889 research outputs found
Information-Based Distance Measures and the Canonical Reflection of View Updates
For the problem of reflecting an update on a database view to the main schema, the constant-complement strategies are precisely those which avoid all update anomalies, and so define the gold standard for well-behaved solutions to the problem. However, the families of view updates which are supported under such strategies are limited, so it is sometimes necessary to go beyond them, albeit in a systematic fashion. In this work, an investigation of such extended strategies is initiated for relational schemata. The approach is to characterize the information content of a database instance, and then require that the optimal reflection of a view update to the main schema embody the least possible change of information. The key property is identified to be strong monotonicity of the view, meaning that view insertions may always be reflected as insertions to the main schema, and likewise for deletions. In that context it is shown that for insertions and deletions, an optimal update, entailing the least change of information, exists and is unique up to isomorphism for wide classes of constraints
Constant Delay Enumeration with FPT-Preprocessing for Conjunctive Queries of Bounded Submodular Width
Marx (STOC 2010, J. ACM 2013) introduced the notion of submodular width of a conjunctive query (CQ) and showed that for any class Phi of Boolean CQs of bounded submodular width, the model-checking problem for Phi on the class of all finite structures is fixed-parameter tractable (FPT). Note that for non-Boolean queries, the size of the query result may be far too large to be computed entirely within FPT time. We investigate the free-connex variant of submodular width and generalise Marx\u27s result to non-Boolean queries as follows: For every class Phi of CQs of bounded free-connex submodular width, within FPT-preprocessing time we can build a data structure that allows to enumerate, without repetition and with constant delay, all tuples of the query result. Our proof builds upon Marx\u27s splitting routine to decompose the query result into a union of results; but we have to tackle the additional technical difficulty to ensure that these can be enumerated efficiently
Propositional update operators based on formula/literal dependence
International audienceWe present and study a general family of belief update operators in a propositional setting. Its operators are based on formula/literal dependence, which is more fine-grained than the notion of formula/variable dependence that was proposed in the literature: formula/variable dependence is a particular case of formula/literal dependence. Our update operators are defined according to the "forget-then-conjoin" scheme: updating a belief base by an input formula consists in first forgetting in the base every literal on which the input formula has a negative influence, and then conjoining the resulting base with the input formula. The operators of our family differ by the underlying notion of formula/literal dependence, which may be defined syntactically or semantically, and which may or may not exploit further information like known persistent literals and pre-set dependencies. We argue that this allows to handle the frame problem and the ramification problem in a more appropriate way. We evaluate the update operators of our family w.r.t. two important dimensions: the logical dimension, by checking the status of the Katsuno-Mendelzon postulates for update, and the computational dimension, by identifying the complexity of a number of decision problems (including model checking, consistency and inference), both in the general case and in some restricted cases, as well as by studying compactability issues. It follows that several operators of our family are interesting alternatives to previous belief update operators
Decidability Results for the Boundedness Problem
We prove decidability of the boundedness problem for monadic least
fixed-point recursion based on positive monadic second-order (MSO) formulae
over trees. Given an MSO-formula phi(X,x) that is positive in X, it is
decidable whether the fixed-point recursion based on phi is spurious over the
class of all trees in the sense that there is some uniform finite bound for the
number of iterations phi takes to reach its least fixed point, uniformly across
all trees. We also identify the exact complexity of this problem. The proof
uses automata-theoretic techniques. This key result extends, by means of
model-theoretic interpretations, to show decidability of the boundedness
problem for MSO and guarded second-order logic (GSO) over the classes of
structures of fixed finite tree-width. Further model-theoretic transfer
arguments allow us to derive major known decidability results for boundedness
for fragments of first-order logic as well as new ones
Integrating OLAP and Ranking: The Ranking-Cube Methodology
