Eugénie Foustoucos

Developing query patterns

Query patterns enable effective information tools and provide guidance to users interested in posing complex questions about objects. Semantically, query patterns represent important questions, while syntactically they impose the correct formulation of queries. In this paper we address the development of query patterns at successive representation layers so as to expose dominant information requirements on one hand, and structures that can support effective user interaction and efficient implementation of query processing on the other. An empirical study for the domain of cultural heritage reveals an initial set of recurrent questions, which are then reduced to a modestly sized set of query patterns. A set of Datalog rules is developed in order to formally define these patterns which are also expressed as SPARQL queries.

Datalog programs and their persistency numbers

The relation between Datalog programs and homomorphism problems and between Datalog programs and bounded treewidth structures has been recognized for some time and given much attention recently. Additionally, the essential role of persistent variables (of program expansions) in solving several relevant problems has also started to be observed. It turns out that to understand the contribution of these persistent variables to the difficulty of some expressibility problems, we need to understand the interrelationship among different notions of persistency numbers, some of which we introduce and/or formalize in the present work.This article is a first foundational study of the various persistency numbers and their interrelationships. To prove the relations among these persistency numbers, we had to develop some nontrivial technical tools that promise to help in proving other interesting results too. More precisely, we define the adorned dependency graph of a program, a useful tool for visualizing sets of persistent variables, and we define automata that recognize persistent sets in expansions.We start by elaborating on finer definitions of expansions and queries, which capture aspects of homomorphism problems on bounded treewidth structures. The main results of this article are (a) a program transformation technique, based on automata-theoretic tools, which manipulates persistent variables (leading, in certain cases, to programs of fewer persistent variables); (b) a categorization of the different roles of persistent variables; this is done by defining four notions of persistency numbers which capture the propagation of persistent variables from a syntactical level to a semantical one; (c) decidability results concerning the syntactical notions of persistency numbers that we have defined; and (d) the exhibition of new classes of programs for which boundedness is undecidable.

On temporal logic versus datalog

We provide a direct and modular translation from the temporal logics CTL, ETL, FCTL (CTL extended with the ability to express fairness) and the Modal µ-calculus to Monadic inf-Datalog with built-in predicates. We call it inf-Datalog because the semantics we provide is a little different from the conventional Datalog least fixed point semantics, in that some recursive rules (corresponding to least fixed points) are allowed to unfold only finitely many times, whereas others (corresponding to greatest fixed points) are allowed to unfold infinitely many times.We characterize the fragments of Monadic inf-Datalog that have the same expressive power as Modal Logic (resp. CTL, alternation-free Modal µ-calculus and Modal µ-calculus). Our translation is interesting because it is direct and succinct. Moreover the fragments of Monadic inf-Datalog that we have exhibited have very simple syntactic characterizations as subsets of what we call Modal inf-Datalog programs.

From CTL to datalog

We provide a translation from CTL to DatalogSucc. The translation has the following advantages: a) It is natural. b) It provides intuition to the expressive power of CTL and its various fragments. c) It uses a fragment of DatalogSucc which is close to the expressive power of CTL.

Undecidability and intractability results concerning datalog programs and their persistency numbers

The relation between Datalog programs and homomorphism problems, and, between Datalog programs and bounded treewidth structures has been recognized for some time and given much attention recently. Additionally, the essential role of persistent variables (in program expansions) for solving several relevant problems has also started to be observed. In Afrati et al. [2005] the general notion of program persistencies was refined into four notions (two syntactical ones and two semantical ones) and the interrelationship between these four persistency numbers was studied. In the present article (1) we prove undecidability results concerning the semantical notions of persistency number--modulo equivalence, of persistency number and of characteristic integer, (2) we exhibit new classes of programs for which boundedness is undecidable and (3) we prove intractabiltity results concerning the syntactical notions of weak persistency number and of weak characteristic integer.