Skip to main content
SpringerLink
Log in

Axioms for Deliberative Stit

  • Published:
Journal of Philosophical Logic Aims and scope Submit manuscript

Abstract

Based on a notion of “companions to stit formulas” applied in other papers dealing with astit logics, we introduce “choice formulas” and “nested choice formulas” to prove the completeness theorems for dstit logics in a language with the dstit operator as the only non-truth-functional operator. The main logic discussed in this paper is the basic logic of dstit with multiple agents, other logics discussed include the basic logic of dstit with a single agent and some logics of dstit with multiple agents each of which corresponds to a semantic condition concerning the number of possible choices for agents.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. Bartha, P.: 1993, “Conditional obligation, deontic paradoxes, and the logic of agency”. Annals of Mathematics and Artificial Inteligence 9, 1–23.

    Google Scholar 

  2. Belnap, N.: 1991, “Backwards and forwards in the model logic of agency”. Philosophy and phenomenological research 51, 777–807.

    Google Scholar 

  3. Belnap, N.: 1991a, “Before refraining: concepts for agency”. Erkenntnis 34, 137–169.

    Google Scholar 

  4. Belnap, N.: Forthcoming, “Agents in branching time”. In Logic and Reality: Essays in Pure and Applied Logic, In Memory of Arthur Prior, Oxford University Press.

  5. Belnap, N. and Bartha, P.: 1993, “Marcus and the problem of nested deontic modalities”, Forthcoming in Modality, Morality, and Belief, Walter Sinnott-Armstrong, Diana Raffman, Nicholas Asher (eds.), Cambrige University Press.

  6. Belnap, N. and Perloff, M.: 1988, “Seeing to it that: a canonical form for agentives”. Theoria 54, 175–199. Belnap noted that the informal semantic account of stit is garbled in this paper; the account is correct in the version of this paper republished in Knowledge representation and defeasible reasoning, H. E. Kyburg, Jr., R. P. Loui, and G. H. Carlson (eds.), Dordrecht/Boston/London, 1990, pp. 167–190; and it is correct in the version in other papers (such as Belnap 1991 above).

    Google Scholar 

  7. Belnap, N. and Perloff, M.: 1992, “The way of agent”, Studia Logica 51, 463–484.

    Google Scholar 

  8. Belnap, N. and Perloff, M.: 1993, “In the realm of agents”, Annals of Mathematics and Artificial Intelligence 9, 25–48.

    Google Scholar 

  9. Brown, M.: 1995, “Stit in time” (abstract). The Bulletin of Symbolic Logic, 1, 1995, 88–89.

    Google Scholar 

  10. Chellas, B. F.: 1969, The Logical Form of Imperatives, Perry Lane Press, Stanford.

    Google Scholar 

  11. Chellas, B. F.: 1992, “Time and modality in the logic of agency”. Studia Logica 51, 485–517.

    Google Scholar 

  12. Dummett, M. and Lemmon, E.: 1959, “Modal logics between S4 and S5”, Zeitschrift für Mathematics Logik und Grundlagen der Mathematik 5, 250–264.

    Google Scholar 

  13. Horty, J. F.: 1989, “An alternative stit operator”. Unpublisher manuscript, Philosophy Department, University of Maryland.

  14. Horty, J. F. and Belnap, N.: 1995, “The deliberative stit: a study of action, omission, ability, and obligation.” Journal of Philosophical Logic 24, 583–644.

    Google Scholar 

  15. Parry, W. T.: 1939, “Modalities in the survey system of strict implication”. The Journal of Symbolic Logic 4, 137–154.

    Google Scholar 

  16. Perloff, M.: 1991, “Stit and the language of agency”. Synthese 86, 379–408.

    Google Scholar 

  17. Perloff, M.: 1993, “On the logical grammar of imperatives”. Unpublished manuscript, Department of Philosophy, University of Pittsburgh.

  18. Prior, A.: 1967, Past, present and future. Oxford University Press.

  19. Segerberg, K.: 1992, “Getting started: Beginning in the logic of action”. Studia Logica 51, 347–378.

    Google Scholar 

  20. Thomason, R. H.: 1970, “Indeterminist time and truth-value gaps”. Theoria 36, 264–281.

    Google Scholar 

  21. Thomason, R. H.: 1981, “Deontic logic as founded on tense logic”. In New Studies in Deontic Logic, R. Hilpinen (ed.), D. Reidel Publishing Company, 1981, 165–176.

  22. Thomason, R. H.: 1984, “Combinations of tense and modality”. In Handbook of Philosophical Logic, vol. II, D. Gabbay and G. Guenthner (eds.), D. Reidel Publishing Company, 1984, pp. 135–165.

  23. Von Kutschera, F.: 1986, “Bewirken”. Erdenntnis 24, 253–281.

    Google Scholar 

  24. Xu, M.: 1994, “Decidability of stit theory with a single agent and refref equivalence”. Studia Logica 53, 259–298.

    Google Scholar 

  25. Xu, M.: 1994a, “Decidability of deliberative stit theories with multiple agents”. Temporal Logic, first international conference, ICTL'94, Bonn, Germany, 1994, proceedings, Dov M. Gabbay and Jans J. Ohlbach (eds.), Springer-Verlag, Berlin, Heidelberg, pp. 332–348.

    Google Scholar 

  26. Xu, M.: 1994b, “Doing and refraining from refraining”. Journal of Philosophical Logic 23, 621–632.

    Google Scholar 

  27. Xu, M.: 1995, “On the basic logic of stit with a single agent”. The Journal of Symbolic Logic 60, 459–483.

    Google Scholar 

  28. Xu, M.: 1995a, “Busy choice sequences, refraining formulas and modalities”. Studia Logica 54, 267–301.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Cycorp Inc, 3721 Executive Center Dr. Suite 100 Austin, TX 78731, U.S.A. E-mail

    Ming Xu

Authors
  1. Ming Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xu, M. Axioms for Deliberative Stit. Journal of Philosophical Logic 27, 505–552 (1998). https://doi.org/10.1023/A:1004274131669

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1004274131669

Search

Navigation