Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
126 tokens/sec
GPT-4o
47 tokens/sec
Gemini 2.5 Pro Pro
43 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
47 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

On Propositional Dynamic Logic and Concurrency (2403.18508v2)

Published 27 Mar 2024 in cs.LO

Abstract: Dynamic logic in the setting of concurrency has proved problematic because of the challenge of capturing interleaving. This challenge stems from the fact that the operational semantics for programs considered in these logics is tailored on trace reasoning for sequential programs. In this work, we generalise propositional dynamic logic (PDL) to a logic framework we call operational propositional dynamic logic (OPDL) in which we are able to reason on sets of programs provided with arbitrary operational semantics. We prove cut-elimination and adequacy of a sequent calculus for PDL and we extend these results to OPDL. We conclude by discussing OPDL for Milner's CCS and Choreographic Programming.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (69)
  1. Matteo Acclavio and Davide Catta. 2023. Lorenzen-Style Strategies as Proof-Search Strategies. In Multi-Agent Systems, Vadim Malvone and Aniello Murano (Eds.). Springer Nature Switzerland, Cham, 150–166.
  2. Infinitary cut-elimination via finite approximations. CoRR abs/2308.07789 (2023). https://doi.org/10.48550/ARXIV.2308.07789 arXiv:2308.07789
  3. Infinitary cut-elimination via finite approximations. arXiv:2308.07789 [cs.LO]
  4. Structural Operational Semantics. In Handbook of Process Algebra, Jan A. Bergstra, Alban Ponse, and Scott A. Smolka (Eds.). North-Holland / Elsevier, 197–292. https://doi.org/10.1016/B978-044482830-9/50021-7
  5. The algorithmics of bisimilarity. Cambridge University Press, 100–172.
  6. Jean-Marc Andreoli. 1992. Logic programming with focusing proofs in linear logic. Journal of logic and computation 2, 3 (1992), 297–347.
  7. Infinitary Proof Theory: the Multiplicative Additive Case. In 25th EACSL Annual Conference on Computer Science Logic, CSL 2016, August 29 - September 1, 2016, Marseille, France (LIPIcs, Vol. 62), Jean-Marc Talbot and Laurent Regnier (Eds.). Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 42:1–42:17. https://doi.org/10.4230/LIPIcs.CSL.2016.42
  8. Mario Benevides. 2017. Bisimilar and logically equivalent programs in PDL with parallel operator. Theoretical Computer Science 685 (2017), 23–45. https://doi.org/10.1016/j.tcs.2017.02.037 Logical and Semantic Frameworks with Applications.
  9. Mario R.F. Benevides and L. Menasché Schechter. 2010. A Propositional Dynamic Logic for Concurrent Programs Based on the π𝜋\piitalic_π-Calculus. Electronic Notes in Theoretical Computer Science 262 (2010), 49–64. https://doi.org/10.1016/j.entcs.2010.04.005 Proceedings of the 6th Workshop on Methods for Modalities (M4M-6 2009).
  10. Comparing Recursion, Replication, and Iteration in Process Calculi. In Automata, Languages and Programming, Josep Díaz, Juhani Karhumäki, Arto Lepistö, and Donald Sannella (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 307–319.
