Reasoning about equations and functional dependencies on complex objects

Bommel, Martin F. van; Weddell, Grant E.

doi:10.1109/69.334857

Cited by 20 publications

(7 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Another form of constraints defined in terms of navigation paths, called path functional dependencies, has been studied by Weddell et al [8,29]. These constraints differ significantly from the path constraints investigated here because they are a generalization of functional dependencies for a restricted type system, while P c constraints can be viewed as a generalization of inclusion dependencies for both semistructured and structured databases.…”

Section: Schools: Set(school-db);mentioning

confidence: 96%

Path Constraints in Semistructured Databases

Buneman¹,

Fan²,

Weinstein³

2000

Journal of Computer and System Sciences

View full text Add to dashboard Cite

We investigate a class of path constraints that is of interest in connection with both semistructured and structured data. In standard database systems, constraints are typically expressed as part of the schema, but in semistructured data there is no explicit schema and path constraints provide a natural alternative. As with structured data, path constraints on semistructured data express integrity constraints associated with the semantics of data and are important in query optimization. We show that in semistructured databases, despite the simple syntax of the constraints, their associated implication problem is r.e. complete and finite implication problem is co-r.e. complete. However, we establish the decidability of the implication and finite implication problems for several fragments of the path constraint language and demonstrate that these fragments suffice to express important semantic information such as extent constraints, inverse relationships, and local database constraints commonly found in object-oriented databases.

show abstract

Section: Schools: Set(school-db);mentioning

confidence: 96%

Path Constraints in Semistructured Databases

Buneman¹,

Fan²,

Weinstein³

2000

Journal of Computer and System Sciences

View full text Add to dashboard Cite

show abstract

“…Weddell and van Bommel [Weddell 1992;van Bommel and Weddell 1994] generalize FDs for a data model similar to the one used in our study. They allow path expressions in FDs.…”

Section: Weddell Et Al's Path Fdmentioning

confidence: 96%

“…From the relation EMP_O it is clear that Jim has worked for only one department. Objects including references to other objects may be called complex objects, as in van Bommel and Weddell [1994]. Third, it is well-known (see, for example, Clifford et al [1994]) that in the presence of group identifiers, one can ungroup a temporally grouped relation without loss of information.…”

Section: Motivation For Oidsmentioning

confidence: 98%

Temporal FDs on complex objects

Wijsen

1999

ACM Trans. Database Syst.

View full text Add to dashboard Cite

Temporal functional dependencies (TFD) are defined for temporal databases that include object identity. It is argued that object identity can overcome certain semantic difficulties with existing temporal relational data models. Practical applications of TFDs in object bases are discussed. Reasoning about TFDs is at the center of this paper. It turns out that the distinction between acyclic and cyclic schemas is significant. For acyclic schemas, a complete axiomatization for finite implication is given and an algorithm for deciding finite implication provided. The same axiomatization is proven complete for unrestricted implication in unrestricted schemas, which can be cyclic. An interesting result is that there are cyclic schemas for which unrestricted and finite implication do not coincide. TFDs relate and extend some earlier work on dependency theory in temporal databases. Throughout this paper, the construct of TFD is compared with the notion of temporal FD introduced by Wang et al. [1997]. A comparison with other related work is provided at the end of the article.

show abstract

“…Path functional constraints have also been studied (see, e.g., Ito and Weddell [1995] and van Bommel and Weddell [1994]). These constraints are not capable of expressing inclusion and inverse constraints.…”

Section: Related Workmentioning

confidence: 99%

Interaction between path and type constraints

Buneman

Fan²,

Weinstein

2003

ACM Trans. Comput. Logic

View full text Add to dashboard Cite

Path constraints are capable of expressing inclusion and inverse relationships and have proved useful in modeling and querying semistructured data [Abiteboul and Vianu 1999;Buneman et al. 2000]. Types also constrain the structure of data and are commonly found in traditional databases. There has also been work on imposing structure or a type system on semistructured data for storing and querying semistructured data in a traditional database system [Alon et al. 2001;Deutsch et al. 1999a;Florescu and Kossmann 1999;Shanmugasundaram et al. 1999]. One wants to know whether complexity results for reasoning about path constraints established in the untyped (semistructured) context could carry over to traditional databases, and vice versa. It is therefore appropriate to understand the interaction between types and path constraints. In addition, XML [Bray et al. 1998], which may involve both an optional schema (e.g., DTDs or XML Schema [Thompson et al. 2001]) and integrity constraints, highlights the importance of the study of the interaction.This article investigates that interaction. In particular it studies constraint implication problems, which are important both in understanding the semantics of type/constraint systems and in query optimization. It shows that path constraints interact with types in a highly intricate way. For that purpose a number of results on path constraint implication are established in the presence and absence of type systems. These results demonstrate that adding a type system may in some cases simplify reasoning about path constraints and in other cases make it harder. For example, it is shown that there is a path constraint implication problem that is decidable in PTIME in the untyped context, but that becomes undecidable when a type system is added. On the other hand, The article is based on an extended abstract that appeared in • 531 there is an implication problem that is undecidable in the untyped context, but becomes not only decidable in cubic time but also finitely axiomatizable when a type system is imposed.

show abstract

Reasoning about equations and functional dependencies on complex objects

Cited by 20 publications

References 30 publications

Path Constraints in Semistructured Databases

Path Constraints in Semistructured Databases

Temporal FDs on complex objects

Interaction between path and type constraints

Contact Info

Product

Resources

About