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On the Dynamic Logic of Agency and Action

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Abstract

We present a Hilbert style axiomatization and an equational theory for reasoning about actions and capabilities. We introduce two novel features in the language of propositional dynamic logic, converse as backwards modality and abstract processes specified by preconditions and effects, written as \({\varphi \Rightarrow \psi}\) and first explored in our recent paper (Hartonas, Log J IGPL Oxf Univ Press, 2012), where a Gentzen-style sequent calculus was introduced. The system has two very natural interpretations, one based on the familiar relational semantics and the other based on type semantics, where action terms are interpreted as types of actions (sets of binary relations). We show that the proof systems do not distinguish between the two kinds of semantics, by completeness arguments. Converse as backwards modality together with action types allow us to produce a new purely equational axiomatization of Dynamic Algebras, where iteration is axiomatized independently of box and where the fixpoint and Segerberg induction axioms are derivable. The system also includes capabilities operators and our results provide then a finitary Hilbert-style axiomatization and a decidable system for reasoning about agent capabilities, missing in the KARO framework.

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References

  1. Carbone, M., K. Honda, N. Yoshida, R. Milner, G. Brown and S. Ross- Talbot, A theoretical basis of communication-based concurrent programming, http://www.w3.org/2002/ws/chor/edcopies/theory/note.pdf.

  2. Erol K., Hendler J., Nau D. S.: Complexity results for HTN planning. Annals of Mathematics and Artificial Intelligence 18, 69–93 (1996)

    Article  Google Scholar 

  3. Harel D., Kozen D., Tiuryn J.: Dynamic Logic, Foundations of Computing Series. MIT Press, Cambridge (2000)

    Google Scholar 

  4. Hartonas C.: Duality for modal μ-logics. Theoretical Computer Science 201, 193–222 (1998)

    Article  Google Scholar 

  5. Hartonas, C., Reasoning about types of action and agent capabilities, Logic Journal of the IGPL, Oxford University Press, Oxford (in print, published electronically in November 2012).

  6. Kozen D.: Kleene algebra with tests. ACM Transactions on Programming Languages and Systems 19, 427–443 (1997)

    Article  Google Scholar 

  7. Kozen, D., On Kleene algebras and closed semirings, in Proceedings of the Mathematical Foundations of Computer Science, vol 452 of Lecture Notes in Computer Science, Springer, Berlin, 1990, pp. 26–47.

  8. Kozen, D., On action algebras, in J. van Eijck and A. Visser (eds.), Logic and Information Flow, MIT Press, Cambridge, 1994, pp. 78–88.

  9. Martin, D., et al, OWL-S: Semantic markup for web services, http://www.w3.org/Submission/OWL-S/#5, 2004.

  10. Pratt, V., Dynamic algebras: examples, constructions, applications, Technical Report MIT/LCS/TM-138, M.I.T Laboratory for Computer Science, July 1979.

  11. Pratt, V., Dynamic algebras and the nature of induction, in STOC’80, Proceedings of the Twelfth Annual ACM Symposium on Theory of Computing, pp. 22–28, 1980.

  12. Pratt, V., Dynamic algebras as a well-behaved fragment of relation algebras, Algebraic Logic and Universal Algebra in Computer Science, 77–110, 1988.

  13. Pratt, V., Action logic and pure induction, in Proceedings of the JELIA 1990, LNCS, vol 478, Springer, Berlin, 1991, pp. 97–120.

  14. Rao, A., and M. Georgeff, Modeling rational agents within a bdi-architecture, in Principles of Knowledge Representation and Reasoning: Proceedings of the Second International Conference—KR 91, 1991, pp. 473–484.

  15. Rao, A., and M. Georgeff, Bdi agents: from theory to practice, in Proceedings of the First International Conference on Multi-agent Systems—ICMAS 95, San Francisco, USA, 1995.

  16. van der Hoek, W., and M. Wooldridge, Towards a logic of rational agency, Logic Journal of the IGPL 11(2):133–157, March 2003.

    Google Scholar 

  17. van der Hoek, W., B. van Linder, and J. J. Ch. Meyer, A logic of capabilities, in A. Nerode and Y. Matiyasevich (eds.), Proceedings of the 3rd International Symposium on the Logical Foundations of Computer Science (LFCS 94), Springer, Berlin, 1994, pp. 366–378.

  18. van der Hoek, W., B. van Linder, and J. J. Ch. Meyer, An integrated modal approach to rational agents, in M. Wooldridge and A. Rao (eds.), Foundations of Rational Agency, Kluwer, Dordrecht, 1999, pp. 37–75.

  19. Wu, D., E. Sirin, J. Hendler, D. Nau, and B. Parsia, Automatic web services composition using SHOP2, in Workshop on Planning for Web Services, Trento, Italy, June 2003.

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  1. Department of Computer Science and Telecommunications, TEI Larissa, Larissa, Greece

    Chrysafis Hartonas

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  1. Chrysafis Hartonas
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Correspondence to Chrysafis Hartonas.

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Hartonas, C. On the Dynamic Logic of Agency and Action. Stud Logica 102, 441–478 (2014). https://doi.org/10.1007/s11225-013-9473-8

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