scholarly journals On Querying Incomplete Information in Databases under Bag Semantics

2017 ◽  
Author(s):  
Marco Console ◽  
Paolo Guagliardo ◽  
Leonid Libkin
Keyword(s):  
Incomplete Data ◽  
Real Life ◽  
Relational Algebra ◽  
Approximation Schemes ◽  
Query Rewriting ◽  
Possible World ◽  
First Order ◽  
Minimum Number ◽  
Database Technology ◽  
Certain Answers

Querying incomplete data is an important task both in data management, and in many AI applications that use query rewriting to take advantage of relational database technology. Usually one looks for answers that are certain, i.e., true in every possible world represented by an incomplete database. For positive queries, expressed either in positive relational algebra or as unions of conjunctive queries, finding such answers can be done efficiently when databases and query answers are sets. Real-life databases however use bag, rather than set, semantics. For bags, instead of saying that a tuple is certainly in the answer, we have more detailed information: namely, the range of the numbers of occurrences of the tuple in query answers. We show that the behavior of positive queries is different under bag semantics: finding the minimum number of occurrences can still be done efficiently, but for maximum it becomes intractable. We use these results to investigate approximation schemes for computing certain answers to arbitrary first-order queries that have been proposed for set semantics. One of them cannot be adapted to bags, as it relies on the intractable maxima of occurrences, but another scheme only deals with minima, and we show how to adapt it to bag semantics without losing efficiency.

scholarly journals Best Answers over Incomplete Data : Complexity and First-Order Rewritings

2019 ◽  
Author(s):  
Amélie Gheerbrant ◽  
Cristina Sirangelo
Keyword(s):  
Incomplete Data ◽  
Decision Problem ◽  
Possible Worlds ◽  
Query Answering ◽  
Query Rewriting ◽  
Conjunctive Queries ◽  
First Order ◽  
Database Technology ◽  
Practical Algorithm ◽  
Certain Answers

Answering queries over incomplete data is ubiquitous in data management and in many AI applications that use query rewriting to take advantage of relational database technology. In these scenarios one lacks full information on the data but queries still need to be answered with certainty. The certainty aspect often makes query answering unfeasible except for restricted classes, such as unions of conjunctive queries. In addition often there are no, or very few certain answers, thus expensive computation is in vain. Therefore we study a relaxation of certain answers called best answers. They are defined as those answers for which there is no better one (that is, no answer true in more possible worlds). When certain answers exist the two notions coincide. We compare different ways of casting query answering as a decision problem and characterise its complexity for first-order queries, showing significant differences in the behavior of best and certain answers.We then restrict attention to best answers for unions of conjunctive queries and produce a practical algorithm for finding them based on query rewriting techniques.

scholarly journals Conservative Intensional Extension of Tarski's Semantics

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Zoran Majkić
Keyword(s):  
Free Algebra ◽  
Possible Worlds ◽  
Order Logic ◽  
Point Of View ◽  
Relational Algebra ◽  
First Order Logic ◽  
Cylindric Algebras ◽  
Possible World ◽  
Logic Formula ◽  
First Order

We considered an extension of the first-order logic (FOL) by Bealer's intensional abstraction operator. Contemporary use of the term “intension” derives from the traditional logical Frege-Russell doctrine that an idea (logic formula) has both an extension and an intension. Although there is divergence in formulation, it is accepted that the “extension” of an idea consists of the subjects to which the idea applies, and the “intension” consists of the attributes implied by the idea. From the Montague's point of view, the meaning of an idea can be considered as particular extensions in different possible worlds. In the case of standard FOL, we obtain a commutative homomorphic diagram, which is valid in each given possible world of an intensional FOL: from a free algebra of the FOL syntax, into its intensional algebra of concepts, and, successively, into an extensional relational algebra (different from Cylindric algebras). Then we show that this composition corresponds to the Tarski's interpretation of the standard extensional FOL in this possible world.

scholarly journals Query Rewriting for Ontology-Mediated Conditional Answers

2020 ◽  
Vol 34 (03) ◽  
pp. 2734-2741 ◽  
Author(s):  
Medina Andresel ◽  
Magdalena Ortiz ◽  
Mantas Simkus
Keyword(s):  
Incomplete Data ◽  
Domain Knowledge ◽  
Query Rewriting ◽  
Data Complexity ◽  
World Assumptions ◽  
Worst Case ◽  
First Order ◽  
Case Complexity ◽  
Open World ◽  
Worst Case Complexity

Among many solutions for extracting useful answers from incomplete data, ontology-mediated queries (OMQs) use domain knowledge to infer missing facts. We propose an extension of OMQs that allows us to make certain assumptions—for example, about parts of the data that may be unavailable at query time, or costly to query—and retrieve conditional answers, that is, tuples that become certain query answers when the assumptions hold. We show that querying in this powerful formalism often has no higher worst-case complexity than in plain OMQs, and that these queries are first-order rewritable for DL-Liteℛ. Rewritability is preserved even if we allow some use of closed predicates to combine the (partial) closed- and open-world assumptions. This is remarkable, as closed predicates are a very useful extension of OMQs, but they usually make query answering intractable in data complexity, even in very restricted settings.

