356 research outputs found
Towards an Efficient Evaluation of General Queries
Database applications often require to
evaluate queries containing quantifiers or disjunctions,
e.g., for handling general integrity constraints. Existing
efficient methods for processing quantifiers depart from the
relational model as they rely on non-algebraic procedures.
Looking at quantified query evaluation from a new angle,
we propose an approach to process quantifiers that makes
use of relational algebra operators only. Our approach
performs in two phases. The first phase normalizes the
queries producing a canonical form. This form permits to
improve the translation into relational algebra performed
during the second phase. The improved translation relies
on a new operator - the complement-join - that generalizes
the set difference, on algebraic expressions of universal
quantifiers that avoid the expensive division operator in
many cases, and on a special processing of disjunctions by
means of constrained outer-joins. Our method achieves an
efficiency at least comparable with that of previous
proposals, better in most cases. Furthermore, it is considerably
simpler to implement as it completely relies on
relational data structures and operators
Complexity of Nested Circumscription and Nested Abnormality Theories
The need for a circumscriptive formalism that allows for simple yet elegant
modular problem representation has led Lifschitz (AIJ, 1995) to introduce
nested abnormality theories (NATs) as a tool for modular knowledge
representation, tailored for applying circumscription to minimize exceptional
circumstances. Abstracting from this particular objective, we propose L_{CIRC},
which is an extension of generic propositional circumscription by allowing
propositional combinations and nesting of circumscriptive theories. As shown,
NATs are naturally embedded into this language, and are in fact of equal
expressive capability. We then analyze the complexity of L_{CIRC} and NATs, and
in particular the effect of nesting. The latter is found to be a source of
complexity, which climbs the Polynomial Hierarchy as the nesting depth
increases and reaches PSPACE-completeness in the general case. We also identify
meaningful syntactic fragments of NATs which have lower complexity. In
particular, we show that the generalization of Horn circumscription in the NAT
framework remains CONP-complete, and that Horn NATs without fixed letters can
be efficiently transformed into an equivalent Horn CNF, which implies
polynomial solvability of principal reasoning tasks. Finally, we also study
extensions of NATs and briefly address the complexity in the first-order case.
Our results give insight into the ``cost'' of using L_{CIRC} (resp. NATs) as a
host language for expressing other formalisms such as action theories,
narratives, or spatial theories.Comment: A preliminary abstract of this paper appeared in Proc. Seventeenth
International Joint Conference on Artificial Intelligence (IJCAI-01), pages
169--174. Morgan Kaufmann, 200
On the Succinctness of Query Rewriting over OWL 2 QL Ontologies with Shallow Chases
We investigate the size of first-order rewritings of conjunctive queries over
OWL 2 QL ontologies of depth 1 and 2 by means of hypergraph programs computing
Boolean functions. Both positive and negative results are obtained. Conjunctive
queries over ontologies of depth 1 have polynomial-size nonrecursive datalog
rewritings; tree-shaped queries have polynomial positive existential
rewritings; however, in the worst case, positive existential rewritings can
only be of superpolynomial size. Positive existential and nonrecursive datalog
rewritings of queries over ontologies of depth 2 suffer an exponential blowup
in the worst case, while first-order rewritings are superpolynomial unless
. We also analyse rewritings of
tree-shaped queries over arbitrary ontologies and observe that the query
entailment problem for such queries is fixed-parameter tractable
Polynomial conjunctive query rewriting under unary inclusion dependencies
Ontology-based data access (OBDA) is widely accepted as an important ingredient of the new generation of information systems. In the OBDA paradigm, potentially incomplete relational data is enriched by means of ontologies, representing intensional knowledge of the application domain. We consider the problem of conjunctive query answering in OBDA. Certain ontology languages have been identified as FO-rewritable (e.g., DL-Lite and sticky-join sets of TGDs), which means that the ontology can be incorporated into the user's query, thus reducing OBDA to standard relational query evaluation. However, all known query rewriting techniques produce queries that are exponentially large in the size of the user's query, which can be a serious issue for standard relational database engines. In this paper, we present a polynomial query rewriting for conjunctive queries under unary inclusion dependencies. On
the other hand, we show that binary inclusion dependencies do not admit
polynomial query rewriting algorithms
αCheck: a mechanized metatheory model-checker
The problem of mechanically formalizing and proving metatheoretic properties
of programming language calculi, type systems, operational semantics, and
related formal systems has received considerable attention recently. However,
the dual problem of searching for errors in such formalizations has attracted
comparatively little attention. In this article, we present Check, a
bounded model-checker for metatheoretic properties of formal systems specified
using nominal logic. In contrast to the current state of the art for metatheory
verification, our approach is fully automatic, does not require expertise in
theorem proving on the part of the user, and produces counterexamples in the
case that a flaw is detected. We present two implementations of this technique,
one based on negation-as-failure and one based on negation elimination, along
with experimental results showing that these techniques are fast enough to be
used interactively to debug systems as they are developed.Comment: Under consideration for publication in Theory and Practice of Logic
Programming (TPLP
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