Abstract
We give a unified account of some results in the development of Polyadic Inductive Logic in the last decade with particular reference to the Principle of Spectrum Exchangeability, its consequences for Instantial Relevance, Language Invariance and Johnson’s Sufficientness Principle, and the corresponding de Finetti style representation theorems.
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Carnap R. (1947a) On the application of Inductive Logic. Philosophy and Phenomenology Research 8: 133–147
Carnap R. (1947b) Reply to Nelson Goodman. Philosophy and Phenomenology Research 8: 461–462
Carnap, R. (1950). Logical foundations of probability. Chicago: University of Chicago Press and London: Routledge & Kegan Paul Ltd.
Carnap R. (1952) The continuum of inductive methods. University of Chicago Press, Chicago
Carnap R. (1953) On the comparative concept of confirmation. British Journal for the Philosophy of Science 3(12): 311–318
Carnap R. (1963) Replies and systematic expositions. In: Schlipp P.A. (eds) The philosophy of Rudolf Carnap. Open Court, La Salle, IL
Carnap, R. (1971). In R. Carnap & R. C. Jeffrey (Eds.), Studies in inductive logic and probability, Vol. I. Berkeley: University of California Press.
Carnap, R. (1980). A basic system of inductive logic. In R. C. Jeffrey (Ed.), Studies in inductive logic and probability (Vol. II, pp. 7–155). Berkeley: University of California Press.
Carnap R., Stegmüller W. (1959) Induktive Logik und Wahrscheinlichkeit. Springer, Wien
de Cooman G., Miranda E., Quaeghebeur E. (2009) Representation insensitivity in immediate prediction under exchangeability. International Journal of Approximate Reasoning 50(2): 204–216
de Finetti B. (1931) Sul Significato Soggettivo della Probabilità. Fundamenta Mathematicae 17: 298–329
de Finetti, B. (1974). Theory of probability (Vol. 1). New York: Wiley.
Forrest, P. (2008). The identity of indiscernibles. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (Fall 2008 Edition). Available from http://plato.stanford.edu/archives/fall2008/entries/identity-indiscernible/
Gaifman H. (1964) Concerning measures on first order calculi. Israel Journal of Mathematics 2: 1–18
Gaifman, H. (1971). Applications of de Finetti’s theorem to inductive logic. In R. Carnap & R. C. Jeffrey, Studies in inductive logic and probability (Vol. I). Berkeley: University of California Press.
Goodman N. (1946) A query on confirmation. Journal of Philosophy 43: 383–385
Goodman N. (1947) On infirmities in confirmation-theory. Philosophy and Phenomenology Research 8: 149–151
Hoover, D. N. (1979). Relations on probability spaces and arrays of random variables, Preprint. Institute of Advanced Study: Princeton.
Johnson W. E. (1932) Probability: The deductive and inductive problems. Mind 49: 409–423
Kemeny J.G. (1963) Carnap’s theory of probability and induction. In: Schilpp P.A. (eds) The philosophy of Rudolf Carnap. Open Court, La Salle, IL, pp 711–738
Kingman J. F. C. (1978) The representation of partition structures. Journal of the London Mathematical Society 18: 374–380
Kingman J. F. C. (1980) The mathematics of genetic diversity. SIAM, Philadelphia
Krauss P. H. (1969) Representation of symmetric probability models. Journal of Symbolic Logic 34(2): 183–193
Landes, J. (2009). The principle of spectrum exchangeability with inductive logic. Ph.D. Thesis, University of Manchester. Available from http://www.maths.manchester.ac.uk/~jeff/+
Landes, J., Paris, J. B., & Vencovská, A. (2007). Language invariance and spectrum exchangeability in inductive logic, Symbolic and quantitative approaches to reasoning with uncertainty. In Proceedings of the 9th European conference, ECSQARU, Hammamet, Tunisia, Springer LNAI 4724, pp. 151–160.
Landes, J., Paris, J. B., & Vencovská, A. (2008a). The principle of conformity and spectrum exchangeability, to appear. In B. Löwe & J.-W. Romeijn (Eds.), Foundations of formal sciences VI. Studies in Logic, College Publications.
Landes J., Paris J. B., Vencovská A. (2008b) Some aspects of Polyadic Inductive Logic. Studia Logica 90: 3–16
Landes J., Paris J. B., Vencovská A. (2009a) Representation theorems for probability functions satisfying spectrum exchangeability in inductive logic. International Journal of Approximate Reasoning 51(1): 35–55
Landes, J., Paris, J. B., & Vencovská, A. (2009). Instantial relevance in polyadic inductive logic. In R. Ramanujam & S. Sarukkai (Eds.), Procedings of the third Indian conference on logic and its applications, ICLA 2009, LNAI 5378 (pp. 162–169). Berlin: Springer
Leibniz, G. W. (1969). Philosophical papers and letters (L. Loemker, Trans.). Dordrecht: Reidel.
Maher P. (2000) Probabilities for two properties. Erkenntnis 52: 63–91
Maher P. (2001) Probabilities for multiple properties: The models of Hesse, Carnap and Kemeny. Erkenntnis 55: 183–216
Nix, C. J. (2005). Probabilistic induction in the predicate calculus. Ph.D. Thesis, University of Manchester. Available from http://www.maths.manchester.ac.uk/~jeff/
Nix C. J., Paris J. B. (2006) A continuum of inductive methods arising from a generalized principle of instantial relevance. Journal of Philosophical Logic 35(1): 83–115
Nix C. J., Paris J. B. (2007) A note on Binary Inductive Logic. Journal of Philosophical Logic 36(6): 735–771
Paris, J. B., & Vencovská, A. (2007). From unary to binary inductive logic, to appear in the Procedings of the second Indian conference on logic and its applications. Mumbai: IIT.
Paris, J. B., & Vencovská, A. Symmetry’s end? Submitted to Erkenntnis.
Paris, J. B., & Vencovská, A. (2009). General representation theorem for probability functions satisfying spectrum exchangeability. In K. Ambros-Spies, B. Löwe, & W. Merkle (Eds.), CiE 2009, LNCS 5635 (pp. 379–388). Berlin: Springer.
Paris J. B., Waterhouse P. (2009) Atom exchangeability and Instantial Relevance. Journal of Philosophical Logic 38(3): 313–332
Romeijn J. W. (2006) Analogical predictions for explicit similarity. Erkenntnis 64(2): 253–280
Vencovská, A. (2006). Binary induction and Carnap’s Continuum. In Proceedings of the 7th workshop on uncertainty processing (WUPES), Mikulov, 2006. See http://mtr.utia.cas.cz/wupes06/articles/data/vencovska.pdf
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J. Landes’s work was supported by MATHLOGAPS Research Studentship, MEST-CT-2004-504029.
A. Vencovská’s work was supported by UK Engineering and Physical Sciences Research Council (EPSRC) Research Associateship.
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Landes, J., Paris, J.B. & Vencovská, A. A survey of some recent results on Spectrum Exchangeability in Polyadic Inductive Logic. Synthese 181 (Suppl 1), 19–47 (2011). https://doi.org/10.1007/s11229-009-9711-9
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DOI: https://doi.org/10.1007/s11229-009-9711-9
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