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.
The termination proofs we do are related to the notion of in programs @cite_17 , however Liberal Safety requires either specific acyclicity conditions (which are absent in our encodings), or conditions on finiteness of the domain of certain attributes of the external atom (that our Skolemization atoms do not fulfill). Hence we had to prove termination without using Liberal Safety.
@cite_17
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Answer set programs with external source access may introduce new constants that are not present in the program, which is known as value invention. As naive value invention leads to programs with infinite grounding and answer sets, syntactic safety criteria are imposed on programs. However, traditional criteria are in many cases unnecessarily strong and limit expressiveness. We present liberal domain-expansion (de-) safe programs, a novel generic class of answer set programs with external source access that has a finite grounding and allows for value invention. De-safe programs use so-called term bounding functions as a parameter for modular instantiation with concrete--e.g., syntactic or semantic or both--safety criteria. This ensures extensibility of the approach in the future. We provide concrete instances of the framework and develop an operator that can be used for computing a finite grounding. Finally, we discuss related notions of safety from the literature, and show that our approach is strictly more expressive.