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.
In this paper, we argue that the resolution of anaphoric expressions in an utterance is essentially an abductive task following [12] who use a weighted abduction scheme on horn clauses to deal with reference. We give a semantic representation for utterances containing anaphora that enables us to compute possible antecedents by abductive inference. We extend the disjunctive model construction procedure of hyper tableaux [3, 14] with a clause transformation turning the abductive task into a model generation problem and show the completeness of this transformation with respect to the computation of abductive explanations. This abductive inference is applied to the resolution of anaphoric expressions in our general model constructing framework for incremental discourse representation which we argue to be useful for computing information updates from natural language utterances. This paper describes the First-Order Form (FOF) and Clause Normal Form (CNF) parts of the TPTP problem library, and the associated infrastructure. TPTP v3.5.0 was the last release containing only FOF and CNF problems, and thus serves as the exemplar. This paper summarizes the history and development of the TPTP, describes the structure and contents of the TPTP, and gives an overview of TPTP related projects and tools.