Bayesian Propositional Logic

Tomasz Jarmużek; Mateusz Klonowski; Jacek Malinowski

Bulletin of the Section of Logic (2017)

  • Volume: 46, Issue: 3/4
  • ISSN: 0138-0680

Abstract

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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.

How to cite

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Tomasz Jarmużek, Mateusz Klonowski, and Jacek Malinowski. "Bayesian Propositional Logic." Bulletin of the Section of Logic 46.3/4 (2017): null. <http://eudml.org/doc/295575>.

@article{TomaszJarmużek2017,
abstract = {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.},
author = {Tomasz Jarmużek, Mateusz Klonowski, Jacek Malinowski},
journal = {Bulletin of the Section of Logic},
keywords = {logical entailment; statistical inference; Bayesian inference; corroboration; confirmation},
language = {eng},
number = {3/4},
pages = {null},
title = {Bayesian Propositional Logic},
url = {http://eudml.org/doc/295575},
volume = {46},
year = {2017},
}

TY - JOUR
AU - Tomasz Jarmużek
AU - Mateusz Klonowski
AU - Jacek Malinowski
TI - Bayesian Propositional Logic
JO - Bulletin of the Section of Logic
PY - 2017
VL - 46
IS - 3/4
SP - null
AB - 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.
LA - eng
KW - logical entailment; statistical inference; Bayesian inference; corroboration; confirmation
UR - http://eudml.org/doc/295575
ER -

References

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

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