{"type":"ScholarlyArticle","title":"Guarantees for Sound Abstractions for Generalized Planning","authors":[{"name":"Blai Bonet","slug":"blai-bonet","given":"Blai","family":"Bonet","affiliation":"Universidad Simón Bolívar , Venezuela; Universidad Carlos III de Madrid , Spain"},{"name":"Raquel Fuentetaja","slug":"raquel-fuentetaja","given":"Raquel","family":"Fuentetaja","affiliation":"Universidad Carlos III de Madrid , Spain"},{"name":"Yolanda E-Martín","slug":"yolanda-e-martin","given":"Yolanda","family":"E-Martín","affiliation":"Universidad Carlos III de Madrid , Spain"},{"name":"Daniel Borrajo","slug":"daniel-borrajo","given":"Daniel","family":"Borrajo","affiliation":"Universidad Carlos III de Madrid , Spain"}],"abstract":"Generalized planning is about finding plans that solve collections of planning instances, often infinite collections, rather than single instances. Recently it has been shown how to reduce the planning problem for generalized planning to the planning problem for a qualitative numerical problem; the latter being a reformulation that simultaneously captures all the instances in the collection. An important thread of research thus consists in finding such reformulations, or abstractions, automatically. A recent proposal learns the abstractions inductively from a finite and small sample of transitions from instances in the collection. However, as in all inductive processes, the learned abstraction is not guaranteed to be correct for the whole collection. In this work we address this limitation by performing an analysis of the abstraction with respect to the collection, and show how to obtain formal guarantees for generalization. These guarantees, in the form of first-order formulas, may be used to 1) define subcollections of instances on which the abstraction is guaranteed to be sound, 2) obtain necessary conditions for generalization under certain assumptions, and 3) do automated synthesis of complex invariants for planning problems. Our framework is general, it can be extended or combined with other approaches, and it has applications that go beyond generalized planning.","doi":"10.24963/ijcai.2019/217","url":"https://ijcai.org/proceedings/2019/217","pdf":"https://ijcai.org/proceedings/2019/0217.pdf","markdown":"https://ijcai.org/proceedings/2019/217.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/217","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Knowledge Representation and Reasoning","track":"Main track","number":217,"pages":{"first":1566,"last":1573},"keywords":["Planning and Scheduling: Other approaches to planning","Knowledge Representation and Reasoning: Action, Change and Causality","Agent-based and Multi-agent Systems: Formal Verification, Validation and Synthesis","Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving"],"videos":[],"references":[{"position":1,"raw":"[Baader et al., 2003] Franz Baader, Diego Calvanese, Deb- orah McGuinness, Daniele Nardi, and Peter Patel- Schneider. The description logic handbook: Theory, im- plementation and applications. Cambridge University Press, 2003.","title":"The description logic handbook: Theory, implementation and applications","authors":"Baader","year":"2003","venue":null,"doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Belle and Levesque, 2016] Vaishak Belle and Hector J. Levesque. Foundations for generalized planning in un- bounded stochastic domains. In Proc. 15th Int. Conf. on Principles of Knowledge Representation and Reasoning, pages 380-389, 2016.","title":"Vaishak Belle and Hector J. Levesque. Foundations for generalized planning in unbounded stochastic domains","authors":"Belle, Levesque","year":"2016","venue":"Proc. 15th Int. Conf. on Principles of Knowledge Representation and Reasoning","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Bonet and Geffner, 2018] Blai Bonet and Hector Geffner. Features, projections, and representation change for gener- alized planning. In Proc. 27th Int. Joint Conf. on Artificial Intelligence, pages 4667-4673, 2018.","title":"Features, projections, and representation change for generalized planning","authors":"Geffner Bonet, Blai Bonet, Hector Geffner","year":"2018","venue":"Proc. 27th Int. Joint Conf. on Artificial