  11. Luís Caires and Frank Pfenning. 2010. Session Types as Intuitionistic Linear Propositions. In CONCUR 2010 - Concurrency Theory, 21th International Conference, CONCUR 2010, Paris, France, August 31-September 3, 2010. Proceedings (Lecture Notes in Computer Science, Vol. 6269), Paul Gastin and François Laroussinie (Eds.). Springer, 222–236. https://doi.org/10.1007/978-3-642-15375-4_16
  12. An Overview of the mCRL2 Toolset and Its Recent Advances. In Tools and Algorithms for the Construction and Analysis of Systems - 19th International Conference, TACAS 2013, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2013, Rome, Italy, March 16-24, 2013. Proceedings (Lecture Notes in Computer Science, Vol. 7795), Nir Piterman and Scott A. Smolka (Eds.). Springer, 199–213. https://doi.org/10.1007/978-3-642-36742-7_15
  13. Modular Compilation for Higher-Order Functional Choreographies. In 37th European Conference on Object-Oriented Programming, ECOOP 2023, July 17-21, 2023, Seattle, Washington, United States (LIPIcs, Vol. 263), Karim Ali and Guido Salvaneschi (Eds.). Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 7:1–7:37. https://doi.org/10.4230/LIPICS.ECOOP.2023.7
  14. Reasoning About Choreographic Programs. In Coordination Models and Languages (Lecture Notes in Computer Science, Vol. 13908), Sung-Shik Jongmans and Antónia Lopes (Eds.). Springer, 144–162. https://doi.org/10.1007/978-3-031-35361-1_8
  15. Luís Cruz-Filipe and Fabrizio Montesi. 2017. Procedural Choreographic Programming. In Formal Techniques for Distributed Objects, Components, and Systems - 37th IFIP WG 6.1 International Conference, FORTE 2017, Held as Part of the 12th International Federated Conference on Distributed Computing Techniques, DisCoTec 2017, Neuchâtel, Switzerland, June 19-22, 2017, Proceedings (Lecture Notes in Computer Science, Vol. 10321), Ahmed Bouajjani and Alexandra Silva (Eds.). Springer, 92–107. https://doi.org/10.1007/978-3-319-60225-7_7
  16. A Formal Theory of Choreographic Programming. Journal of Automated Reasoning 67, 21 (2023), 1–34. https://doi.org/10.1007/s10817-023-09665-3
  17. Anupam Das and Marianna Girlando. 2022a. Cyclic Proofs, Hypersequents, and Transitive Closure Logic. arXiv:2205.08616 [cs.LO]
  18. Anupam Das and Marianna Girlando. 2022b. Cyclic Proofs, Hypersequents, and Transitive Closure Logic. In Automated Reasoning, Jasmin Blanchette, Laura Kovács, and Dirk Pattinson (Eds.). Springer International Publishing, Cham, 509–528.
  19. Anupam Das and Marianna Girlando. 2023. Cyclic Hypersequent System for Transitive Closure Logic. Journal of Automated Reasoning 67, 3 (2023), 27. https://doi.org/10.1007/s10817-023-09675-1
  20. Applied Choreographies. In Formal Techniques for Distributed Objects, Components, and Systems - 38th IFIP WG 6.1 International Conference, FORTE 2018, Held as Part of the 13th International Federated Conference on Distributed Computing Techniques, DisCoTec 2018, Madrid, Spain, June 18-21, 2018, Proceedings (Lecture Notes in Computer Science, Vol. 10854), Christel Baier and Luís Caires (Eds.). Springer, 21–40. https://doi.org/10.1007/978-3-319-92612-4_2
  21. Choral: Object-oriented Choreographic Programming. ACM Trans. Program. Lang. Syst. 46, 1, Article 1 (Jan. 2024), 59 pages. https://doi.org/10.1145/3632398
  22. Jean-Yves Girard. 1987. Linear logic. Theoretical Computer Science 50, 1 (1987), 1–101. https://doi.org/10.1016/0304-3975(87)90045-4
  23. Jean-Yves Girard. 1998. Light Linear Logic. Information and Computation 143, 2 (1998), 175–204. https://doi.org/10.1006/inco.1998.2700
  24. Proofs and types. Vol. 7. Cambridge university press Cambridge.
  25. Jan Friso Groote and Frits W. Vaandrager. 1992. Structured Operational Semantics and Bisimulation as a Congruence. Inf. Comput. 100, 2 (1992), 202–260. https://doi.org/10.1016/0890-5401(92)90013-6
  26. Dynamic Logic. Springer Netherlands, Dordrecht, 99–217. https://doi.org/10.1007/978-94-017-0456-4_2
  27. Propositional dynamic logic of nonregular programs. J. Comput. System Sci. 26, 2 (1983), 222–243.
  28. D. Harel and R. Sherman. 1985. Propositional dynamic logic of flowcharts. Information and Control 64, 1 (1985), 119–135. https://doi.org/10.1016/S0019-9958(85)80047-4 International Conference on Foundations of Computation Theory.
