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Eliminating Unfounded Set Checking for HEX-Programs [article]

Thomas Eiter, Michael Fink, Thomas Krennwallner, Christoph Redl, and Peter Schüller
2013 arXiv   pre-print
Developing native solvers for HEX-programs based on an appropriate notion of unfounded sets has been subject to recent research for reasons of efficiency.  ...  Moreover, we develop criteria for decomposing a program into components, such that the search for unfounded sets can be restricted.  ...  In this scenario, the decision criterion eliminates all unfounded set checks.  ... 
arXiv:1301.1390v1 fatcat:2gorw6xdorfzrcuefloyuqr4t4

Exploiting Unfounded Sets for HEX-Program Evaluation [chapter]

Thomas Eiter, Michael Fink, Thomas Krennwallner, Christoph Redl, Peter Schüller
2012 Lecture Notes in Computer Science  
We thus extend an approach based on unfounded sets to HEX and integrate it in a Conflict Driven Clause Learning framework for HEX program evaluation.  ...  It reduces the check to a search for unfounded sets, which is more efficiently implemented as a SAT problem. We give a basic encoding for HEX and show optimizations by additional clauses.  ...  Starting from this idea, we define unfounded sets for HEX-programs following [11] and explore their efficiency for FLP checking.  ... 
doi:10.1007/978-3-642-33353-8_13 fatcat:i5nti3lmr5hz5kuhbnukkpk55i

Efficient HEX-Program Evaluation Based on Unfounded Sets

T. Eiter, M. Fink, T. Krennwallner, C. Redl, P. Schüller
2014 The Journal of Artificial Intelligence Research  
To this end, we present an approach based on unfounded sets as a generalization of related techniques for ASP programs.  ...  HEX-programs extend logic programs under the answer set semantics with external computations through external atoms.  ...  We are grateful to the anonymous reviewers for their helpful and constructive comments.  ... 
doi:10.1613/jair.4175 fatcat:hcxe3ullanbztaafzxk6g6ekie

Answer Set Programming with External Sources

Christoph Redl, Marc Herbstritt
2012 International Conference on Logic Programming  
To this end, HEX-programs are an extension and generalization of answer set programs by external sources which can be tightly coupled to the reasoner.  ...  They attracted my interest and supported my decision for doing my theses in the area of answer set programming.  ...  Lemma 3.7 (EA-Input Unfoundedness). Let U be an unfounded set of Π wrt. an assignment A.  ... 
doi:10.4230/lipics.iclp.2012.469 dblp:conf/iclp/Redl12 fatcat:2yxyy6gqzrforanlqayak5cvxq

On Equivalence and Inconsistency of Answer Set Programs with External Sources

Christoph Redl
2017 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
for sets R of facts.  ...  HEX-programs extend of answer-set programs (ASP) with ex-ternal sources. In previous work, notions of equivalence ofASP programs under extensions have been developed.  ...  For a HEX-program P and a model A of P , a set of atoms U is an unfounded set of P wrt. A iff A \ U |= fP A .  ... 
doi:10.1609/aaai.v31i1.10671 fatcat:lob4bz67fjeshpexcwpebfdkrm

Technical Report: Inconsistency in Answer Set Programs and Extensions [article]

Christoph Redl
2018 arXiv   pre-print
In this work we consider inconsistent ASP- and HEX-programs, i.e., programs without answer sets.  ...  The second application is a new evaluation algorithm for HEX-programs based on conflict-driven learning for programs with multiple components: while for certain program classes previous techniques suffer  ...  But then adding c R to u to u does not eliminate answer sets since u∪facts(F ) is inconsistent anyway. Proposition 18 A model M of a HEX-program P is an answer set of P iff it is unfounded-free.  ... 
arXiv:1806.00119v1 fatcat:gtivh7eg3rbabencjzeyv5yjri

Conflict-driven ASP solving with external sources

THOMAS EITER, MICHAEL FINK, THOMAS KRENNWALLNER, CHRISTOPH REDL
2012 Theory and Practice of Logic Programming  
To enable access to external information,hex-programs extend programs withexternal atoms, which allow for a bidirectional communication between the logic program and external sources of computation (e.g  ...  AbstractAnswer Set Programming (ASP) is a well-known problem solving approach based on nonmonotonic logic programs and efficient solvers.  ...  In this case, a final unfounded set check is necessary due to disjunctive heads. If the candidate is founded, it is an answer set.  ... 
doi:10.1017/s1471068412000233 fatcat:hbeuim23yzhd7kw3vlruoubl34

Inlining External Sources in Answer Set Programs

CHRISTOPH REDL
2019 Theory and Practice of Logic Programming  
The traditional evaluation algorithm for hex-programs is based on guessing truth values of external atoms and verifying them by explicit calls of the external source.  ...  Besides performance improvements, we further exploit inlining for extending previous (semantic) characterizations of program equivalence from ASP to hex-programs, including those of strong equivalence,  ...  Support sets were previously exploited for HEX-program evaluation ); however, this was only for speeding up but not for eliminating the necessary verification step.  ... 
doi:10.1017/s147106841800056x fatcat:dhywmhrekrb4tbayu2eajn4jza