Recent years have witnessed an enormous growth of data in business, industry, and Web applications. Database search often returns a large collection of results, which poses challenges to both efficient query processing and effective digest of the query results. To address this problem, ranked search has been introduced to database systems. We study the problem of On-Line Analytical Processing (OLAP) of ranked queries, where ranked queries are conducted in the arbitrary subset of data defined by multi-dimensional selections. While pre-computation and multi-dimensional aggregation is the standard solution for OLAP, materializing dynamic ranking results is unrealistic because the ranking criteria are not known until the query time. To overcome such difficulty, we develop a new ranking cube method that performs semi on-line materialization and semi online computation in this thesis. Its complete life cycle, including cube construction, incremental maintenance, and query processing, is also discussed. We further extend the ranking cube in three dimensions. First, how to answer queries in high-dimensional data. Second, how to answer queries which involves joins over multiple relations. Third, how to answer general preference queries (besides ranked queries, such as skyline queries). Our performance studies show that ranking-cube is orders of magnitude faster than previous approaches
Computer-Aided Discovery and Categorisation of Personality Axioms
We propose a computer-algebraic, order-theoretic framework based on
intuitionistic logic for the computer-aided discovery of personality axioms
from personality-test data and their mathematical categorisation into formal
personality theories in the spirit of F.~Klein's Erlanger Programm for
geometrical theories. As a result, formal personality theories can be
automatically generated, diagrammatically visualised, and mathematically
characterised in terms of categories of invariant-preserving transformations in
the sense of Klein and category theory. Our personality theories and categories
are induced by implicational invariants that are ground instances of
intuitionistic implication, which we postulate as axioms. In our mindset, the
essence of personality, and thus mental health and illness, is its invariance.
The truth of these axioms is algorithmically extracted from histories of
partially-ordered, symbolic data of observed behaviour. The personality-test
data and the personality theories are related by a Galois-connection in our
framework. As data format, we adopt the format of the symbolic values generated
by the Szondi-test, a personality test based on L.~Szondi's unifying,
depth-psychological theory of fate analysis.Comment: related to arXiv:1403.200
Ranked Enumeration for MSO on Trees via Knowledge Compilation
We study the problem of enumerating the satisfying assignments for circuit
classes from knowledge compilation, where assignments are ranked in a specific
order. In particular, we show how this problem can be used to efficiently
perform ranked enumeration of the answers to MSO queries over trees, with the
order being given by a ranking function satisfying a subset-monotonicity
property.
Assuming that the number of variables is constant, we show that we can
enumerate the satisfying assignments in ranked order for so-called multivalued
circuits that are smooth, decomposable, and in negation normal form (smooth
multivalued DNNF). There is no preprocessing and the enumeration delay is
linear in the size of the circuit times the number of values, plus a
logarithmic term in the number of assignments produced so far. If we further
assume that the circuit is deterministic (smooth multivalued d-DNNF), we can
achieve linear-time preprocessing in the circuit, and the delay only features
the logarithmic term.Comment: 26 pages; this is the authors version of the corresponding ICDT'24
articl
On the Implementation of the Probabilistic Logic Programming Language ProbLog
The past few years have seen a surge of interest in the field of
probabilistic logic learning and statistical relational learning. In this
endeavor, many probabilistic logics have been developed. ProbLog is a recent
probabilistic extension of Prolog motivated by the mining of large biological
networks. In ProbLog, facts can be labeled with probabilities. These facts are
treated as mutually independent random variables that indicate whether these
facts belong to a randomly sampled program. Different kinds of queries can be
posed to ProbLog programs. We introduce algorithms that allow the efficient
execution of these queries, discuss their implementation on top of the
YAP-Prolog system, and evaluate their performance in the context of large
networks of biological entities.Comment: 28 pages; To appear in Theory and Practice of Logic Programming
(TPLP
A Circuit-Based Approach to Efficient Enumeration
We study the problem of enumerating the satisfying valuations of a circuit while bounding the delay, i.e., the time needed to compute each successive valuation. We focus on the class of structured d-DNNF circuits originally introduced in knowledge compilation, a sub-area of artificial intelligence. We propose an algorithm for these circuits that enumerates valuations with linear preprocessing and delay linear in the Hamming weight of each valuation. Moreover, valuations of constant Hamming weight can be enumerated with linear preprocessing and constant delay.
Our results yield a framework for efficient enumeration that applies to all problems whose solutions can be compiled to structured d-DNNFs. In particular, we use it to recapture classical results in database theory, for factorized database representations and for MSO evaluation. This gives an independent proof of constant-delay enumeration for MSO formulae with first-order free variables on bounded-treewidth structures
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