273 research outputs found
Query Rewriting with Disjunctive Existential Rules and Mappings
We consider the issue of answering unions of conjunctive queries (UCQs) with
disjunctive existential rules and mappings. While this issue has already been
well studied from a chase perspective, query rewriting within UCQs has hardly
been addressed yet. We first propose a sound and complete query rewriting
operator, which has the advantage of establishing a tight relationship between
a chase step and a rewriting step. The associated breadth-first query rewriting
algorithm outputs a minimal UCQ-rewriting when one exists. Second, we show that
for any ``truly disjunctive'' nonrecursive rule, there exists a conjunctive
query that has no UCQ-rewriting. It follows that the notion of finite
unification sets (fus), which denotes sets of existential rules such that any
UCQ admits a UCQ-rewriting, seems to have little relevance in this setting.
Finally, turning our attention to mappings, we show that the problem of
determining whether a UCQ admits a UCQ-rewriting through a disjunctive mapping
is undecidable. We conclude with a number of open problems.Comment: This report contains the paper accepted at KR 2023 and an appendix
with full proofs. 24 page
A Survey on Causal Discovery: Theory and Practice
Understanding the laws that govern a phenomenon is the core of scientific
progress. This is especially true when the goal is to model the interplay
between different aspects in a causal fashion. Indeed, causal inference itself
is specifically designed to quantify the underlying relationships that connect
a cause to its effect. Causal discovery is a branch of the broader field of
causality in which causal graphs is recovered from data (whenever possible),
enabling the identification and estimation of causal effects. In this paper, we
explore recent advancements in a unified manner, provide a consistent overview
of existing algorithms developed under different settings, report useful tools
and data, present real-world applications to understand why and how these
methods can be fruitfully exploited
An empirical study of negation in datalog programs
Datalog is the fusion of prolong and database technologies aimed at producing an difficultly logic-based, declarative language for databases. Since negation was added to Datalog, Datalog has become more expressive. In this thesis, I focus my attention on adding negation to DatalogIC which is a language which has been implemented by Mark P. Wassell, a past MSc student in the Department of Computer Science at UCT. I analyse and compare stratified, well-founded and inflationary semantics for negation, each of which has been implemented on top of INFORMIX; we call the resulting system NDatalog. According to the test results, we find that some results are unexpected. For example, when we evaluate a recursive stratified program, the results show that NDatalogstra is slower than NDatalogwellf although NDatalogwellf is more complex. After further investigation, I find the problem is that the NDatalog system has to spend a lot of time imitating the MINUS function, which does not exist in INFORMIX-SQL. So the running time depends on what kind of database system is used as backend. When we consider the time spent on pure evaluation, excluding auxiliary functions, we find that the results support our expectations, namely, that NDatalogstra is faster than NDatalogwellf which is faster than NDataloginf
LIPIcs, Volume 258, SoCG 2023, Complete Volume
LIPIcs, Volume 258, SoCG 2023, Complete Volum
Modular quantum signal processing in many variables
Despite significant advances in quantum algorithms, quantum programs in
practice are often expressed at the circuit level, forgoing helpful structural
abstractions common to their classical counterparts. Consequently, as many
quantum algorithms have been unified with the advent of quantum signal
processing (QSP) and quantum singular value transformation (QSVT), an
opportunity has appeared to cast these algorithms as modules that can be
combined to constitute complex programs. Complicating this, however, is that
while QSP/QSVT are often described by the polynomial transforms they apply to
the singular values of large linear operators, and the algebraic manipulation
of polynomials is simple, the QSP/QSVT protocols realizing analogous
manipulations of their embedded polynomials are non-obvious. Here we provide a
theory of modular multi-input-output QSP-based superoperators, the basic unit
of which we call a gadget, and show they can be snapped together with LEGO-like
ease at the level of the functions they apply. To demonstrate this ease, we
also provide a Python package for assembling gadgets and compiling them to
circuits. Viewed alternately, gadgets both enable the efficient block encoding
of large families of useful multivariable functions, and substantiate a
functional-programming approach to quantum algorithm design in recasting QSP
and QSVT as monadic types.Comment: 15 pages + 9 figures + 4 tables + 45 pages supplement. For codebase,
see https://github.com/ichuang/pyqsp/tree/bet
Ontology-Mediated Query Answering over Log-Linear Probabilistic Data: Extended Version
Large-scale knowledge bases are at the heart of modern information systems. Their knowledge is inherently uncertain, and hence they are often materialized as probabilistic databases. However, probabilistic database management systems typically lack the capability to incorporate implicit background knowledge and, consequently, fail to capture some intuitive query answers. Ontology-mediated query answering is a popular paradigm for encoding commonsense knowledge, which can provide more complete answers to user queries. We propose a new data model that integrates the paradigm of ontology-mediated query answering with probabilistic databases, employing a log-linear probability model. We compare our approach to existing proposals, and provide supporting computational results
A tetrachotomy of ontology-mediated queries with a covering axiom
Our concern is the problem of efficiently determining the data complexity of answering queries mediated by descrip- tion logic ontologies and constructing their optimal rewritings to standard database queries. Originated in ontology- based data access and datalog optimisation, this problem is known to be computationally very complex in general, with no explicit syntactic characterisations available. In this article, aiming to understand the fundamental roots of this difficulty, we strip the problem to the bare bones and focus on Boolean conjunctive queries mediated by a simple cov- ering axiom stating that one class is covered by the union of two other classes. We show that, on the one hand, these rudimentary ontology-mediated queries, called disjunctive sirups (or d-sirups), capture many features and difficulties of the general case. For example, answering d-sirups is Π2p-complete for combined complexity and can be in AC0 or L-, NL-, P-, or coNP-complete for data complexity (with the problem of recognising FO-rewritability of d-sirups be- ing 2ExpTime-hard); some d-sirups only have exponential-size resolution proofs, some only double-exponential-size positive existential FO-rewritings and single-exponential-size nonrecursive datalog rewritings. On the other hand, we prove a few partial sufficient and necessary conditions of FO- and (symmetric/linear-) datalog rewritability of d- sirups. Our main technical result is a complete and transparent syntactic AC0 / NL / P / coNP tetrachotomy of d-sirups with disjoint covering classes and a path-shaped Boolean conjunctive query. To obtain this tetrachotomy, we develop new techniques for establishing P- and coNP-hardness of answering non-Horn ontology-mediated queries as well as showing that they can be answered in NL
2021-2022, University of Memphis bulletin
University of Memphis bulletin containing the graduate catalog for 2021-2022.https://digitalcommons.memphis.edu/speccoll-ua-pub-bulletins/1441/thumbnail.jp
2013-2014, University of Memphis bulletin
University of Memphis bulletin containing the graduate catalog for 2013-2014.https://digitalcommons.memphis.edu/speccoll-ua-pub-bulletins/1434/thumbnail.jp
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