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Proof-Carrying Plans: a Resource Logic for AI Planning [article]

Alasdair Hill, Ekaterina Komendantskaya, Ronald P. A. Petrick
2020 pre-print
In this paper, we present a novel resource logic, the Proof Carrying Plans (PCP) logic that can be used to verify plans produced by AI planners.  ...  From the practical perspective, we present a complete Agda formalisation of the PCP logic and of its soundness proof.  ...  We thank EPSRC DTA PhD Scheme for funding the first author.  ... 
doi:10.1145/3414080.3414094 arXiv:2008.04165v1 fatcat:nbjidbuvjnahjm2erpgoraau6e

On linear logic planning and concurrency

Ozan Kahramanoğulları
2009 Information and Computation  
We present an approach to linear logic planning where an explicit correspondence between partial order plans and multiplicative exponential linear logic proofs is established.  ...  Relying on this fact, we argue that this work is a crucial step for establishing a common language for concurrency and planning that will allow to carry techniques and methods between these two fields.  ...  Acknowledgments The author would like to thank Alessio Guglielmi, Steffen Hölldobler, Luca Cardelli, Max Kanovich and anonymous referees for valuable comments and improvements.  ... 
doi:10.1016/j.ic.2009.02.008 fatcat:zsj3ooi2ejdbjmwhbgvqeum6le

Let's plan it deductively!

W. Bibel
1998 Artificial Intelligence  
The paper describes a transition logic, TL, and a deductive formalism for it.  ...  (The deductive formalism for) TL extends the linear connection method proposed earlier by the author by embedding the latter into classical logic, so that classical and resource-sensitive reasoning coexist  ...  The author is indebted to his students and collaborators for their continuing support.  ... 
doi:10.1016/s0004-3702(98)00064-2 fatcat:d23xyfi57ve2lk4aw2hgkiulhm

Generating plans in linear logic

M. Masseron, C. Tollu, J. Vauzeilles
1993 Theoretical Computer Science  
We think that these attempts, though promising, miss their objectives, for a lack of a suitable logic, and that the effort must be pursued.  ...  In this paper, we show how to obtain a strong and clean correspondence between proofs and sequences of actions by using only Girard's linear logic, eliminating from the classical logic the structural rules  ...  Acknowledgment We are deeply indebted to Jean-Yves Girard for having encouraged us to attack the problem.  ... 
doi:10.1016/0304-3975(93)90007-g fatcat:hl3q4gavqjapjlkt42j6g7qlwu

Knowledge-based proof planning

Erica Melis, Jörg Siekmann
1999 Artificial Intelligence  
This outline, i.e., the abstract proof plan, can be recursively expanded and it will thus construct a proof within a logical calculus.  ...  Knowledge-based proof planning is a new paradigm in automated theorem proving (ATP) which swings the motivational pendulum back to its AI origins in that it employs and further develops many AI principles  ...  Last but not least we thank my students Carsten Ullrich and Jürgen Zimmer who implemented much of the knowledge-based proof planning and kept abreast of the many changes of the MEGA system while this work  ... 
doi:10.1016/s0004-3702(99)00076-4 fatcat:f4ux6wsnvnaf3eipgpvrot7tme

Actions You Can Handle: Dependent Types for AI Plans [article]

Alasdair Hill, Ekaterina Komendantskaya, Matthew L. Daggitt, Ronald P. A. Petrick
2021 arXiv   pre-print
plans, and also provides a more holistic programming language infrastructure for modelling plan execution.  ...  This paper proposes a methodology for embedding plans produced by AI planners into dependently-typed language Agda, which enables users to reason about and verify more general and abstract properties of  ...  The authors also thank the TyDe'21 reviewers for their valuable input, which lead to substantial clarification and simplifaction of some of the code accompanying this paper.  ... 
arXiv:2105.11267v2 fatcat:4dyoouzo6rci3glbbyfw35d5wi

Planning Agents [chapter]

John L. Pollock
1999 Applied Logic Series  
Although it is a start, the planner described above should be viewed as a proof of concept for the idea of planning by reasoning rather than as a solution to the problem of building a truly sophisticated  ...  a discussion of the logic of the reasoning involved in the comparison. 9 See Weld[1994] for a general discussion of least commitment planning. must decide precisely how and when to do it.  ...  Planning separately for the different conjuncts of a conjunctive goal is accomplished by using the following backwards-reason: (def-backwards-reason SPLIT-CONJUNCTIVE-GOAL :conclusions "(plan-for plan&  ... 
doi:10.1007/978-94-015-9204-8_4 fatcat:unctri2rcravla7xwapxm7fo5a

Encoding of Planning Problems and Their Optimizations in Linear Logic [chapter]

