  Weakly-Sticky(WS) Datalog+/- is an expressive member of the family of
Datalog+/- program classes that is defined on the basis of the conditions of
stickiness and weak-acyclicity. Conjunctive query answering (QA) over the WS
programs has been investigated, and its tractability in data complexity has
been established. However, the design and implementation of practical QA
algorithms and their optimizations have been open. In order to fill this gap,
we first study Sticky and WS programs from the point of view of the behavior of
the chase procedure. We extend the stickiness property of the chase to that of
generalized stickiness of the chase (GSCh) modulo an oracle that selects (and
provides) the predicate positions where finitely values appear during the
chase. Stickiness modulo a selection function S that provides only a subset of
those positions defines sch(S), a semantic subclass of GSCh. Program classes
with selection functions include Sticky and WS, and another syntactic class
that we introduce and characterize, namely JWS, of jointly-weakly-sticky
programs, which contains WS. The selection functions for these last three
classes are computable, and no external, possibly non-computable oracle is
needed. We propose a bottom-up QA algorithm for programs in the class sch(S),
for a general selection function S. As a particular case, we obtain a
polynomial-time QA algorithm for JWS and weakly-sticky programs. Unlike WS, JWS
turns out to be closed under magic-sets query optimization. As a consequence,
both the generic polynomial-time QA algorithm and its magic-set optimization
can be particularized and applied to WS.
