1,731 research outputs found
Global Numerical Constraints on Trees
We introduce a logical foundation to reason on tree structures with
constraints on the number of node occurrences. Related formalisms are limited
to express occurrence constraints on particular tree regions, as for instance
the children of a given node. By contrast, the logic introduced in the present
work can concisely express numerical bounds on any region, descendants or
ancestors for instance. We prove that the logic is decidable in single
exponential time even if the numerical constraints are in binary form. We also
illustrate the usage of the logic in the description of numerical constraints
on multi-directional path queries on XML documents. Furthermore, numerical
restrictions on regular languages (XML schemas) can also be concisely described
by the logic. This implies a characterization of decidable counting extensions
of XPath queries and XML schemas. Moreover, as the logic is closed under
negation, it can thus be used as an optimal reasoning framework for testing
emptiness, containment and equivalence
Querying Best Paths in Graph Databases
Querying graph databases has recently received much attention. We propose a new approach to this problem, which balances competing goals of expressive power, language clarity and computational complexity. A distinctive feature of our approach is the ability to express properties of minimal (e.g. shortest) and maximal (e.g. most valuable) paths satisfying given criteria. To express complex properties in a modular way, we introduce labelling-generating ontologies. The resulting formalism is computationally attractive - queries can be answered in non-deterministic
logarithmic space in the size of the database
Queries with Guarded Negation (full version)
A well-established and fundamental insight in database theory is that
negation (also known as complementation) tends to make queries difficult to
process and difficult to reason about. Many basic problems are decidable and
admit practical algorithms in the case of unions of conjunctive queries, but
become difficult or even undecidable when queries are allowed to contain
negation. Inspired by recent results in finite model theory, we consider a
restricted form of negation, guarded negation. We introduce a fragment of SQL,
called GN-SQL, as well as a fragment of Datalog with stratified negation,
called GN-Datalog, that allow only guarded negation, and we show that these
query languages are computationally well behaved, in terms of testing query
containment, query evaluation, open-world query answering, and boundedness.
GN-SQL and GN-Datalog subsume a number of well known query languages and
constraint languages, such as unions of conjunctive queries, monadic Datalog,
and frontier-guarded tgds. In addition, an analysis of standard benchmark
workloads shows that most usage of negation in SQL in practice is guarded
negation
On defining irreducibility
We show that irreducibility is not a first-order definable property of real
algebraic varieties. The proof is based on the recent o-minimality result for
the exponential function. We conjecture that irreducibility is not a definable
property of complex algebraic varieties
Acceptability with general orderings
We present a new approach to termination analysis of logic programs. The
essence of the approach is that we make use of general orderings (instead of
level mappings), like it is done in transformational approaches to logic
program termination analysis, but we apply these orderings directly to the
logic program and not to the term-rewrite system obtained through some
transformation. We define some variants of acceptability, based on general
orderings, and show how they are equivalent to LD-termination. We develop a
demand driven, constraint-based approach to verify these
acceptability-variants.
The advantage of the approach over standard acceptability is that in some
cases, where complex level mappings are needed, fairly simple orderings may be
easily generated. The advantage over transformational approaches is that it
avoids the transformation step all together.
{\bf Keywords:} termination analysis, acceptability, orderings.Comment: To appear in "Computational Logic: From Logic Programming into the
Future
MLPQ: A LINEAR CONSTRAINT DATABASE SYSTEM WITH AGGREGATE OPERATORS
In this project report, I will discuss a Multiple Linear Programming Query (MLPQ) system and the theoretical background of this system.The MPLQ system is developed to solve some realistic problems involving both linear programming (UP) techniques and linear constraint databases (LCDBs) theory. The MLPQ system is aimed at providing a mechanism of bridging these two important areas. system basically consists of three parts which are a linear constraint database, an LP solver, and an interface between the LCDB and the LP solver. The LCDB of the MLPQ system contains multiple linear programming problems. The LP solver used in the MPLQ is an implementation Of the SIMPLEX method. An important feature of the MLPQ system is that it can handle the SQL aggregate Operators, such as minimum Min, maximum Max, summation Sum, and average Avg. The MLPQ system provides an efficient way of evaluation of aggregate operators for linear constraint databases
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