Modeling Variations of First-Order Horn Abduction in Answer Set
  Programming
  We study abduction in First Order Horn logic theories where all atoms can be
abduced and we are looking for preferred solutions with respect to three
objective functions: cardinality minimality, coherence, and weighted abduction.
We represent this reasoning problem in Answer Set Programming (ASP), in order
to obtain a flexible framework for experimenting with global constraints and
objective functions, and to test the boundaries of what is possible with ASP.
Realizing this problem in ASP is challenging as it requires value invention and
equivalence between certain constants, because the Unique Names Assumption does
not hold in general. To permit reasoning in cyclic theories, we formally
describe fine-grained variations of limiting Skolemization. We identify term
equivalence as a main instantiation bottleneck, and improve the efficiency of
our approach with on-demand constraints that were used to eliminate the same
bottleneck in state-of-the-art solvers. We evaluate our approach experimentally
on the ACCEL benchmark for plan recognition in Natural Language Understanding.
Our encodings are publicly available, modular, and our approach is more
efficient than state-of-the-art solvers on the ACCEL benchmark.