Intelligence","doi":null,"url":null,"internal_url":"/proceedings/2018/649"},{"position":4,"raw":"[Bonet et al., 2017] Blai Bonet, Giuseppe De Giacomo, Hec- tor Geffner, and Sasha Rubin. Generalized planning: Non- deterministic abstractions and trajectory constraints. In Proc. 26th Int. Joint Conf. on Artificial Intelligence, pages 873-879, 2017.","title":"Generalized planning: Nondeterministic abstractions and trajectory constraints","authors":"Blai Bonet, Giuseppe De Giacomo, Hector Geffner, Sasha Rubin","year":"2017","venue":"Proc. 26th Int. Joint Conf. on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Bonet et al., 2019a] Blai Bonet, Guillem Francès, and Hec- tor Geffner. Learning features and abstract actions for computing generalized plans. In Proc. 33rd AAAI Conf. on Artificial Intelligence, 2019.","title":"Learning features and abstract actions for computing generalized plans","authors":"Bonet","year":"2019","venue":"Proc. 33rd AAAI Conf. on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Bonet et al., 2019b] Blai Bonet, Raquel Fuentetaja, Yolanda E-Martin, and Daneil Borrajo. Guarantees for sound abstractions for generalized planning (extended paper). arXiv e-prints, page arXiv:1905.12071, 2019.","title":"Guarantees for sound abstractions for generalized planning","authors":"Bonet","year":"2019","venue":null,"doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Boutilier et al., 2001] Craig Boutilier, Ray Reiter, and Bob Price. Symbolic dynamic programming for first-order MDPs. In Proc. 17th Int. Joint Conf. on Artificial Intel- ligence, pages 690-700, 2001.","title":"Symbolic dynamic programming for first-order MDPs","authors":"Craig Boutilier, Ray Reiter, Bob Price","year":"2001","venue":"Proc. 17th Int. Joint Conf. on Artificial Intelligence","doi":null,"url":null,"internal_url":"/proceedings/2001/95"},{"position":8,"raw":"[Fox and Long, 1998] Maria Fox and Derek Long. The au- tomatic inference of state invariants in TIM. Journal of Artificial Intelligence Research, 9:317-371, 1998.","title":"The automatic inference of state invariants in TIM","authors":"Maria Fox, Derek Long","year":"1998","venue":"Journal of Artificial Intelligence Research","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Geffner and Bonet, 2013] Hector Geffner and Blai Bonet. A Concise Introduction to Models and Methods for Auto- mated Planning. Morgan & Claypool Publishers, 2013.","title":"A Concise Introduction to Models and Methods for Automated Planning","authors":"Bonet Geffner, Hector Geffner, Blai Bonet","year":"2013","venue":null,"doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Gerevini and Schubert, 1998] Alfonso Gerevini and Lenhart Schubert. Inferring state constraints for domain- independent planning. In Proc. 15th Nat. Conf. on Artificial Intelligence, pages 905-912, 1998.","title":"Inferring state constraints for domainindependent planning","authors":"Alfonso Gerevini, Lenhart Schubert","year":"1998","venue":"Proc. 15th Nat. Conf. on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Helmert, 2002] Malte Helmert. Decidability and undecid- ability results for planning with numerical state variables. In Proc. 6th Int. Conf. on Artificial Intelligence Planning Systems, pages 44-53, 2002.","title":"Decidability and undecidability results for planning with numerical state variables","authors":"Malte Helmert, Helmert","year":"2002","venue":"Proc. 6th Int. Conf. on Artificial Intelligence Planning Systems","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Helmert, 2009] Malte Helmert. Concise finite-domain rep- resentations for PDDL planning tasks. Artificial Intelli- gence, 173:503-535, 2009.","title":"Concise finite-domain representations for PDDL planning tasks","authors":"Malte Helmert, Helmert","year":"2009","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Hu and De Giacomo, 2011] Yuxiao Hu and Giuseppe De Giacomo. Generalized planning: Synthesizing plans that work for multiple environments. In Proc. 22nd Int. Joint Conf. on Artificial Intelligence, pages 918-923, 2011.","title":"Generalized planning: Synthesizing plans that work for multiple environments","authors":"De Hu, ; Yuxiao Giacomo, Giuseppe Hu, Giacomo De","year":"2011","venue":"Proc. 22nd Int. Joint Conf. on Artificial