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@article{swefrkd2014-ai, abstract = {The answer set semantics presented by Faber et al. (2011) has been widely used to define so called FLP answer sets for different types of logic programs. However, it was recently observed that when being extended from normal to more general classes of logic programs, this approach may produce answer sets with circular justifications that are caused by self-supporting loops. The main reason for this behavior is that the FLP answer set semantics is not fully constructive by a bottom up construction of answer sets. In this paper, we overcome this problem by enhancing the FLP answer set semantics with a level mapping formalism such that every answer set I can be built by fixpoint iteration of a one-step provability operator (more precisely, an extended van Emden-Kowalski operator for the FLP reduct fΠ^I). This is inspired by the fact that under the standard answer set semantics, each answer set I of a normal logic program Π is obtainable by fixpoint iteration of the standard van Emden-Kowalski one-step provability operator for the Gelfond-Lifschitz reduct Π^I, which induces a level mapping. The enhanced FLP answer sets, which we call well-justified FLP answer sets, are thanks to the level mapping free of circular justifications. As a general framework, the well-justified FLP answer set semantics applies to logic programs with first-order formulas, logic programs with aggregates, description logic programs, HEX-programs etc., provided that the rule satisfaction is properly extended to such general logic programs. We study in depth the computational complexity of FLP and well-justified FLP answer sets for general classes of logic programs. Our results show that the level mapping does not increase the worst-case complexity of FLP answer sets. Furthermore, we describe an implementation of the well-justified FLP answer set semantics, and report about an experimental evaluation, which indicates a potential for performance improvements by the level mapping in practice.}, author = {Yi-Dong Shen and Kewen Wang and Thomas Eiter and Michael Fink and Christoph Redl and Thomas Krennwallner and Jun Deng}, date-added = {2014-02-03 10:24:50 +0000}, date-modified = {2014-07-31 10:45:50 +0000}, doi = {10.1016/j.artint.2014.05.001}, issn = {0004-3702}, journal = {Artificial Intelligence}, keywords = {Answer set programming, Knowledge representation, Nonmonotonic reasoning, Logic programs with first-order formulas, Level mappings, Circular justifications}, month = {August}, pages = {1--41}, projectref = {FWF-P24090}, title = {{FLP answer set semantics without circular justifications for general logic programs}}, volume = {213}, year = {2014}, bdsk-url-1 = {http://dx.doi.org/10.1016/j.artint.2014.05.001} }

@article{efkrs2014-jair, abstract = {HEX-programs extend logic programs under the answer set semantics with external computations through external atoms. As reasoning from ground Horn programs with nonmonotonic external atoms of polynomial complexity is already on the second level of the polynomial hierarchy, minimality checking of answer set candidates needs special attention. To this end, we present an approach based on unfounded sets as a generalization of related techniques for ASP programs. The unfounded set detection is expressed as a propositional SAT problem, for which we provide two different encodings and optimizations to them. We then integrate our approach into a previously developed evaluation framework for HEX-programs, which is enriched by additional learning techniques that aim at avoiding the reconstruction of the same or related unfounded sets. Furthermore, we provide a syntactic criterion that allows one to skip the minimality check in many cases. An experimental evaluation shows that the new approach significantly decreases runtime.}, author = {Thomas Eiter and Michael Fink and Thomas Krennwallner and Christoph Redl and Peter Sch{\"u}ller}, date-added = {2014-02-03 10:20:15 +0000}, date-modified = {2014-02-27 06:17:17 +0000}, doi = {10.1613/jair.4175}, issn = {1076-9757}, journal = {Journal of Artificial Intelligence Research}, keywords = {Answer Set Programming, External source access, Unfounded Sets}, month = {February}, pages = {269--321}, projectref = {FWF-P24090}, title = {{Efficient HEX-Program Evaluation based on Unfounded Sets}}, url = {http://www.jair.org/papers/paper4175.html}, volume = {49}, year = {2014}, bdsk-url-1 = {http://www.jair.org/papers/paper4175.html}, bdsk-url-2 = {http://dx.doi.org/10.1613/jair.4175} }

@inproceedings{efkr2013-inap, abstract = {HEX-programs extend ASP by external sources. In this paper, we present domain-specific existential quantifiers on top of HEX-programs, i.e., ASP programs with external access which may introduce new values that also show up in the answer sets. Pure logical existential quantification corresponds to a specific instance of our approach. Programs with existential quantifiers may have infinite groundings in general, but for specific reasoning tasks a finite subset of the grounding can suffice. We introduce a generalized grounding algorithm for such problems, which exploits domain-specific termination criteria in order to generate a finite grounding for bounded model generation. As an application we consider query answering over existential rules. In contrast to other approaches, several extensions can be naturally integrated into our approach. We further show how terms with function symbols can be handled by HEX-programs, which in fact can be seen as a specific form of existential quantification.}, author = {Thomas Eiter and Michael Fink and Thomas Krennwallner and Christoph Redl}, booktitle = {20th International Conference on Applications of Declarative Programming and Knowledge Management (INAP'13), Kiel, Germany, September 11-13, 2013}, conference = {http://www.dcc.fc.up.pt/INAP-2013/}, date = {September 11-13, 2013}, date-added = {2013-08-05 13:30:58 +0000}, date-modified = {2014-07-31 10:41:10 +0000}, doi = {10.1007/978-3-319-08909-6_7}, editor = {Michael Hanus and Ricardo Rocha}, keywords = {Answer Set Programming, External source access, Existential Quantification}, location = {Kiel, Germany}, month = {July}, pages = {99--117}, projectref = {FWF-P24090}, publisher = {Springer}, series = {LNAI}, title = {{HEX-Programs with Existential Quantification}}, volume = {8439}, year = {2014}, bdsk-url-1 = {http://www.dcc.fc.up.pt/INAP-2013/}, bdsk-url-2 = {http://dx.doi.org/10.1007/978-3-319-08909-6_7} }