273 research outputs found

    Query Rewriting with Disjunctive Existential Rules and Mappings

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    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

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    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

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    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

    24th Nordic Conference on Computational Linguistics (NoDaLiDa)

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    LIPIcs, Volume 258, SoCG 2023, Complete Volume

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    LIPIcs, Volume 258, SoCG 2023, Complete Volum

    Modular quantum signal processing in many variables

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    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

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    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

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    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

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    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

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    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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