Intelligence","doi":null,"url":null,"internal_url":"/proceedings/2011/159"},{"position":14,"raw":"[van Otterlo, 2012] Martijn van Otterlo. Solving relational and first-order logical markov decision processes: A sur- vey. In M. Wiering and M. van Otterlo, editors, Reinforce- ment Learning, pages 253-292. Springer, 2012.","title":"Solving relational and first-order logical markov decision processes: A survey","authors":"Martijn Van Otterlo","year":"2012","venue":"Reinforcement Learning","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Rintanen, 2000] Jussi Rintanen. An iterative algorithm for synthesizing invariants. In Proc. 17th Nat. Conf. on Artifi- cial Intelligence, pages 806-811, 2000.","title":"An iterative algorithm for synthesizing invariants","authors":"Jussi Rintanen","year":"2000","venue":"Proc. 17th Nat. Conf. on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Rintanen, 2008] Jussi Rintanen. Regression for classical and nondeterministic planning. In Proc. 18th European Conf. on Artificial Intelligence, pages 568-572, 2008.","title":"Jussi Rintanen. Regression for classical and nondeterministic planning","authors":"Rintanen","year":"2008","venue":"Proc. 18th European Conf. on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Segovia et al., 2016] Javier Segovia, Sergio Jiménez, and Anders Jonsson. Generalized planning with procedural do- main control knowledge. In Proc. 26nd Int. Conf. on Au- tomated Planning and Scheduling, pages 285-293, 2016.","title":"Generalized planning with procedural domain control knowledge","authors":"Segovia","year":"2016","venue":"Proc. 26nd Int. Conf. on Automated Planning and Scheduling","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Slind and Norrish, 2008] Konrad Slind and Michael Nor- rish. A brief overview of HOL4. In Proc. 21st Int. Conf. on Theorem Proving in Higher Order Logics (TPHOLs), volume LNCS 5170, pages 28-32, 2008.","title":"A brief overview of HOL4","authors":"Norrish Slind, Konrad Slind, Michael Norrish","year":"2008","venue":"Proc. 21st Int. Conf. on Theorem Proving in Higher Order Logics (TPHOLs)","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Srivastava et al., 2008] Siddarth Srivastava, Neil Immer- man, and Shlomo Zilberstein. Learning generalized plans using abstract counting. In Proc. 23rd AAAI Conf. on Ar- tificial Intelligence, pages 991-997, 2008.","title":"Learning generalized plans using abstract counting","authors":"Siddarth Srivastava, Neil Immerman, Shlomo Zilberstein","year":"2008","venue":"Proc. 23rd AAAI Conf. on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Srivastava et al., 2011a] Siddarth Srivastava, Neil Immer- man, and Shlomo Zilberstein. A new representation and associated algorithms for generalized planning. Artificial Intelligence, 175(2):615-647, 2011.","title":"a] Siddarth Srivastava, Neil Immerman, and Shlomo Zilberstein. A new representation and associated algorithms for generalized planning","authors":"Srivastava","year":"2011","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Srivastava et al., 2011b] Siddarth Srivastava, Shlomo Zil- berstein, Neil Immerman, and Hector Geffner. Qualitative numeric planning. In Proc. 25th AAAI Conf. on Artificial Intelligence, pages 1010-1016, 2011.","title":"Qualitative numeric planning","authors":"Srivastava","year":"2011","venue":"Proc. 25th AAAI Conf. on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Vardi, 1982] Moshe Y. Vardi. The complexity of relational query languages. In Proc. 14th Annual ACM Symp. on Theory of Computing (STOC), pages 137-146, 1982.","title":"The complexity of relational query languages","authors":"Moshe Y Vardi","year":"1982","venue":"Proc. 14th Annual ACM Symp. on Theory of Computing (STOC)","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Wang et al., 2008] Chenggang Wang, Saket Joshi, and Roni Khardon. First order decision diagrams for relational MDPs. Journal of Artificial Intelligence Research, 31:431-472, 2008.","title":"First order decision diagrams for relational MDPs","authors":"Chenggang Wang, Saket Joshi, Roni Khardon","year":"2008","venue":"Journal of Artificial Intelligence Research","doi":null,"url":null,"internal_url":"/proceedings/2007/177"}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}