Abstract
Groenendijk and Stokhof (Varieties of formal semantics, 143–170, 1984) propose a version of partition-based semantics to analyse questions and answers. In order to compare the goodness of answers, they use qualitative orderings among answers. Groenendijk and Stokhof’s qualitative method is too coarse-grained to achieve the goal. In order to overcome the limitations, van Rooij (Formal theories of information: from Shannon to semantic information theory and general concepts of information, LNCS, 161–192, 2009) proposes an information-theoretic approach based on conditional entropy. The aims of this paper are to construct a qualitative approach that is as fine-grained as the information-theoretic one, in terms of measurement theory on the basis of Domotor (Information and inference, 148–194, 1970), and to propose a new version of complete logic for better questions and answers—Better-Question-and-Answer Logic (\(\mathsf {BQAL}\))—the model of the language of which is based on the qualitative and measurement-theoretic approach.
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Notes
- 1.
We owe this section to van Rooij (2009).
- 2.
- 3.
- 4.
Roberts (1979) gives a comprehensive survey of measurement theory. The mathematical foundation of measurement had not been studied before Hölder (1901) developed his axiomatisation for the measurement of mass. Krantz et al. (1971), Suppes et al. (1989) and Luce et al. (1990) are seen as milestones in the history of measurement theory.
- 5.
We owe this subsection to Domotor (1970).
- 6.
We owe this subsection to Domotor (1970).
References
Domotor, Z. (1969). Probabilistic relational structures and their applications. Technical report No. 144, Institute for Mathematical Studies in the Social Sciences, Stanford University.
Domotor, Z. (1970). Qualitative information and entropy structures. In J. Hintikka & P. Suppes (Eds.), Information and inference (pp. 148–194). Dordrecht: Reidel.
Groenendijk, J., & Stokhof, M. (1984). On the semantics of questions and the pragmatics of answers. In F. Landman & F. Veltman (Eds.), Varieties of formal semantics (pp. 143–170). Dordrecht: Foris.
Hölder, O. (1901). Die Axiome der Quantität und die Lehre vom Mass. Berichte über die Verhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaften zu Leipzig. Mathematisch-Physikalische Klasse, 53, 1–64.
Krantz, D. H., et al. (1971). Foundations of measurement (Vol. 1). New York: Academic Press.
Luce, R. D., et al. (1990). Foundations of measurement (Vol. 3). San Diego: Academic Press.
Roberts, F. S. (1979). Measurement theory. Reading: Addison-Wesley.
Segerberg, K. (1971). Qualitative probability in a modal setting. In J. E. Fenstad (Ed.), Proceedings of the second Scandinavian logic symposium (pp. 341–352). Amsterdam: North-Holland.
Suppes, P., et al. (1989). Foundations of measurement (Vol. 2). San Diego: Academic Press.
Suzuki, S. (2008). Preference logic and its measurement-theoretic semantics. In Electronic Proceedings of the 8th Conference on Logic and the Foundations of Game and Decision Theory (LOFT 2008), Paper No. 42.
Suzuki, S. (2009a). Measurement-theoretic foundation of preference-based dyadic deontic logic. In X. He, et al. (Eds.), Proceedings of the Second International Workshop on Logic, Rationality, and Interaction (LORI-II). LNCS (Vol. 5834, pp. 278–291). Heidelberg: Springer.
Suzuki, S. (2009b). Prolegomena to dynamic epistemic preference logic. In H. Hattori, et al. (Eds.), New Frontiers in artificial intelligence. LNCS (Vol. 5447, pp. 177–192). Heidelberg: Springer.
Suzuki, S. (2010). Prolegomena to threshold utility maximiser’s preference logic. In Electronic Proceedings of the 9th Conference on Logic and the Foundations of Game and Decision Theory (LOFT 2010), Paper No. 44.
Suzuki, S. (2011a). A measurement-theoretic foundation of threshold utility maximiser’s preference logic. Journal of Applied Ethics and Philosophy, 3, 17–25.
Suzuki, S. (2011b). Measurement-theoretic foundations of probabilistic model of JND-based vague predicate logic. In H. van Ditmarsch, et al. (Eds.), Proceedings of the Third International Workshop on Logic, Rationality, and Interaction (LORI-III). LNCS (Vol. 6953, pp. 272–285). Heidelberg: Springer.
Suzuki, S. (2011c). Prolegomena to salient-similarity-based vague predicate logic. In T. Onada, et al. (Eds.), New Frontiers in artificial intelligence. LNCS (Vol. 6797, pp. 75–89). Heidelberg: Springer.
Suzuki, S. (2012a). Measurement-theoretic foundations of gradable-predicate logic. In M. Okumura, et al. (Eds.), New Frontiers in artificial intelligence. LNCS (Vol. 7258, pp. 82–95). Heidelberg: Springer.
Suzuki, S. (2012b). Measurement-theoretic foundations of interadjective-comparison logic. In A. Aguilar-Guevara, et al. (Eds.), Proceedings of Sinn und Bedeutung 16 (Vol. 2, pp. 571–584). Cambridge: MIT Working Papers in Linguistics.
Suzuki, S. (2013a). Epistemic modals, qualitative probability, and nonstandard probability. In M. Aloni, et al. (Eds.), Proceedings of the 19th Amsterdam Colloquium (AC 2013) (pp. 211–218).
Suzuki, S. (2013b). Measurement-theoretic bases of multidimensional-predicate logic. Manuscript.
Suzuki, S. (2013c). Measurement-theoretic foundations of many-sorted preference aggregation logic for Nash collective utility function. Manuscript.
Suzuki, S. (2013d). Measurement-theoretic foundations of preference aggregation logic for weighted utilitarianism. In T. Yamada (Ed.), Electronic Post-Proceedings of the Third International Workshop on Philosophy and Ethics of Social Reality (SOCREAL 2013) (pp. 68–79).
Suzuki, S. (2013e). Remarks on decision-theoretic foundations of doxastic and epistemic logic (revised version). Studies in Logic, 6, 1–12.
Suzuki, S. (2014). Measurement-theoretic foundations of dynamic epistemic preference logic. In E. McCready, et al. (Eds.), Formal approaches to semantics and pragmatics. Studies in Linguistics and Philosophy (Vol. 95, pp. 295–324). Heidelberg: Springer.
van Rooij, R. (2009). Comparing questions and answers: A bit of logic, a bit of language, and some bits of information. In G. Sommaruga (Ed.), Formal theories of information: From Shannon to semantic information theory and general concepts of information. LNCS (Vol. 5363, pp. 161–192). Heidelberg: Springer.
Acknowledgments
The author would like to thank two anonymous reviewers of BNLSP 13 for their helpful comments.
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Suzuki, S. (2015). Measurement-Theoretic Foundations of Logic for Better Questions and Answers. In: Zeevat, H., Schmitz, HC. (eds) Bayesian Natural Language Semantics and Pragmatics. Language, Cognition, and Mind, vol 2. Springer, Cham. https://doi.org/10.1007/978-3-319-17064-0_3
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