Bayesian Propositional Logic

• Autorzy: Tomasz Jarmużek , Mateusz Klonowski , Jacek Malinowski
• Języki publikacji: EN

Abstrakty

EN

We define and investigate from a logical point of view a family of consequence relations defined in probabilistic terms. We call them relations of supporting, and write: |≈w where w is a probability function on a Boolean language. A |≈w B iff the fact that A is the case does not decrease a probability of being B the case. Finally, we examine the intersection of |≈w , for all w, and give some formal properties of it.

Słowa kluczowe

EN

logical entailment; statistical inference; Bayesian inference; corroboration; confirmation

• Wydawca: Wydawnictwo Uniwersytetu Łódzkiego
• Czasopismo: Bulletin of the Section of Logic
• Rocznik: 2017
• Tom: 46
• Numer: 3/4

Daty

wydano

2017-12-30

Twórcy

autor

Tomasz Jarmużek

• Department of Logic, Nicolaus Copernicus University in Toruń

autor

Mateusz Klonowski

autor

Jacek Malinowski

• Institute of Philosophy and Sociology, Polish Academy of Sciences

Bibliografia

• [1] R. Carnap, Logical Foundation of Probability, Routledge and Kegan Paul, London (1951).
• [2] C. Howson, P. Urbach Scientific reasoning: the Bayesian approach, La Salle, Illinois (1990).
• [3] A. N. Kolmogorov, Foundations of the theory of probability second english edition, Chelsea Publishing Company, New York (1956).
• [4] S. Kraus, D. Lehmann and M. Magidor, Nonmonotonic Reasoning, Preferential Models and Cumulative Logics, Artificial Intelligence 44 (1990), pp. 167–207.
• [5] T. Kuipers, Studies in Inductive Probability and Rational Expectation, Reidel, Dordrecht (1978).
• [6] T. Kuipers, From Instrumentalism to Constructive Realism, Synthese Library 287, Kluwer Academic Press, Dordrecht (2000).
• [7] D. Makinson, Bridges from Classical to Nonmonotonic Logic, Texts in Computing, Kings College, London (2005).
• [8] J. Pearl, Probabilistic Reasoning in Intelligent Systems, Morgan Kaufman, San Mateo, CA (1978).
• [9] J. Pearl, On Two Pseudo-Paradoxes in Bayesian Analysis, Annals of Mathematics and Artificial Intelligence 32(2001), pp. 171–177.
• [10] K. Popper, The Logic of Scientific Discovery, revised edition, Hutchinson, London (1968).

Identyfikatory

DOI

10.18778/0138-0680.46.3.4.01