Lukáš Chrpa, Pavel Surynek, Jiří Vyskočil
2009 Lecture Notes in Computer Science  
Girard's Linear Logic is a formalism which can be used to manage a lot of problems with consumable resources. Its expressiveness is quite good for an easily understandable encoding of many problems.  ...  We concentrated on expressing planning problems by linear logic in this paper. We observed a rich usage of a construct of consumable resources in planning problem formulations.  ...  Acknowledgements We thank the reviewers for the comments.  ... 
doi:10.1007/978-3-642-00675-3_4 fatcat:yykw6lzx6jajrppkmhrw6e7rbm

Planning control rules for reactive agents

F. Kabanza, M. Barbeau, R. St-Denis
1997 Artificial Intelligence  
A traditional approach for planning is to evaluate goal statements over state trajectories modeling predicted behaviors of an agent.  ...  We describe goals by using a modal temporal logic that can express quite complex time, safety, and liveness constraints.  ...  A proof of this theorem is given in Appendix A.3. Theorem 12. Extracting a reactive plan Formalizing a process for extracting a reactive plan from such paths requires some definitions.  ... 
doi:10.1016/s0004-3702(97)00031-3 fatcat:a5btk23nbnda7bc54nwwp7nomi

Predictive Control, Competitive Model Business Planning, and Innovation ERP

Cyrus F. Nourani, Codrina Lauth
2015 Procedia Computer Science  
Systemic decisions are based on common organizational goals, and as such business planning and resource assignments should strive to satisfy higher organizational goals.  ...  The paper starts with introducing a systems approach to business modeling. A competitive business modeling technique, based on the author's planning techniques is applied.  ...  That part of the plan that involves free Skolemized trees [39, 40] is carried along with the proof tree for a plan goal.  ... 
doi:10.1016/j.procs.2015.09.048 fatcat:x73t2cfxdfd6hdoa5dqbjyr6eq

Relaxed Exists-Step Plans in Planning as SMT

Miquel Bofill, Joan Espasa, Mateu Villaret
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
In this paper we introduce a new encoding for planning as SMT, which adheres to the relaxed relaxed ∃-step (R 2 ∃-step) semantics for parallel plans.  ...  Under this setting, planning as SAT is generalized to planning as SMT.  ...  We would like to thank the reviewers for their constructive comments and the observations regarding Constraint (5) of the encoding. We also thank Dr. Alan Frisch for his helpful comments.  ... 
doi:10.24963/ijcai.2017/79 dblp:conf/ijcai/BofillEV17 fatcat:og7mqelxfndi5fndbcmsycgfge

Recent Advances in AI Planning

Daniel S. Weld
1999 The AI Magazine  
search can find a plan.  ...  normal form formulas for solution using systematic or stochastic SAT methods.  ...  Because this article requires minimal AI background (for example, simple logic and basic search algorithms), it's suitable for a wide audience, but my treatment is not exhaustive because I don't have the  ... 
doi:10.1609/aimag.v20i2.1459 dblp:journals/aim/Weld99 fatcat:wdc3oslle5h4dlvzwhp65ku6va

Universal Planning: An (Almost) Universally Bad Idea

Matthew L. Ginsberg
1989 The AI Magazine  
I Proof. The proof is just a matter of count- argue that this approach is only viable for ing.  ...  multivalued logics, modal logics, real-time problem 2.  ... 
doi:10.1609/aimag.v10i4.964 dblp:journals/aim/Ginsberg89 fatcat:4ikqh2nbffghvivuawdm5qnvga

Planning under Incomplete Knowledge [chapter]

Thomas Eiter, Wolfgang Faber, Nicola Leone, Gerald Pfeifer, Axel Polleres
2000 Lecture Notes in Computer Science  
We propose a new declarative planning language, called K, which is based on principles and methods of logic programming.  ...  Our results form the theoretical basis for the DLV K system, which implements the language K on top of the DLV logic programming system.  ...  Smith, and Dan Weld for kindly supplying explanations, support, and comments on the systems that we used for comparison.  ... 
doi:10.1007/3-540-44957-4_54 fatcat:faywdkcyujhklpxdphwdewyg24

Strong planning under uncertainty in domains with numerous but identical elements (a generic approach)

Max Kanovich, Jacqueline Vauzeilles
2007 Theoretical Computer Science  
As a result, AI planners are very sensitive to the number of the variables involved in making a plan, the inherent symmetry of the problem, and the nature of the logical formalisms being used.  ...  This paper shows that linear logic provides a convenient and adequate tool for representing strong and weak planning problems in non-deterministic domains.  ...  For further reading [7, 9, 10, 17, 34] .  ... 
doi:10.1016/j.tcs.2007.01.022 fatcat:knpq53nvjbf77dqu6x5zjngztq
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