of deterministic stable models and strictly non-deterministic ones. Deterministic stable models form an interesting family, having a lattice structure where the well-founded model serves as the bottom; the top of the lattice, the maximum deterministic stable model, resolves differences between any two P-stable models in the family. On the other hand, every two models in a fam...

The expressiveness and complexity of several calculus-based 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 higher-order types has direct impact on query complexity. The use of fixpoint operators is shown to yield languages well-behaved 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 range-restricted queries. 1 Introduction Complex objects are increasingly part of advanced database systems. They provide the structural core of object-oriented databases. Several query languages for complex objects have been propo...

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This paper provides an overview of recent results on this topic with the aim of providing an introduction to the theory and practice of non-determinism in deductive databases. In particular we (i) recall the main results linking non-deterministic constructs in database languages to the theory of data complexity and the expressibility hierarchy of query languages (ii) provide a reasoned introduction to effective programming with nondeterministic constructs (iii) compare the usage of non-deterministic constructs in languages such as

This paper introduces a unified solution to the problem of extending stratified DATALOG to express DB-complexity classes ranging from P to D^P. The solution...

Data Types New base types can be added to the EXTRA data model via the EXTRA abstract data type facility. To add a new ADT, the person responsible for adding the type begins by writing (and debugging) the code for the type in the E programming language. E is an extension of C++ [Stro86] that was developed as part of the EXODUS project. E serves as the implementation language for access methods and operators for systems developed using EXODUS. It is also the target language for the query compiler, and (most importantly for our purposes here) the language in which base type extensions will be defined. E extends C++ with a number of features to aid programmers in data- 89 base system programming, including "dbclasses" for persistent storage, class generators for implementing "generic" classes and functions, iterators for use as a control abstraction in writing set operations, and built-in class generators for typed files and variable-length arrays [Rich87]. Suppose that we wanted to add...