Abstract
Hamblin’s Action-State Semantics provides a sound philosophical foundation for understanding the character of the imperative. Taking this as our inspiration, in this paper we present a logic of action, which we call ST, that captures the clear ontological distinction between being responsible for the achievement of a state of affairs and being responsible for the performance of an action. We argue that a relativised modal logic of type RT founded upon a ternary relation over possible worlds integrated with a basic tense logic captures intuitions of the Hamblinian model of imperatives. The logic implements a direct mapping of each of Hamblin’s key concepts: strategies, partial strategies and wholehearted satisfaction.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Åqvist, L.: 1975, A New Approach to the Logical Theory of Interrogatives, TBL Verlag Gunter Barr, Tubingen, Germany.
Aumann, R. J.: 1976, Agreeing to disagree, Annals of Statistics 4(6), 1236–1239.
Austin, J.: 1962, How to do Things with Words, Oxford University Press, London, UK.
Barringer, H., Fisher, M., Gabbay, D., Gough, G., and Owens, R.: 1995, MetateM: an introduction, Formal Aspects of Computing 7(5), 533–549.
Belnap, N. and Perloff, M.: 1988, Seeing to it that: A canonical form for agentives, Theroria 9, 175–199.
Belnap, N. and Perloff, M.: 1992, The way of the agent, Studia Logica 51(3/4), 463–484.
Belnap, N., Perloff, M., and Xu, M.: 2001, Facing the Future, Oxford University Press, London, UK.
Blackburn, P., de Rijke, M., and Venema, Y.: 2001, Modal Logic, Vol. 53 of Cambridge Tracts in Theoretical Computer Science, Cambridge University Press, Cambridge, UK.
Blum, A. L. and Furst, M. L.: 1997, Fast planning through planning graph analysis, Artificial Intelligence 90(1,2), 279–298.
Bowen, K. A.: 1979, Model Theory for Modal Logic, Reidel, Amsterdam, The Netherlands.
Chellas, B. F.: 1980, Modal Logic: An Introduction, Cambridge University Press, Cambridge, UK.
Chellas, B. F.: 1992, Time and modality in the logic of agency, Studia Logica 51(3/4), 485–517.
d’Altan, P., Meyer, J.-J. C., and Wieringa, R. J.: 1996, An integrated framework for ought-to-be and ought-to-do constraints, Artificial Intelligence and Law 4(2), 77–111.
Davidson, D.: 2001, Essays on Actions and Events, 2nd edn, Clarendon Press, Oxford.
Dignum, F. and Meyer, J.-J. C.: 1990, Negations of transactions and their use in the specification of dynamic and deontic integrity constraints, in M. Kwiatkowska, M. W. Shields, and R. M. Thomas (eds.), Semantics for Concurrency, Springer, Berlin Heidelberg New York, pp. 61–80.
Elgesem, D.: 1997, The modal logic of agency, Nordic Journal of Philosophical Logic 2(2), 1–46.
Fagin, R., Halpern, J. Y., Moses, Y., and Vardi, M. Y.: 1995, Reasoning about Knowledge, MIT Press, Cambridge, MA.
Feys, R.: 1965, Modal Logics, Louvain, E. Nauwelaerts.
Fikes, R. E. and Nilsson, N. J.: 1971, STRIPS: a new approach to the application of theorem proving to problem solving, Artificial Intelligence 2, 189–208.
Fox, M., Howey, R., and Long, D. P.: 2005, Validating plans in the context of processes and exogenous events, in Proceedings of the Twentieth National Conference on Artificial Intelligence, pp. 1151–1156.
Giunchiglia, F., Lee, J., Lifschitz, V., McCain, N., and Turner, H.: 2004, Nonmonotonic causal theories, Artificial Intelligence 153(1,2), 49–104.
Goranko, V. and Zanardo, A.: 2004, Combining linear orders with modalities for possible histories, in W. A. Carnielli, F. M. Dionísio, and P. Mateus (eds.), The Workshop on Combination of Logics: Theory and Applications (CombLog 04), Vol. 4(5). http://www.cle.unicamp.br/e-prints/vol_4,n_5,2004.html, CLE e-Prints.
Hamblin, C. L.: 1987, Imperatives, Blackwell, Oxford, UK.