scholarly journals Knowledge-Preserving Certain Answers for SQL-like Queries

2020 ◽  
Author(s):  
Etienne Toussaint ◽  
Paolo Guagliardo ◽  
Leonid Libkin
Keyword(s):  
Information Content ◽  
Data Model ◽  
Incomplete Data ◽  
Relational Databases ◽  
Missing Values ◽  
A Priori ◽  
Real Life ◽  
Query Languages ◽  
Incomplete Databases ◽  
Certain Answers

Answering queries over incomplete data is based on finding answers that are certainly true, independently of how missing values are interpreted. This informal description has given rise to several different mathematical definitions of certainty. To unify them, a framework based on "explanations", or extra information about incomplete data, was recently proposed. It partly succeeded in justifying query answering methods for relational databases under set semantics, but had two major limitations. First, it was firmly tied to the set data model, and a fixed way of comparing incomplete databases with respect to their information content. These assumptions fail for real-life database queries in languages such as SQL that use bag semantics instead. Second, it was restricted to queries that only manipulate data, while in practice most analytical SQL queries invent new values, typically via arithmetic operations and aggregation. To leverage our understanding of the notion of certainty for queries in SQL-like languages, we consider incomplete databases whose information content may be enriched by additional knowledge. The knowledge order among them is derived from their semantics, rather than being fixed a priori. The resulting framework allows us to capture and justify existing notions of certainty, and extend these concepts to other data models and query languages. As natural applications, we provide for the first time a well-founded definition of certain answers for the relational bag data model and for value-inventing queries on incomplete databases, addressing the key shortcomings of previous approaches.

scholarly journals Derivative-Free King’s Scheme for Multiple Zeros of Nonlinear Functions

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1242
Author(s):  
Ramandeep Behl ◽  
Sonia Bhalla ◽  
Eulalia Martínez ◽  
Majed Aali Alsulami
Keyword(s):  
Iterative Methods ◽  
Fourth Order ◽  
Order Of Convergence ◽  
Real Life ◽  
Multiple Roots ◽  
Computational Results ◽  
Nonlinear Functions ◽  
First Order ◽  
Life Problems ◽  
Derivative Free

There is no doubt that the fourth-order King’s family is one of the important ones among its counterparts. However, it has two major problems: the first one is the calculation of the first-order derivative; secondly, it has a linear order of convergence in the case of multiple roots. In order to improve these complications, we suggested a new King’s family of iterative methods. The main features of our scheme are the optimal convergence order, being free from derivatives, and working for multiple roots (m≥2). In addition, we proposed a main theorem that illustrated the fourth order of convergence. It also satisfied the optimal Kung–Traub conjecture of iterative methods without memory. We compared our scheme with the latest iterative methods of the same order of convergence on several real-life problems. In accordance with the computational results, we concluded that our method showed superior behavior compared to the existing methods.

Personal Information as Symmetry Breaker in Disagreements

Philosophy ◽  
2021 ◽  
pp. 1-20
Author(s):  
Diego E. Machuca
Keyword(s):  
Personal Information ◽  
Conscious Experience ◽  
Real Life ◽  
Cognitive Capacities ◽  
First Order ◽  
Natural Reaction ◽  
Epistemic Standing

Abstract When involved in a disagreement, a common reaction is to tell oneself that, given that the information about one's own epistemic standing is clearly superior in both amount and quality to the information about one's opponent's epistemic standing, one is justified in one's confidence that one's view is correct. In line with this natural reaction to disagreement, some contributors to the debate on its epistemic significance have claimed that one can stick to one's guns by relying in part on information about one's first-order evidence and the functioning of one's cognitive capacities. In this article, I argue that such a manoeuvre to settle controversies encounters the problem that both disputants can make use of it, the problem that one may be wrong about one's current conscious experience, and the problem that it is a live possibility that many of one's beliefs are the product of epistemically distorting factors. I also argue that, even if we grant that personal information is reliable, when it comes to real-life rather than idealized disagreements, the extent of the unpossessed information about one's opponent's epistemic standing provides a reason for doubting that personal information can function as a symmetry breaker.

scholarly journals Computing possible and certain answers over order-incomplete data

2019 ◽  
Vol 797 ◽  
pp. 42-76
Author(s):  
Antoine Amarilli ◽  
Mouhamadou Lamine Ba ◽  
Daniel Deutch ◽  
Pierre Senellart
Keyword(s):  
Incomplete Data ◽  
Certain Answers

UCQ-Rewritings for disjunctive knowledge and queries with negated atoms

Semantic Web ◽  
2020 ◽  
pp. 1-25
Author(s):  
Enrique Matos Alfonso ◽  
Alexandros Chortaras ◽  
Giorgos Stamou
Keyword(s):  
Incomplete Data ◽  
Knowledge Bases ◽  
Query Answering ◽  
Query Rewriting ◽  
Conjunctive Queries

In this paper, we study the problem of query rewriting for disjunctive existential rules. Query rewriting is a well-known approach for query answering on knowledge bases with incomplete data. We propose a rewriting technique that uses negative constraints and conjunctive queries to remove the disjunctive components of disjunctive existential rules. This process eventually generates new non-disjunctive rules, i.e., existential rules. The generated rules can then be used to produce new rewritings using existing rewriting approaches for existential rules. With the proposed technique we are able to provide complete UCQ-rewritings for union of conjunctive queries with universally quantified negation. We implemented the proposed algorithm in the Completo system and performed experiments that evaluate the viability of the proposed solution.

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