Learnability of Solutions to Conjunctive Queries
Hubie Chen, MATTHEW A. VALERIOTE · BIROn (Birkbeck, University of London) · 2019
The problem of learning the solution space of an unknown formula has been studied inmultiple embodiments in computational learning theory. In this article, we study a familyof such learning problems; this family contains, for each relational structure, the problem oflearning the solution space of an unknown conjunctive query evaluated on the structure. Aprogression 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 previousones. This article completes the classification program towards which this progression ofresults strived, by presenting a negative learnability result that complements the mentionedpositive learnability result. In addition, a further negative learnability result is exhibited,which indicates a dichotomy within the problems to which the first negative result applies.In order to obtain our negative results, we make use of universal-algebraic concepts.