Specification and implementation of programs for updating incomplete information databases

Abstract

The problem of updating incomplete infor mation databases is vieweda sap rogramming problem. From this point of view, for mal denotational semantics are developed for twoa pplicativep rogramming languages, BLU and HLU. BLU is a ver y simple language with only fivep rimitives,a nd is designed primar ily as a tool for the implementation of higher-levell anguages.T he semantics of BLU are for mally developed at twol ev els,p ossible wor lds and clausal, and the latter is shown to be a correct implementation of the for mer. HLU is a "user level" update language.I ti s defined entirely in terms of BLU,a nd so immediately inherits its semantic definition from that language.T his demonstrates a levelo fc ompleteness for BLU as a levelo f pr imitives for update language implementation. The necessity of a particular BLU pr imitive, masking, suggests that there is a high degree of inherent complexity in updating logical databases. IntroductionDatabase systems maybeviewedasconsisting of twocomponents.Adatabase schema specifies the general structure of admissible data, and remains constant. Database instances,onthe other hand, record the actual state of the wor ld at a given point in time,and changes upon update.I nthe case of complete infor mation, there is exactly one instance associated with the system at anyg iven point, whereas in the incomplete infor mation case,t here is a collection of alternativei nstances,o rpossible worlds.In the complete infor mation case,t he representation of the system state is a usually a direct one (such as a set of relations in the relational case), although indirect representation is also possible,a si nt he negation as failure, or closed wor ld clausal representation [3].In the case of incomplete infor mation, on the other hand, direct representation is -1-

LIVE: A Lineage-Supported Versioned DBMS

“…The main result of the paper is to the study a set of data models for uncertainty in terms of their expressiveness in representing results of modifications. In other early work, [31] views the data modification problem as a programming language, and maps programs to operations on possible-worlds (e.g., intersections, unions). While the language of [31] is again quite expressive, no query answering or propagation techniques are presented.…”

“…In other early work, [31] views the data modification problem as a programming language, and maps programs to operations on possible-worlds (e.g., intersections, unions). While the language of [31] is again quite expressive, no query answering or propagation techniques are presented. Similarly, [32] considers approaches for modifying incomplete information, but doesn't consider the problems addressed by our paper.…”

Unique complements and decompositions of database schemata

“…Although relatively little of a practical nature has been developed for this framework, its mathematical underpinnings are nonetheless very well understood, being just first-order model theory. Perhaps the major problem plaguing this framework is its extreme generality; it places so few restrictions on what can be represented that most problems, such as the view update problem, are completely intractable [28] [49]. We believe that by understanding what kinds of conditions must be imposed for such a schema to be decomposed, we may begin to see what kind of restrictions should be made to move closer to computational tractability of updates.…”

A model-based approach to updating databases with incomplete information

“…The first variant was proposed by Hegner [13]. Informally, call an atom f of w irrelevant if the choice of truth valuation for f has no effect on whether w is true.…”

“…Recent work by Hegner [13] offers an important variant on the model-based semantics for updates that is used in this paper; his improvement will be described in Section 6. Hegner also offers a different approach to update algorithms, one that we expect to be advantageous for the average, typical, simple update, though incurring costs exponential in the size of the theory in the worst case.…”