1,192 research outputs found
Using Fuzzy Linguistic Representations to Provide Explanatory Semantics for Data Warehouses
A data warehouse integrates large amounts of extracted and summarized data from multiple sources for direct querying and analysis. While it provides decision makers with easy access to such historical and aggregate data, the real meaning of the data has been ignored. For example, "whether a total sales amount 1,000 items indicates a good or bad sales performance" is still unclear. From the decision makers' point of view, the semantics rather than raw numbers which convey the meaning of the data is very important. In this paper, we explore the use of fuzzy technology to provide this semantics for the summarizations and aggregates developed in data warehousing systems. A three layered data warehouse semantic model, consisting of quantitative (numerical) summarization, qualitative (categorical) summarization, and quantifier summarization, is proposed for capturing and explicating the semantics of warehoused data. Based on the model, several algebraic operators are defined. We also extend the SQL language to allow for flexible queries against such enhanced data warehouses
On Spatial Conjunction as Second-Order Logic
Spatial conjunction is a powerful construct for reasoning about dynamically
allocated data structures, as well as concurrent, distributed and mobile
computation. While researchers have identified many uses of spatial
conjunction, its precise expressive power compared to traditional logical
constructs was not previously known. In this paper we establish the expressive
power of spatial conjunction. We construct an embedding from first-order logic
with spatial conjunction into second-order logic, and more surprisingly, an
embedding from full second order logic into first-order logic with spatial
conjunction. These embeddings show that the satisfiability of formulas in
first-order logic with spatial conjunction is equivalent to the satisfiability
of formulas in second-order logic. These results explain the great expressive
power of spatial conjunction and can be used to show that adding unrestricted
spatial conjunction to a decidable logic leads to an undecidable logic. As one
example, we show that adding unrestricted spatial conjunction to two-variable
logic leads to undecidability. On the side of decidability, the embedding into
second-order logic immediately implies the decidability of first-order logic
with a form of spatial conjunction over trees. The embedding into spatial
conjunction also has useful consequences: because a restricted form of spatial
conjunction in two-variable logic preserves decidability, we obtain that a
correspondingly restricted form of second-order quantification in two-variable
logic is decidable. The resulting language generalizes the first-order theory
of boolean algebra over sets and is useful in reasoning about the contents of
data structures in object-oriented languages.Comment: 16 page
Incorporating generalized quantifiers into description logic for representing data source contents
Title from cover. "January 1998."Includes bibliographical references (p. 19-21).Steven Yi-cheng Tu and Stuart E. Madnick
Nesting Depth of Operators in Graph Database Queries: Expressiveness Vs. Evaluation Complexity
Designing query languages for graph structured data is an active field of
research, where expressiveness and efficient algorithms for query evaluation
are conflicting goals. To better handle dynamically changing data, recent work
has been done on designing query languages that can compare values stored in
the graph database, without hard coding the values in the query. The main idea
is to allow variables in the query and bind the variables to values when
evaluating the query. For query languages that bind variables only once, query
evaluation is usually NP-complete. There are query languages that allow binding
inside the scope of Kleene star operators, which can themselves be in the scope
of bindings and so on. Uncontrolled nesting of binding and iteration within one
another results in query evaluation being PSPACE-complete.
We define a way to syntactically control the nesting depth of iterated
bindings, and study how this affects expressiveness and efficiency of query
evaluation. The result is an infinite, syntactically defined hierarchy of
expressions. We prove that the corresponding language hierarchy is strict.
Given an expression in the hierarchy, we prove that it is undecidable to check
if there is a language equivalent expression at lower levels. We prove that
evaluating a query based on an expression at level i can be done in
in the polynomial time hierarchy. Satisfiability of quantified Boolean formulas
can be reduced to query evaluation; we study the relationship between
alternations in Boolean quantifiers and the depth of nesting of iterated
bindings.Comment: Improvements from ICALP 2016 review comment
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