Abstract
Recently, natural language pragmatics started to make use of decision-, game-, and information theoretical tools to determine the usefulness of questions and assertions in a quantitative way. In the first part of this paper several of these notions are related with each other. It is shown that under particular natural assumptions the utility of questions and answers reduces to their informativity, and that the ordering relation induced by utility sometimes even reduces to the logical relation of entailment. The second part of the paper shows how different proposals (using either protocols or likelihood functions) to measure the relevance/utility of non-partitional questions come down to the same thing.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Bar-Hillel, Y. and Carnap, R. (1953) Semantic information, in Proceedings of the Symposium on Applications of Communication Theory, Butterworth Scientific Publications, London.
Bellman, R. and Kalaba, R. (1956) On the role of dynamic programming in statistical communication theory, IEEE Trans. Inform. Theory 3, 197–203.
Bernardo, J. M. (1979) Expected information as expected utility, Ann. Statist. 7, 686–690.
Bernardo, J. M. and Smith, A. (1994) Bayesian Theory, Wiley, Chichester.
Blackwell, D. (1953) Equivalent comparisons of experiments, Ann. Math. Statist. 24, 265–272.
Carnap, R. (1950) Logical Foundations of Probability, The University of Chicago Press, London.
Cate, B. ten (2000) Dynamic and epistemic semantics of questions: The logic of consultation, Master thesis, Free University of Amsterdam.
Cover, T. M. and Thomas, J. A. (1991) Elements of Information Theory, Wiley Series in Telecommunications, Wiley, New York.
Geanakoplos, J. (1994) Common knowledge, in R. Aumann and S. Hart (eds.), Handbook of Game Theory, Vol. 2, pp. 1438–1496.
Gerbrandy, J. (1999) Bisimulations on Planet Kripke, Ph.D. Dissertation, University of Amsterdam.
Gil, R. D., van der Laan, M. and Robins, J. (1997) Coarsening at random: Characterisations, conjectures and counter-examples, in Proceedings First Seattle Conference on Biostatistics, pp. 255–294.
Good, I. J. (1950) Probability and the Weighing of Evidence, Griffin, London.
Good, I. J. (1972) Information, rewards, and quasi-utilities, in Leach et al. (eds.), Science, Decision, and Value, D. Reidel Publishing Company, Dordrecht, pp. 115–127.
Groenendijk, J. and Stokhof, M. (1984) On the semantics of questions and the pragmatics of answers, in F. Landman and F. Veltman (eds.), Varieties of Formal Semantics, Foris, Dordrecht.
Grünwald, P. D. and Halpern, J. Y. (2003) Updating probabilities, J. Artificial Intelligence Res. 19, 243–278.
Halpern, J. (2003) Reasoning about Uncertainty, MIT Press.
Hintikka, J. and Pietarinen, J. (1966) Semantic information and inductive logic, in J.Hintikka and P. Suppes (eds.), Aspects of Inductive Logic, North-Holland.
Jeffrey, R. (1965) The Logic of Decision, University of Chicago Press, Chicago.
Kelly, J. (1956) A new interpretation of information rate, Bell System Tech. J. 35, 917–26.
Kullback, S. and Leibler, R. (1951) On information and sufficiency, Ann. Math. Statist. 22,79–86.
Levinson, S. C. (2000) Presumptive Meanings. The Theory of Generalized Conversational Implicatures, MIT Press, Cambridge, MA.
Lindley, D. V. (1956) On a measure of information provided by an experiment, Ann. Math. Statist. 29, 986–1005.
Merin, A. (1997) If all our arguments had to be conclusive, there would be few of them, Arbeitspapiere des Sonderforschungsbereichs 340, No. 101, Stuttgart.
Merin, A. (1999a) Die Relevanz der Relevanz: Fallstudie zur formalen Semantik der englischen Konjunktion but, Habilitationschrift, University of Stuttgart.
Merin, A. (1999b) Information, relevance, and social decisionmaking, in L. Moss, J. Ginzburg and M. de Rijke (eds.), Logic, Language, and Computation, Vol. 2, Stanford.
Parikh, P. (1992) A game-theoretical account of implicature, in Y. Vardi (ed.), Proceedings of the Fourth TARK Conference, Monterey, California.
Peirce, C. S. (1878) The probability of induction, in Popular Science Monthly, reprinted in J. R. Newman (ed.), The World of Mathematics, Simon and Schuster, New York, 1956,pp. 1331–1354.
Raiffa, H. and Schlaifer, R. (1961) Applied Statistical Decision Theory, MIT Press, Cambridge, MA.
Rényi, A. (1961) On measures of entropy and information, in Neyman (ed.), Proc. of the Fourth Symp. on Math. Stat. and Probability, California.
Savage, L. J. (1954) The Foundations of Statistics, Wiley, New York.
Schulz, K. (2002) Relevanz und Quantity Implikaturen, Diplomarbeit, University of Stuttgart.
Shannon, C. (1948) The mathematical theory of communication, Bell System Tech. J. 27, 379–423 and 623-656.
van Rooy, R. (2001) The relevance of communicative acts, in J. van Benthem (ed.), Proceedings of the Eighth TARK Conference, pp. 83–96.
van Rooy, R. (2003a) Questioning to resolve decision problems, Linguistics and Philosophy 27, 493–527.
van Rooy, R. (2003b) Negative polarity items in questions, J. Semantics 20, 239–273.
van Rooy, R. (2003c) Quality and quantity of information exchange, J. Logic, Language and Inform. 12, 23–451.
van Rooy, R. (2004) Utility of mention-some questions, Research on Language and Computation 2(3).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
van Rooy, R. Utility, Informativity and Protocols. Journal of Philosophical Logic 33, 389–419 (2004). https://doi.org/10.1023/B:LOGI.0000036830.62877.ee
Issue Date:
DOI: https://doi.org/10.1023/B:LOGI.0000036830.62877.ee