944 research outputs found
Using concept lattices to mine functional dependencies
Concept Lattices have been proved to be a valuable tool to represent
the knowlegde in a database.
In this paper we show how functional dependencies in databases
can be extracted using Concept Lattices, not preprocessing the original
database,
but providing a new closure operator. We also prove that this method
generalizes the previous methods and
closure operators that are being used to find association rules in binary
databases.Postprint (published version
Reasoning about Independence in Probabilistic Models of Relational Data
We extend the theory of d-separation to cases in which data instances are not
independent and identically distributed. We show that applying the rules of
d-separation directly to the structure of probabilistic models of relational
data inaccurately infers conditional independence. We introduce relational
d-separation, a theory for deriving conditional independence facts from
relational models. We provide a new representation, the abstract ground graph,
that enables a sound, complete, and computationally efficient method for
answering d-separation queries about relational models, and we present
empirical results that demonstrate effectiveness.Comment: 61 pages, substantial revisions to formalisms, theory, and related
wor
Querying Schemas With Access Restrictions
We study verification of systems whose transitions consist of accesses to a
Web-based data-source. An access is a lookup on a relation within a relational
database, fixing values for a set of positions in the relation. For example, a
transition can represent access to a Web form, where the user is restricted to
filling in values for a particular set of fields. We look at verifying
properties of a schema describing the possible accesses of such a system. We
present a language where one can describe the properties of an access path, and
also specify additional restrictions on accesses that are enforced by the
schema. Our main property language, AccLTL, is based on a first-order extension
of linear-time temporal logic, interpreting access paths as sequences of
relational structures. We also present a lower-level automaton model,
Aautomata, which AccLTL specifications can compile into. We show that AccLTL
and A-automata can express static analysis problems related to "querying with
limited access patterns" that have been studied in the database literature in
the past, such as whether an access is relevant to answering a query, and
whether two queries are equivalent in the accessible data they can return. We
prove decidability and complexity results for several restrictions and variants
of AccLTL, and explain which properties of paths can be expressed in each
restriction.Comment: VLDB201
A Simple Logic of Functional Dependence
This paper presents a simple decidable logic of functional dependence LFD,
based on an extension of classical propositional logic with dependence atoms
plus dependence quantifiers treated as modalities, within the setting of
generalized assignment semantics for first order logic. The expressive
strength, complete proof calculus and meta-properties of LFD are explored.
Various language extensions are presented as well, up to undecidable
modal-style logics for independence and dynamic logics of changing dependence
models. Finally, more concrete settings for dependence are discussed:
continuous dependence in topological models, linear dependence in vector
spaces, and temporal dependence in dynamical systems and games.Comment: 56 pages. Journal of Philosophical Logic (2021
Evaluating Datalog via Tree Automata and Cycluits
We investigate parameterizations of both database instances and queries that
make query evaluation fixed-parameter tractable in combined complexity. We show
that clique-frontier-guarded Datalog with stratified negation (CFG-Datalog)
enjoys bilinear-time evaluation on structures of bounded treewidth for programs
of bounded rule size. Such programs capture in particular conjunctive queries
with simplicial decompositions of bounded width, guarded negation fragment
queries of bounded CQ-rank, or two-way regular path queries. Our result is
shown by translating to alternating two-way automata, whose semantics is
defined via cyclic provenance circuits (cycluits) that can be tractably
evaluated.Comment: 56 pages, 63 references. Journal version of "Combined Tractability of
Query Evaluation via Tree Automata and Cycluits (Extended Version)" at
arXiv:1612.04203. Up to the stylesheet, page/environment numbering, and
possible minor publisher-induced changes, this is the exact content of the
journal paper that will appear in Theory of Computing Systems. Update wrt
version 1: latest reviewer feedbac
Inquisitive bisimulation
Inquisitive modal logic InqML is a generalisation of standard Kripke-style
modal logic. In its epistemic incarnation, it extends standard epistemic logic
to capture not just the information that agents have, but also the questions
that they are interested in. Technically, InqML fits within the family of
logics based on team semantics. From a model-theoretic perspective, it takes us
a step in the direction of monadic second-order logic, as inquisitive modal
operators involve quantification over sets of worlds. We introduce and
investigate the natural notion of bisimulation equivalence in the setting of
InqML. We compare the expressiveness of InqML and first-order logic in the
context of relational structures with two sorts, one for worlds and one for
information states. We characterise inquisitive modal logic, as well as its
multi-agent epistemic S5-like variant, as the bisimulation invariant fragment
of first-order logic over various natural classes of two-sorted structures.
These results crucially require non-classical methods in studying bisimulation
and first-order expressiveness over non-elementary classes of structures,
irrespective of whether we aim for characterisations in the sense of classical
or of finite model theory
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