Grant E. Weddell

Reasoning about functional dependencies generalized for semantic data models

We propose a more general form of functional dependency for semantic data models that derives from their common feature in which the separate notions of domain and relation in the relational model are combined into a single notion of class. This usually results in a richer terminological component for their query languages, whereby terms may navigate through any number of properties, including none. We prove the richer expressiveness of this more general functional dependency, and exhibit a sound and complete set of inference axioms. Although the general problem of decidability of their logical implication remains open at this time, we present decision procedures for cases in which the dependencies included in a schema correspond to keys, or in which the schema itself is acyclic. The theory is then extended to include a form of conjunctive query. Of particular significance is that the query becomes an additional source of functional dependency. Finally, we outline several applications of the theory to various problems in physical design and in query optimization. The applications derive from an ability to predict when a query can have at most one solution.

On Keys and Functional Dependencies as First-Class Citizens in Description Logics

We investigate whether identification constraints such as keys and functional dependencies can be granted full status as concept constructors in a Boolean-complete description logic. In particular, we show that surprisingly simple forms of such constraints lead to undecidability of the associated logical implication problem if they are allowed within the scope of a negation or on the left-hand side of inclusion dependencies. We then show that allowing a very general form of identification constraint to occur in the scope of monotone concept constructors on the right-hand side of inclusion dependencies still leads to decidable implication problems. We consider the relationship between certain classes of identification constraints and nominals.

Expressive and flexible access to web-extracted data: a keyword-based structured query language

Automated extraction of structured data from Web sources often leads to large heterogeneous knowledge bases (KB), with data and schema items numbering in the hundreds of thousands or millions. Formulating information needs with conventional structured query languages is difficult due to the sheer size of schema information available to the user. We address this challenge by proposing a new query language that blends keyword search with structured query processing over large information graphs with rich semantics. Our formalism for structured queries based on keywords combines the flexibility of keyword search with the expressiveness of structures queries. We propose a solution to the resulting disambiguation problem caused by introducing keywords as primitives in a structured query language. We show how expressions in our proposed language can be rewritten using the vocabulary of the web-extracted KB, and how different possible rewritings can be ranked based on their syntactic relationship to the keywords in the query as well as their semantic coherence in the underlying KB. An extensive experimental study demonstrates the efficiency and effectiveness of our approach. Additionally, we show how our query language fits into QUICK, an end-to-end information system that integrates web-extracted data graphs with full-text search. In this system, the rewritten query describes an arbitrary topic of interest for which corresponding entities, and documents relevant to the entities, are efficiently retrieved.

Two-directional record layout for multiple inheritance

Much recent work in polymorphic programming languages allows subtyping and multiple inheritance for records. In such systems, we would like to extract a field from a record with the same efficiency as if we were not making use of subtyping and multiple inheritance. Methods currently used make field extraction 3-5 times slower, which can produce a significant overall performance slowdown. We describe a record layout algorithm that allows us to assign a fixed offset to each field name. This allows field extraction to done just as quickly as in systems that do not provide multiple inheritance. Assigning fixed offsets may require us to leave gaps in some records (and waste space). However, by placing fields at both positive and negative offsets we can drastically reduce the amount of wasted space. Finding an optimal layout is NP-hard, so we propose and analyze heuristic algorithms for producing good two-direction record layouts. In a trial run, our algorithm produced a fixed layout for the instance variables of the 563 flavors of a Lisp Flavors system; this fixed layout only wastes 6% of the total space consumed by a collection of one instance of each flavor.

On Decidability and Complexity of Description Logics with Uniqueness Constraints

We establish the equivalence of: (1) the logical implication problem for a description logic dialect called DLClass that includes a concept constructor for expressing uniqueness constraints, (2) the logical implication problem for path functional dependencies (PFDs), and (3) the problem of answering queries in deductive databases with limited use of successor functions. As a consequence, we settle an open problem concerning lower bounds for the PFD logical implication problem and show that a regularity condition for DLClass that ensures low order polynomial time decidability for its logical implication problem is tight.

Interpreting keyword queries over web knowledge bases

Many keyword queries issued to Web search engines target information about real world entities, and interpreting these queries over Web knowledge bases can often enable the search system to provide exact answers to queries. Equally important is the problem of detecting when the reference knowledge base is not capable of answering the keyword query, due to lack of domain coverage. In this work we present an approach to computing structured representations of keyword queries over a reference knowledge base. We mine frequent query structures from a Web query log and map these structures into a reference knowledge base. Our approach exploits coarse linguistic structure in keyword queries, and combines it with rich structured query representations of information needs.

Reasoning about Duplicate Elimination with Description Logic

Queries commonly perform much better if they manage to avoid duplicate elimination operations in their execution plans. In this paper, we report on a technique that provides a necessary and sufficient condition for removing such operators from object relational conjunctive queries under the standard duplicate semantics. The condition is fully captured as a membership problem in a dialect of description logic called CFD, which is capable of expressing a number of common constraints implicit in object relational database schemas. We also present a PTIME algorithm for arbitrary membership problems in CFD.

A THEORY OF FUNCTIONAL DEPENDENCIES FOR OBJECT-ORIENTED DATA MODELS

We propose a more expressive form of functional dependency for object oriented data models. The generalization derives mainly from their common feature of combining the separate notions of domain and relation in the relational model into a single notion of class. This results in a richer terminological component for their query languages, in which a single term may traverse any number of properties, including none. A sound and complete axiomatization is presented for a simple choice of semantic data model in which classes can also be organized in a generalization taxonomy. Decision procedures are exhibited that apply when the dependencies included in a schema correspond to keys, or when the schema itself is acyclic. Finally, we outline several applications of the theory to various problems in physical design and in query optimization.

Reasoning about equations and functional dependencies on complex objects

Virtually all semantic or object-oriented data models assume that objects have an identity separate from any of their parts, and allow users to define complex object types in which part values may be any other objects. This often results in a choice of query language in which a user can express navigating from one object to another by following a property value path. We consider a constraint language in which one may express equations and functional dependencies over complex object types. The language is novel in the sense that component attributes of individual constraints may correspond to property paths. The kind of equations we consider are also important, because they are a natural abstraction of the class of conjunctive queries for query languages that support property value navigation. In our introductory comments, we give an example of such a query and outline two applications of the constraint theory to problems relating to a choice of access plan for the query. We present a sound and complete axiomatization of the constraint language for the case in which interpretations are permitted to be infinite, where interpretations themselves correspond to a form of directed labeled graph. Although the implication problem for our form of equational constraint alone over arbitrary schema is undecidable, we present decision procedures for the implication problem for both kinds of constraints when the problem schema satisfies a stratification condition, and when all input functional dependencies are keys. >

Path constraints for graph-based data models: Towards a unified theory of typing constraints, equations, and functional dependencies

Virtually all semantic or object-oriented data models assume objects have an identity separate from any of their parts. These models allow users to define complex object types in which property values may be any other objects. Often the query language allows a user to navigate from object to object by following a property value path. In this paper, we consider the combination of three forms of constraints over complex object types: equations, functional dependencies, and typing constraints. The constraints are novel since component attributes may correspond to property paths instead of single properties. The kind of equational constraint we consider is also important: it abstracts the class of conjunctive queries for query languages that support property value navigation. Our form of typing constraint is novel for two reasons: it allows us to characterize well-formedness conditions on constraints in more appropriate semantic terms, and it can be used to support a form of molecular abstraction.