  Unsatisfiable core analysis can boost the computation of optimum stable
models for logic programs with weak constraints. However, current solvers
employing unsatisfiable core analysis either run to completion, or provide no
suboptimal stable models but the one resulting from the preliminary disjoint
cores analysis. This drawback is circumvented here by introducing a progression
based shrinking of the analyzed unsatisfiable cores. In fact, suboptimal stable
models are possibly found while shrinking unsatisfiable cores, hence resulting
into an anytime algorithm. Moreover, as confirmed empirically, unsatisfiable
core analysis also benefits from the shrinking process in terms of solved
instances. This paper is under consideration for acceptance in TPLP.