Exploiting Partial Assignments for Efficient Evaluation of Answer Set Programs with External Source Access

Thomas Eiter, Tobias Kaminski, Christoph Redl, Antonius Weinzierl
2018 The Journal of Artificial Intelligence Research  
And third, to make a necessary minimality check of candidate answer sets more efficient by exploiting early external evaluation calls.  ...  To address the needs of modern applications, HEX-programs were introduced as an extension of ASP with external atoms for accessing information outside programs via an API style bi-directional interface  ...  To discard the non-answer sets, the evaluation algorithm calls an FLP check which uses unfounded sets to check minimality wrt. f Π A [Eiter et al., 2014a] . Example 2 (cont'd).  ... 
doi:10.1613/jair.1.11221 fatcat:sbm4cn67tvckfhg22hcty5i6wy

Evaluation Techniques and Systems for Answer Set Programming: a Survey

Martin Gebser, Nicola Leone, Marco Maratea, Simona Perri, Francesco Ricca, Torsten Schaub
2018 Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence  
Answer set programming (ASP) is a prominent knowledge representation and reasoning paradigm that found both industrial and scientific applications.  ...  For solving a program P which is not-Head-Cycle-Free (non-HCF), i.e. where checking whether a model of P is ⊆-minimal w.r.t.  ...  for computing answer sets.  ... 
doi:10.24963/ijcai.2018/769 dblp:conf/ijcai/GebserLMPRS18 fatcat:g5iryltonjegveigyx4mobuzua

Answer Set Programming with External Source Access [chapter]

Thomas Eiter, Tobias Kaminski, Christoph Redl, Peter Schüller, Antonius Weinzierl
2017 Lecture Notes in Computer Science  
Access to external information is an important need for Answer Set Programming (ASP), which is a booming declarative problem solving approach these days.  ...  such as logic programs with generalized quantifiers [38] , and later to dlv-ex programs [18] and the more expressive HEX programs [42] .  ...  We also thank Roland Kaminski and Torsten Schaub for comments regarding Clingo.  ... 
doi:10.1007/978-3-319-61033-7_7 fatcat:cvtqcxldljag3kimdtmqy5jori

Conflict-driven ASP Solving with External Sources and Program Splits

Christoph Redl
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
While program splitting techniques allow for eliminating exhaustive pre-grounding, they prohibit effective conflict-driven solving.  ...  HEX-programs extend ASP with external atoms for access to arbitrary external sources, which can also introduce constants that do not appear in the program (value invention).  ...  HEX-Programs.  ... 
doi:10.24963/ijcai.2017/172 dblp:conf/ijcai/Redl17 fatcat:p2f6tcso5zge7psbvpx47fhrb4

A Uniform Integration of Higher-Order Reasoning and External Evaluations in Answer-Set Programming

Thomas Eiter, Giovambattista Ianni, Roman Schindlauer, Hans Tompits
2005 International Joint Conference on Artificial Intelligence  
We introduce HEX programs, which are nonmonotonic logic programs admitting higher-order atoms as well as external atoms, and we extend the wellknown answer-set semantics to this class of programs.  ...  Through external atoms, HEX programs can model some important extensions to ASP, and are a useful KR tool for expressing various applications.  ...  Λ can still be applied to eliminate higher-order atoms from a HEX program P , and a similar correspondence holds.  ... 
dblp:conf/ijcai/EiterIST05 fatcat:ilvfyo7lrrc3ro34ozu5w576cq

A model building framework for answer set programming with external computations

THOMAS EITER, MICHAEL FINK, GIOVAMBATTISTA IANNI, THOMAS KRENNWALLNER, CHRISTOPH REDL, PETER SCHÜLLER
2015 Theory and Practice of Logic Programming  
To cater for this need,hexprograms were designed as a generalization of answer set programs with an API style interface that allows to access arbitrary external sources, providing great flexibility.  ...  We present a new approach for the evaluation of logic programs with external source access, which is based on a configurable framework for dividing the non-ground program into possibly overlapping smaller  ...  for programs with aggregates as it eliminates unintuitive answer sets.  ... 
doi:10.1017/s1471068415000113 fatcat:kq5ya4rvbnhxdd7adsmhyfj32e

Answer Set Programming [chapter]

Piero Bonatti, Francesco Calimeri, Nicola Leone, Francesco Ricca
2010 Lecture Notes in Computer Science  
Answer Set Programming (ASP), referred to also as Disjunctive Logic Programming under the stable model semantics (DLP), is a powerful formalism for Knowledge Representation and Reasoning.  ...  The Italian logic programming community has been very active in this area, some ASP results achieved in Italy are widely recognized as milestones on the road to the current state of the art.  ...  In a disjunctive logic program P, the union of unfounded sets for P may not be an unfounded set for P; thus, the existence of the greatest unfounded set (i.e., an unfounded set that contains all other  ... 
doi:10.1007/978-3-642-14309-0_8 fatcat:m7vjxp43qfbgjpujf7ozr72x5q
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