Section: New Results
Ontological Query Answering with Rules
Participants : Jean-François Baget, Marie-Laure Mugnier, Michaël Thomazo, Michel Leclère, Eric Salvat, Mélanie König.
In collaboration with: Sebastian Rudolph (Karlsruhe Institute of Technology)
We have developed a framework based on rules that have the ability of generating unknown individuals, an ability sometimes called value invention in databases. These rules are of the form body
Building on our previous work on conceptual graphs, while meeting this new trend, we have developed a knowledge representation framework centered on existential rules, which can be seen both as logic-based and graph-based.
Entailment, hence query answering, with existential rules is not decidable, thus finding decidable classes of rules as expressive as possible is a crucial issue. We have pursued our previous work on better understanding the border between decidability and undecidability. We have also extended rule dependency to k-dependency, which takes into account sequences of rule applications.
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Results published in Artificial Intelligence Journal [13] (extending the work in [3] , [44] ); keynote talk synthesizing this work at RR'2011 [20] ; extension to k-dependency at RR'2011 [22]
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For newly exhibited decidable classes (namely, “frontier-one”, “frontier-guarded” and “weakly-frontier-guarded” rules), the problem complexity was unknown, moreover there was no algorithm for computing entailment. First, we have classified these classes with respect to combined complexity (i.e., usual complexity) with both unbounded and bounded predicate arity, and data complexity (i.e., restricting the input of the decision problem to the facts). An interesting result is that some of the new classes (namely frontier-one and frontier-guarded rules) have a polynomial time data complexity. Secondly, we have provided a generic algorithm for query entailment with a large class of rules including these classes, which is worst-case optimal for combined complexity (with or without bounded predicate arity) as well as for data complexity.
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Results partially published at IJCAI'2011 [21] . Long paper in preparation with extended complexity results and all proofs, for submission to a major artificial intelligence journal.