  Answer Set Programming (ASP) is a logic-based knowledge representation
framework, supporting---among other reasoning modes---the central task of query
answering. In the propositional case, query answering amounts to computing
cautious consequences of the input program among the atoms in a given set of
candidates, where a cautious consequence is an atom belonging to all stable
models. Currently, the most efficient algorithms either iteratively verify the
existence of a stable model of the input program extended with the complement
of one candidate, where the candidate is heuristically selected, or introduce a
clause enforcing the falsity of at least one candidate, so that the solver is
free to choose which candidate to falsify at any time during the computation of
a stable model. This paper introduces new algorithms for the computation of
cautious consequences, with the aim of driving the solver to search for stable
models discarding more candidates. Specifically, one of such algorithms
enforces minimality on the set of true candidates, where different notions of
minimality can be used, and another takes advantage of unsatisfiable cores
computation. The algorithms are implemented in WASP, and experiments on
benchmarks from the latest ASP competitions show that the new algorithms
perform better than the state of the art. (Under consideration for acceptance
in TPLP).
