Modeling Variations of First-Order Horn Abduction in Answer Set Programming

Issue title: Special issue of the 22nd RCRA International Workshop on “Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion”

Guest editors: Stefano Bistarelli, Andrea Formisano, Marco Maratea and Paolo Torroni

Article type: Research Article

Authors: Schüller, Peter^*

Affiliations: [a] Computer Engineering Department, Faculty of Engineering Marmara University, Turkey peter.schuller@marmara.edu.tr

Correspondence: [*] This work is a significant extension of [1]; major additions are preference relations coherence and weighted abduction, revised encodings, increased performance, on-demand constraints, and flexible value invention. This work has been supported by Scientific and Technological Research Council of Turkey (TUBITAK) Grant 114E777. Address for correspondence: Computer Engineering Department, Faculty of Engineering, Marmara University, Turkey

Abstract: 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-ofthe- 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.

Keywords: First Order Horn Abduction, Weighted Abduction, Answer Set Programming, Natural Language Understanding

DOI: 10.3233/FI-2016-1446

Journal: Fundamenta Informaticae, vol. 149, no. 1-2, pp. 159-207, 2016