Summary
This paper proposes a common framework for various probabilistic logics. It consists of a set of uncertain premises with probabilities attached to them. This raises the question of the strength of a conclusion, but without imposing a particular semantics, no general solution is possible. The paper discusses several possible semantics by looking at it from the perspective of probabilistic argumentation.
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References
Adams, E.W.: A Primer of Probability Logic. CSLI Publications, Stanford (1998)
Anderson, K.A., Hooker, J.N.: A linear programming framework for logics of uncertainty. Decision Support Systems 16(1), 39–53 (1996)
Bergmann, G.: The logic of probability. American Journal of Physics 9, 263–272 (1941)
Carnap, R.: Logical Foundations of Probability. University of Chicago Press (1950)
Cozman, F.G.: Credal networks. Artificial Intelligence 120(2), 199–233 (2000)
de Finetti, B.: The logic of probability. Philosophical Studies 77(1), 181–190 (1995)
Fagin, R., Halpern, J.Y., Megiddo, N.: A logic for reasoning about probabilities. Information and Computation 87(1/2), 78–128 (1990)
Fox, J.: Probability, logic and the cognitive foundations of rational belief. Journal of Applied Logic 1(3–4), 197–224 (2003)
Gaifman, H.: Concerning measures in first order calculi. Israel Journal of Mathematics 2, 1–18 (1964)
Gerla, G.: Inferences in probability logic. Artificial Intelligence 70(1–2), 33–52 (1994)
Haenni, R.: Towards a unifying theory of logical and probabilistic reasoning. In: Cozman, F.B., Nau, R., Seidenfeld, T. (eds.) ISIPTA 2005, 4th International Symposium on Imprecise Probabilities and Their Applications, Pittsburgh, USA, pp. 193–202 (2005)
Haenni, R.: Using probabilistic argumentation for key validation in public-key cryptography. International Journal of Approximate Reasoning 38(3), 355–376 (2005)
Haenni, R.: Probabilistic argumentation. Journal of Applied Logic (forthcoming, 2008)
Haenni, R., Hartmann, S.: Modeling partially reliable information sources: A general approach based on Dempster-Shafer theory. International Journal of Information Fusion 7(4), 361–379 (2006)
Haenni, R., Kohlas, J., Lehmann, N.: Probabilistic argumentation systems. In: Gabbay, D.M., Smets, P. (eds.) Handbook of Defeasible Reasoning and Uncertainty Management Systems. Algorithms for Uncertainty and Defeasible Reasoning, vol. 5, pp. 221–288. Kluwer Academic Publishers, Dordrecht (2000)
Hailperin, T.: Probability logic. Notre Dame Journal of Formal Logic 25(3), 198–212 (1984)
Hailperin, T.: Sentential Probability Logic. Lehigh University Press (1996)
Halpern, J.Y.: An analysis of first-order logics of probability. Artificial Intelligence 46, 311–350 (1990)
Howson, C.: Probability and logic. Journal of Applied Logic 1(3–4), 151–165 (2003)
Jaynes, E.T.: Probability theory as logic. In: Fougère, P.F. (ed.) 9th Annual Workshop on Maximum Entropy and Bayesian Methods, pp. 1–16 (1990)
Kohlas, J.: Probabilistic argumentation systems: A new way to combine logic with probability. Journal of Applied Logic 1(3–4), 225–253 (2003)
Kyburg, H.E.: Probability and Inductive Logic. Macmillan, New York (1970)
Levi, I.: The Enterprise of Knowledge. The MIT Press, Cambridge (1980)
Ng, R., Subrahmanian, V.S.: Probabilistic logic programming. Information and Computation 101(2), 150–201 (1992)
Nilsson, N.J.: Probabilistic logic. Artificial Intelligence 28(1), 71–87 (1986)
Reichenbach, H.: Wahrscheinlichkeitslogik. Erkenntnis 5, 37–43 (1935)
Richardson, M., Domingos, P.: Markov logic networks. Machine Learning 62(1–2), 107–136 (2006)
Ruspini, E.H.: The logical foundations of evidential reasoning. Tech. Rep. 408, SRI International, AI Center, Menlo Park, USA (1986)
Ruspini, E.H., Lowrance, J., Strat, T.: Understanding evidential reasoning. International Journal of Approximate Reasoning 6(3), 401–424 (1992)
Scott, D., Krauss, P.: Assigning probabilities to logical formulas. In: Hintikka, J., Suppes, P. (eds.) Aspects of Inductive Logic, pp. 219–264. North-Holland, Amsterdam (1966)
Williamson, J.: Probability logic. In: Gabbay, D., et al. (eds.) Handbook of the Logic of Argument and Inference: The Turn Toward the Practical, pp. 397–424. Elsevier, Amsterdam (2002)
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Haenni, R., Romeijn, JW., Wheeler, G., Williamson, J. (2008). Possible Semantics for a Common Framework of Probabilistic Logics. In: Huynh, VN., Nakamori, Y., Ono, H., Lawry, J., Kreinovich, V., Nguyen, H.T. (eds) Interval / Probabilistic Uncertainty and Non-Classical Logics. Advances in Soft Computing, vol 46. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77664-2_21
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DOI: https://doi.org/10.1007/978-3-540-77664-2_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77663-5
Online ISBN: 978-3-540-77664-2
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