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When is naı̈ve evaluation possible?
 IN ACM SYMPOSIUM ON PRINCIPLES OF DATABASE SYSTEMS (PODS)
, 2013
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Naı̈ve Evaluation of Queries over Incomplete Databases
"... The term näıve evaluation refers to evaluating queries over incomplete databases as if nulls were usual data values, i.e., to using the standard database query evaluation engine. Since the semantics of query answering over incomplete databases is that of certain answers, we would like to know when ..."
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The term näıve evaluation refers to evaluating queries over incomplete databases as if nulls were usual data values, i.e., to using the standard database query evaluation engine. Since the semantics of query answering over incomplete databases is that of certain answers, we would like to know when näıve evaluation computes them: i.e., when certain answers can be found without inventing new specialized algorithms. For relational databases it is well known that unions of conjunctive queries possess this desirable property, and results on preservation of formulae under homomorphisms tell us that within relational calculus, this class cannot be extended under the openworld assumption. Our goal here is twofold. First, we develop a general framework that allows us to determine, for a given semantics of incompleteness, classes of queries for which näıve evaluation computes certain answers. Second, we apply this approach to a variety of semantics, showing that for many classes of queries beyond unions of conjunctive queries, näıve evaluation makes perfect sense under assumptions different from openworld. Our key observations are: (1) näıve evaluation is equivalent to monotonicity of queries with respect to a semanticsinduced ordering, and (2) for most reasonable semantics of incompleteness, such monotonicity is captured by preservation under various types of homomorphisms. Using these results we find classes of queries for which näıve evaluation works, e.g., positive firstorder formulae for the closedworld semantics.
Representing and Querying Incomplete Information: a Data Interoperability Perspective
, 2014
"... This thesis is intended to be a succinct and rather informal presentation of some of my most recent work, which has been done in collaboration with several other people. In particular this thesis concentrates on our contributions to the study of incomplete information in the context of data interope ..."
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This thesis is intended to be a succinct and rather informal presentation of some of my most recent work, which has been done in collaboration with several other people. In particular this thesis concentrates on our contributions to the study of incomplete information in the context of data interoperability. In this scenario data is heterogenous and decentralized, needs to be integrated from several sources and exchanged between different applications. Incompleteness, i.e. the presence of “missing” or “unknown” portions of data, is naturally generated in data exchange and integration, due to data heterogeneity. The management of incomplete information poses new challenges in this context. The focus of our study is the development of models of incomplete information suitable to data interoperability tasks, and the study of techniques for efficiently querying several forms of incompleteness. The work presented in Chapter 4 is ongoing in the context of Nadime Francis’s PhD, whom I am cosupervising together with Luc Segoufin.
Finitely Presentable Morphisms in . . .
, 2010
"... ... is short exact, we show that 1) K is finitely generated ⇔ c is finitely presentable; 2) k is finitely presentable ⇔ C is finitely presentable. The “⇐ ” directions fail for semiabelian varieties. We show that all but (possibly) 2)(⇐) follow from analogous properties which hold in all locally fin ..."
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... is short exact, we show that 1) K is finitely generated ⇔ c is finitely presentable; 2) k is finitely presentable ⇔ C is finitely presentable. The “⇐ ” directions fail for semiabelian varieties. We show that all but (possibly) 2)(⇐) follow from analogous properties which hold in all locally finitely presentable categories. As for 2)(⇐), it holds as soon as K is also cohomological, and all its strong epimorphisms are regular. Finally, locally finitely coherent (resp. noetherian) abelian categories are characterized as those for which all finitely presentable morphisms have finitely generated (resp. presentable) kernel objects.
Finitely Presentable Morphisms in . . .
, 2010
"... ... is short exact, we show that 1) K is finitely generated ⇔ c is finitely presentable; 2) k is finitely presentable ⇔ C is finitely presentable. The “⇐ ” directions fail for semiabelian varieties. We show that all but (possibly) 2)(⇐) follow from analogous properties which hold in all locally fin ..."
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... is short exact, we show that 1) K is finitely generated ⇔ c is finitely presentable; 2) k is finitely presentable ⇔ C is finitely presentable. The “⇐ ” directions fail for semiabelian varieties. We show that all but (possibly) 2)(⇐) follow from analogous properties which hold in all locally finitely presentable categories. As for 2)(⇐), it holds as soon as K is also cohomological, and all its strong epimorphisms are regular. Finally, locally finitely coherent (resp. noetherian) abelian categories are characterized as those for which all finitely presentable morphisms have finitely generated (resp. presentable) kernel objects.
1 Relative computability and uniform continuity of relations
, 2013
"... Abstract: A type2 computable real function is necessarily continuous; and this remains true for computations relative to any oracle. Conversely, by the Weierstrass Approximation Theorem, every continuous f: [0; 1] → R is computable relative to some oracle. In their search for a similar topological ..."
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Abstract: A type2 computable real function is necessarily continuous; and this remains true for computations relative to any oracle. Conversely, by the Weierstrass Approximation Theorem, every continuous f: [0; 1] → R is computable relative to some oracle. In their search for a similar topological characterization of relatively computable multivalued functions f: [0; 1] ⇒ R (also known as multifunctions or relations), Brattka and Hertling (1994) have considered two notions: weak continuity (which is weaker than relative computability) and strong continuity (which is stronger than relative computability). Observing that uniform continuity plays a crucial role in the Weierstrass Theorem, we propose and compare several notions of uniform continuity for relations. Here, due to the additional quantification over values y ∈ f (x), new ways arise of (linearly) ordering quantifiers—yet none turns out as satisfactory. We are thus led to a concept of uniform continuity based on the Henkin quantifier; and prove it necessary for relative computability of compact real relations. In fact iterating this condition yields a strict hierarchy of notions each necessary — and the ωth level also sufficient — for relative computability. A refined, quantitative analysis exhibits a similar topological characterization of relative polynomialtime computability.