Abstract
The purpose of this paper is to present axiomatizations for some dstit (deliberatively seeing-to-it-that) logics with multiple agents, and prove the completeness and decidability by way of finite model property. The dstit logics considered in this paper include the basic dstit logic, and for every n≥1, a logic in which every agent has at most n possible choices at every moment.
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Bartha, P.: 1993, “Conditional obligation, deontic paradoxes, and the logic of agency”. Annals of Mathematics and Artificial Intelligence9, 1–23.
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.), Cambridge University Press.
Belnap, N.: 1991, “Backwards and forwards in the modal logic of agency”. Philosophy and phenomenological research51, 777–807.
Belnap, N.: 1991a, “Before refraining: concepts for agency”. Erkenntnis34, 137–169.
Belnap, N.: 1991b, “Agents in branching time”. Forthcoming in Logic and Reality: Essays in Pure and Applied Logic, In Memory of Arthur Prior, Oxford University Press.
Belnap, N. and Perloff, M.: 1988, “Seeing to it that: a canonical form for agentives”. Theoria54, 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. N. Carlson (eds.), Dordrecht/Boston/London, 1990, 167–190; and it is correct in the version in other papers.
Belnap, N. and Perloff, M.: 1992, “The way of the agent”. Studia Logica51, 463–484.
Belnap, N. and Perloff, M.: 1993, “In the realm of agents”. Annals of Mathematics and Artificial Intelligence9, 25–48.
Chellas, B. F.: 1969, The Logical Form of Imperatives, Perry Lane Press, Stanford.
Chellas, B. F.: 1992, “Time and modality in the logic of agency”. Studia Logica51, 485–517.
Gurevich, Y. and Shelah, S.: 1985, “The decision problem for branching time logic”. The Journal of Symbolic Logic50, 668–681.
Gurevich, Y. and Shelah, S.: 1985a, “To the decision problem for branching time logic”. Foundations of logic and linguistics: Problems and their solutions, Plenum Press, 1985, 181–198.
Horty, J. F.: 1989, “An alternative stit operator”. Unpublished manuscript, Philosophy Department, University of Maryland.
Horty, J. F. and Belnap, N.: 1993, “The deliberative stit: a study of action, omission, ability, and obligation.” Forthcoming in Journal of Philosophical Logic.
Perloff, M.: 1991, “Stit and the language of agency”. Synthese86, 379–408.
Prior, A.: 1967, Past, Present and Future. Oxford University Press.
Segerberg, K.: 1992, “Getting started: Beginnings in the logic of action”. Studia Logica51, 437–378.
Thomason, R. H.: 1970, “Indeterminist time and truth-value gaps”. Theoria36, 264–281.
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.
von Kutschera, F.: 1986, “Bewirden”. Erdenntnis24, 253–281.
von Wright, G. H.: 1963, Norm and Action: A Logical Enquiry. Routledge and Kegan Paul.
Xu, M.: 1993, “Doing and refraining from refraining”. Forthcoming in Journal of Philosophical logic.
Xu, M.: 1993a, “Decidability of stit theory with a single agent and refref equivalence”. Forthcoming in Studia Logica.
Xu, M.: 1994, “On the basic logic of stit with a single agent”. Unpublished manuscript, Department of Philosophy, University of Pittsburgh.
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© 1994 Springer-Verlag Berlin Heidelberg
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Xu, M. (1994). Decidability of deliberative stit theories with multiple agents. In: Gabbay, D.M., Ohlbach, H.J. (eds) Temporal Logic. ICTL 1994. Lecture Notes in Computer Science, vol 827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013997
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DOI: https://doi.org/10.1007/BFb0013997
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