Learnability of Solutions to Conjunctive Queries: The Full Dichotomy
نویسندگان
چکیده
The problem of learning the solution space of an unknown formula has been studied in multiple embodiments in computational learning theory. In this article, we study a family of such learning problems; this family contains, for each relational structure, the problem of learning the solution space of an unknown conjunctive query evaluated on the structure. A progression of results aimed to classify the learnability of each of the problems in this family, and thus far a culmination thereof was a positive learnability result generalizing all previous ones. This article completes the classification program towards which this progression of results strived, by presenting a negative learnability result that complements the mentioned positive learnability result. In order to obtain our negative result, we make use of universal-algebraic concepts, and our result is phrased in terms of the varietal property of non-congruence modularity.
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