  29. David Harel and Eli Singerman. 1996. More on nonregular PDL: Finite models and Fibonacci-like programs. information and computation 128, 2 (1996), 109–118.
  30. Don’t care non-determinism in logic program refinement. Electronic Notes in Theoretical Computer Science 61 (2002), 101–121.
  31. Brian Hill and Francesca Poggiolesi. 2010. A Contraction-free and Cut-free Sequent Calculus for Propositional Dynamic Logic. Studia Logica 94, 1 (2010), 47–72. https://doi.org/10.1007/s11225-010-9224-z
  32. Andrew K. Hirsch and Deepak Garg. 2022. Pirouette: higher-order typed functional choreographies. Proc. ACM Program. Lang. 6, POPL (2022), 1–27. https://doi.org/10.1145/3498684
  33. Introduction to automata theory, languages, and computation. Acm Sigact News 32, 1 (2001), 60–65.
  34. John E Hoperoft and Jeffrey D Ullman. 1979. Introduction to automata theory, languages, and computation. Addison-Welsey, NY (1979).
  35. Xiao Jun Chen and Rocco De Nicola. 2001. Algebraic characterizations of trace and decorated trace equivalences over tree-like structures. Theoretical Computer Science 254, 1 (2001), 337–361. https://doi.org/10.1016/S0304-3975(99)00300-X
  36. Kleene Algebra with Observations. In 30th International Conference on Concurrency Theory, CONCUR 2019, August 27-30, 2019, Amsterdam, the Netherlands (LIPIcs, Vol. 140), Wan J. Fokkink and Rob van Glabbeek (Eds.). Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 41:1–41:16. https://doi.org/10.4230/LIPICS.CONCUR.2019.41
  37. Dexter Kozen. 1996. Kleene algebra with tests and commutativity conditions. In Tools and Algorithms for the Construction and Analysis of Systems, Tiziana Margaria and Bernhard Steffen (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 14–33.
  38. Dexter Kozen. 1997. Kleene Algebra with Tests. ACM Trans. Program. Lang. Syst. 19, 3 (1997), 427–443. https://doi.org/10.1145/256167.256195
  39. Dexter Kozen and Rohit Parikh. 1981. An elementary proof of the completeness of PDL. Theoretical Computer Science 14, 1 (1981), 113–118. https://doi.org/10.1016/0304-3975(81)90019-0
  40. Dexter C Kozen. 2007. Automata and computability. Springer Science & Business Media.
  41. Yves Lafont. 2004. Soft linear logic and polynomial time. Theoretical computer science 318, 1-2 (2004), 163–180.
  42. Martin Lange. 2003. Games for modal and temporal logics. (2003).
  43. Chuck Liang and Dale Miller. 2021. Focusing Gentzen’s LK proof system. (Nov. 2021). https://hal.science/hal-03457379 working paper or preprint.
  44. John W Lloyd. 2012. Foundations of logic programming. Springer Science & Business Media.
  45. Alain J. Mayer and Larry J. Stockmeyer. 1996. The complexity of PDL with interleaving. Theoretical Computer Science 161, 1 (1996), 109–122. https://doi.org/10.1016/0304-3975(95)00095-X
  46. Damiano Mazza. 2006. Linear logic and polynomial time. Mathematical Structures in Computer Science 16, 6 (2006), 947–988. https://doi.org/10.1017/S0960129506005688
  47. Damiano Mazza. 2015. Simple Parsimonious Types and Logarithmic Space. In 24th EACSL Annual Conference on Computer Science Logic, CSL 2015 (LIPIcs, Vol. 41). Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 24–40. https://doi.org/10.4230/LIPIcs.CSL.2015.24
  48. Damiano Mazza and Kazushige Terui. 2015. Parsimonious Types and Non-uniform Computation. In Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Kyoto, Japan, July 6-10, 2015, Proceedings, Part II (Lecture Notes in Computer Science, Vol. 9135), Magnús M. Halldórsson, Kazuo Iwama, Naoki Kobayashi, and Bettina Speckmann (Eds.). Springer, 350–361. https://doi.org/10.1007/978-3-662-47666-6_28
  49. Uniform proofs as a foundation for logic programming. Annals of Pure and Applied Logic 51, 1 (1991), 125–157. https://doi.org/10.1016/0168-0072(91)90068-W
  50. Robin Milner. 1980. A Calculus of Communicating Systems. Lecture Notes in Computer Science, Vol. 92. Springer. https://doi.org/10.1007/3-540-10235-3
  51. A calculus of mobile processes, I. Information and Computation 100, 1 (1992), 1–40. https://doi.org/10.1016/0890-5401(92)90008-4
  52. Fabrizio Montesi. 2013. Choreographic Programming. Ph.D. Thesis. IT University of Copenhagen. https://www.fabriziomontesi.com/files/choreographic-programming.pdf.
