24 research outputs found
A SAT-based System for Consistent Query Answering
An inconsistent database is a database that violates one or more integrity
constraints, such as functional dependencies. Consistent Query Answering is a
rigorous and principled approach to the semantics of queries posed against
inconsistent databases. The consistent answers to a query on an inconsistent
database is the intersection of the answers to the query on every repair, i.e.,
on every consistent database that differs from the given inconsistent one in a
minimal way. Computing the consistent answers of a fixed conjunctive query on a
given inconsistent database can be a coNP-hard problem, even though every fixed
conjunctive query is efficiently computable on a given consistent database.
We designed, implemented, and evaluated CAvSAT, a SAT-based system for
consistent query answering. CAvSAT leverages a set of natural reductions from
the complement of consistent query answering to SAT and to Weighted MaxSAT. The
system is capable of handling unions of conjunctive queries and arbitrary
denial constraints, which include functional dependencies as a special case. We
report results from experiments evaluating CAvSAT on both synthetic and
real-world databases. These results provide evidence that a SAT-based approach
can give rise to a comprehensive and scalable system for consistent query
answering.Comment: 25 pages including appendix, to appear in the 22nd International
Conference on Theory and Applications of Satisfiability Testin
Relating Structure and Power: Comonadic Semantics for Computational Resources
Combinatorial games are widely used in finite model theory, constraint
satisfaction, modal logic and concurrency theory to characterize logical
equivalences between structures. In particular, Ehrenfeucht-Fraisse games,
pebble games, and bisimulation games play a central role. We show how each of
these types of games can be described in terms of an indexed family of comonads
on the category of relational structures and homomorphisms. The index k is a
resource parameter which bounds the degree of access to the underlying
structure. The coKleisli categories for these comonads can be used to give
syntax-free characterizations of a wide range of important logical
equivalences. Moreover, the coalgebras for these indexed comonads can be used
to characterize key combinatorial parameters: tree-depth for the
Ehrenfeucht-Fraisse comonad, tree-width for the pebbling comonad, and
synchronization-tree depth for the modal unfolding comonad. These results pave
the way for systematic connections between two major branches of the field of
logic in computer science which hitherto have been almost disjoint: categorical
semantics, and finite and algorithmic model theory.Comment: To appear in Proceedings of Computer Science Logic 201
How many variables are needed to express an existential positive query?
The number of variables used by a first-order query is
a fundamental measure which has been studied in numerous contexts,
and
which is known to be highly relevant to the task of query evaluation.
In this article, we study this measure in the context of
existential positive queries.
Building on previous work,
we present a combinatorial quantity defined on
existential positive queries;
we show that
this quantity not only characterizes the minimum number of variables
needed to express a given existential positive query
by another existential positive query,
but also that
it characterizes the minimum number of variables needed
to express a given existential positive query,
over all first-order queries.
Put differently and loosely,
we show that for any existential positive query,
no variables can ever be saved by moving
out of existential positive logic to first-order logic.
One component of this theorem's proof
is the construction of a winning strategy
for a certain Ehrenfeucht-Fra\"{i}ss\'{e} type game
On The Power of Tree Projections: Structural Tractability of Enumerating CSP Solutions
The problem of deciding whether CSP instances admit solutions has been deeply
studied in the literature, and several structural tractability results have
been derived so far. However, constraint satisfaction comes in practice as a
computation problem where the focus is either on finding one solution, or on
enumerating all solutions, possibly projected to some given set of output
variables. The paper investigates the structural tractability of the problem of
enumerating (possibly projected) solutions, where tractability means here
computable with polynomial delay (WPD), since in general exponentially many
solutions may be computed. A general framework based on the notion of tree
projection of hypergraphs is considered, which generalizes all known
decomposition methods. Tractability results have been obtained both for classes
of structures where output variables are part of their specification, and for
classes of structures where computability WPD must be ensured for any possible
set of output variables. These results are shown to be tight, by exhibiting
dichotomies for classes of structures having bounded arity and where the tree
decomposition method is considered
Deciding the Bell Number for Hereditary Graph Properties
The paper [J. Balogh, B. Bollobás, D. Weinreich, J. Combin. Theory Ser. B, 95 (2005), pp. 29--48] identifies a jump in the speed of hereditary graph properties to the Bell number and provides a partial characterization of the family of minimal classes whose speed is at least . In the present paper, we give a complete characterization of this family. Since this family is infinite, the decidability of the problem of determining if the speed of a hereditary property is above or below the Bell number is questionable. We answer this question positively by showing that there exists an algorithm which, given a finite set of graphs, decides whether the speed of the class of graphs containing no induced subgraphs from the set is above or below the Bell number. For properties defined by infinitely many minimal forbidden induced subgraphs, the speed is known to be above the Bell number.
Read More: http://epubs.siam.org/doi/abs/10.1137/15M102421
Fuzzy positive primitive formulas
Can non-classical logic contribute to the analysis of complexity in computer science? In this paper, we give an step towards the solution of this open problem, taking a logical model-theoretic approach to the analysis of complexity in fuzzy constraint satisfaction. We study fuzzy positive-primitive sentences, and we present an algebraic characterization of classes axiomatized by these kind of sentences in terms of homomorphisms and finite direct products. The ultimate goal is to study the expressiveness and reasoning mechanisms of non-classical languages, with respect to constraint satisfaction problems and, in general, in modelling decision scenario
On the unusual effectiveness of logic in computer science
§1. Introduction and overview. In 1960, E. P. Wigner, a joint winner of th