Hintikka, J., Halonen, I., and Mutanen, A.: 2000, Interrogative logic as a general theory of reasoning, in R. H. Johnson and J. Woods (eds.), Handbook of Practical Reasoning, Kluwer, Dordrecht.
Horty, J. F.: 2001, Agency and Deontic Logic, Oxford University Press, London, UK.
Horty, J. F. and N. Belnap: 1995, The deliberative stit: A study of action, omission, ability, and obligation, Journal of Philosophical Logic 24, 583–644.
Hughes, G. E. and Cresswell, M. J.: 1996, A New Introduction to Modal Logic, Routledge, London, UK.
Jones, A. I. J. and Sergot, M. J.: 1996, A formal characterisation of institutionalised power, Journal of the IGPL 4(3), 429–445.
Kowalski, R. A. and Sergot, M. J.: 1986, A logic-based calculus of events, New Generation Computing 4, 67–95.
Lemmon, E. J.: 1957, New foundations for Lewis modal systems, Journal of Symbolic Logic 22, 176–186.
Levesque, H. J., Reiter, R., Lesperance, Y., Lin, F., and Scherl, R. B.: 1997,GOLOG: A logic programming language for dynamic domains, Journal of Logic Programming 31, 59–84.
Macleod, M. C. and Schotch, P. K.: 2000, Remarks on the modal logic of Henry Bradford Smith, Journal of Philosophical Logic 29, 603–615.
McCarthy, J. and Hayes, P.: 1969, Some philosophical problems from the standpoint of artificial intelligence, in D. Michie and B. Meltzer (eds.), Machine Intelligence, Vol. 4, Edinburgh University Press, pp. 463–502.
Migita, T. and Hosoi, T.: 1997, Gentzen-types formulation of some modal logics, SUT Journal of Mathematics 33(2), 207–237.
Norman, T. J. and Reed, C. A.: 2002, Group delegation and responsibility, in Proceedings of the First International Joint Conference on Autonomous Agents and Multi-Agent Systems, pp. 491–498.
Pirri, F. and Reiter, R.: 1999, Some contributions to the metatheory of the situation calculus, Journal of the ACM 46(3), 325–361.
Prior, A.: 1967, Past, Present and Future, Clarendon Press, Oxford.
Santos, F., Jones, A. J. I., and Carmo, J.: 1997, Responsibility for action in organisations: a formal model, in G. Holmström-Hintikka and R. Tuomela (eds.), Contemporary Action Theory, Vol. 2, Kluwer, Dordrecht, pp. 333–350.
Searle, J. R.: 1969, Speech Acts: An Essay in the Philosophy of Language, Cambridge University Press, Cambridge, UK.
Segerberg, K.: 1989, Bringing it about, Journal of Philosophical Logic 18, 327–347.
Shafer, G., Gillet, P. R., and Sckerl, R.: 2000, The logic of events, Annals of Mathematics and AI 28(1–4), 315–389.
Shanahan, M.: 1997, Solving the Frame Problem: A Mathematical Investigation of the Common Sense Law of Inertia, MIT Press, Cambridge, MA.
Singh, M. P.: 1991, Towards a formal theory of communication for multi-agent systems, in Proceedings of the Twelth International Joint Conference on Artificial Intelligence, pp. 69–74.
Singh, M. P.: 1993, A semantics for speech acts, Annals of Mathematics and Artificial Intelligence 8, 47–71.
Thomason, R. H.: 1984, Combinations of tense and modality, in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, Vol. II, Reidel, Dordrecht, pp. 135–166.
von Wright, G. H.: 1968, An essay in deontic logic and the general theory of action, Vol. 21 of Acta Philosophica Fennica, North-Holland, Amsterdam.
Walton, D. N. and Krabbe, E. C. W.: 1995, Commitment in Dialogue: Basic Concepts of Interpersonal Reasoning, SUNY, New York.
Xu, M.: 1995, On the basic logic of STIT with a single agent, Journal of Symbolic Logic 60(2), 459–483.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Reed, C., Norman, T.J. A Formal Characterisation of Hamblin’s Action-State Semantics. J Philos Logic 36, 415–448 (2007). https://doi.org/10.1007/s10992-006-9041-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10992-006-9041-z