  53. Fabrizio Montesi. 2023. Introduction to Choreographies. Cambridge University Press. https://doi.org/10.1017/9781108981491
  54. Damian Niwiński and Igor Walukiewicz. 1996. Games for the μ𝜇\muitalic_μ-calculus. Theoretical Computer Science 163, 1 (1996), 99–116. https://doi.org/10.1016/0304-3975(95)00136-0
  55. Object Management Group. 2011. Business Process Model and Notation. http://www.omg.org/spec/BPMN/2.0/.
  56. Michel Parigot. 1992. λ𝜆\lambdaitalic_λμ𝜇\muitalic_μ-Calculus: An algorithmic interpretation of classical natural deduction. In Logic Programming and Automated Reasoning, Andrei Voronkov (Ed.). Springer Berlin Heidelberg, Berlin, Heidelberg, 190–201.
  57. David Peleg. 1987a. Communication in concurrent dynamic logic. J. Comput. System Sci. 35, 1 (1987), 23–58. https://doi.org/10.1016/0022-0000(87)90035-3
  58. David Peleg. 1987b. Concurrent dynamic logic. J. ACM 34, 2 (apr 1987), 450–479. https://doi.org/10.1145/23005.23008
  59. David Peleg. 1987c. Concurrent program schemes and their logics. Theoretical Computer Science 55, 1 (1987), 1–45. https://doi.org/10.1016/0304-3975(87)90088-0
  60. V. R. Pratt. 1982. Using graphs to understand PDL. In Logics of Programs, Dexter Kozen (Ed.). Springer Berlin Heidelberg, Berlin, Heidelberg, 387–396.
  61. Davide Sangiorgi and David Walker. 2001. The Pi-Calculus - a theory of mobile processes. Cambridge University Press.
  62. A Complete Inference System for Skip-free Guarded Kleene Algebra with Tests. In Programming Languages and Systems - 32nd European Symposium on Programming, ESOP 2023, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2023, Paris, France, April 22-27, 2023, Proceedings (Lecture Notes in Computer Science, Vol. 13990), Thomas Wies (Ed.). Springer, 309–336. https://doi.org/10.1007/978-3-031-30044-8_12
  63. HasChor: Functional Choreographic Programming for All (Functional Pearl). Proc. ACM Program. Lang. 7, ICFP (2023), 541–565. https://doi.org/10.1145/3607849
  64. Colin Stirling and David Walker. 1991. Local model checking in the modal mu-calculus. Theoretical Computer Science 89, 1 (1991), 161–177.
  65. Thomas Studer. 2008. On the Proof Theory of the Modal mu-Calculus. Studia Logica: An International Journal for Symbolic Logic 89, 3 (2008), 343–363. http://www.jstor.org/stable/40268983
  66. A. S. Troelstra and H. Schwichtenberg. 2000. Basic Proof Theory (2 ed.). Cambridge University Press. https://doi.org/10.1017/CBO9781139168717
  67. R. J. van Glabbeek. 1990. The linear time - branching time spectrum. In CONCUR ’90 Theories of Concurrency: Unification and Extension, J. C. M. Baeten and J. W. Klop (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 278–297.
  68. W3C. 2004. WS Choreography Description Language. http://www.w3.org/TR/ws-cdl-10/.
  69. Philip Wadler. 2015. Propositions as types. Commun. ACM 58, 12 (2015), 75–84. https://doi.org/10.1145/2699407
Citations (3)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now