Papers
Topics
Authors
Recent
Search
2000 character limit reached

Finite Groundings for ASP with Functions: A Journey through Consistency

Published 8 May 2024 in cs.AI and cs.LO | (2405.15794v1)

Abstract: Answer set programming (ASP) is a logic programming formalism used in various areas of artificial intelligence like combinatorial problem solving and knowledge representation and reasoning. It is known that enhancing ASP with function symbols makes basic reasoning problems highly undecidable. However, even in simple cases, state of the art reasoners, specifically those relying on a ground-and-solve approach, fail to produce a result. Therefore, we reconsider consistency as a basic reasoning problem for ASP. We show reductions that give an intuition for the high level of undecidability. These insights allow for a more fine-grained analysis where we characterize ASP programs as "frugal" and "non-proliferous". For such programs, we are not only able to semi-decide consistency but we also propose a grounding procedure that yields finite groundings on more ASP programs with the concept of "forbidden" facts.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (28)
  1. The Disjunctive Datalog System DLV. In Oege de Moor, Georg Gottlob, Tim Furche, and Andrew Jon Sellers, editors, Datalog Reloaded - First International Workshop, Datalog 2010, Oxford, UK, March 16-19, 2010. Revised Selected Papers, volume 6702 of Lecture Notes in Computer Science, pages 282–301. Springer, 2010.
  2. Function Symbols in ASP: Overview and Perspectives. 2012.
  3. Enumeration of Minimal Models and MUSes in WASP. In LPNMR, volume 13416 of Lecture Notes in Computer Science, pages 29–42. Springer, 2022.
  4. Clingcon: The next generation. Theory Pract. Log. Program., 17(4):408–461, 2017.
  5. lpopt: A Rule Optimization Tool for Answer Set Programming. Fundamenta Informaticae, 177(3-4):275–296, 2020.
  6. Handbook of Satisfiability, volume 185 of Frontiers in Artificial Intelligence and Applications. IOS Press, 2009.
  7. Answer set programming at a glance. Communications of the ACM, 54(12):92–103, 2011.
  8. A uniform treatment of aggregates and constraints in hybrid ASP. In KR, pages 193–202, 2020.
  9. Computable functions in ASP: theory and implementation. In Maria Garcia de la Banda and Enrico Pontelli, editors, Logic Programming, 24th International Conference, ICLP 2008, Udine, Italy, December 9-13 2008, Proceedings, volume 5366 of Lecture Notes in Computer Science, pages 407–424. Springer, 2008.
  10. I-DLV: the new intelligent grounder of DLV. Intelligenza Artificiale, 11(1):5–20, 2017.
  11. Complexity and expressive power of logic programming. ACM Comput. Surv., 33(3):374–425, September 2001.
  12. Adding disjunction to datalog (extended abstract). In PODS ’94, pages 267–278, New York, NY, USA, 1994. Assoc. Comput. Mach., New York.
  13. Complexity results for answer set programming with bounded predicate arities and implications. 51(2-4):123–165, 2007.
  14. Simulating sets in answer set programming. In Luc De Raedt, editor, Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence, IJCAI 2022, Vienna, Austria, 23-29 July 2022, pages 2634–2640. ijcai.org, 2022.
  15. Solution enumeration for projected boolean search problems. In CPAIOR’09, volume 5547, pages 71–86, 2009.
  16. Answer Set Solving in Practice. Morgan & Claypool, 2012.
  17. Multi-shot ASP solving with clingo. Theory Pract. Log. Program., 19(1):27–82, 2019.
  18. David Harel. Effective transformations on infinite trees, with applications to high undecidability, dominoes, and fairness. J. ACM, 33(1):224–248, 1986.
  19. Estimating grounding sizes of logic programs under answer set semantics. In JELIA, volume 12678, pages 346–361. Springer, 2021.
  20. T. Janhunen and I. Niemelä. The answer set programming paradigm. AI Magazine, 37(3):13–24, 2016.
  21. Clingo goes linear constraints over reals and integers. Theory Pract. Log. Program., 17(5-6):872–888, 2017.
  22. On the foundations of grounding in answer set programming. CoRR, abs/2108.04769, 2021.
  23. Propositional logic: deduction and algorithms. Cambridge University Press, Cambridge, 1999.
  24. Effectively Reasoning about Infinite Sets in Answer Set Programming. In Marcello Balduccini and Tran Cao Son, editors, Logic Programming, Knowledge Representation, and Nonmonotonic Reasoning: Essays Dedicated to Michael Gelfond on the Occasion of His 65th Birthday, Lecture Notes in Computer Science, pages 131–147. Springer, Berlin, Heidelberg, 2011.
  25. Autoepistemic logic. J. of the ACM, 38(3):588–619, 1991.
  26. The Stable Models of a Predicate Logic Program. The Journal of Logic Programming, 21(3):129–154, November 1994.
  27. Hartley Rogers, Jr. Theory of recursive functions and effective computability (Reprint from 1967). MIT Press, 1987.
  28. Advancing Lazy-Grounding ASP Solving Techniques - Restarts, Phase Saving, Heuristics, and More. Theory Pract. Log. Program., 20(5):609–624, 2020.

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Collections

Sign up for free to add this paper to one or more collections.

Sign Up

Tweets

Sign up for free to view the 2 tweets with 0 likes about this paper.

Sign Up for Free