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  1.  21
    The Modal Logic of Bayesian Belief Revision.Zalán Gyenis, Miklós Rédei & William Brown - forthcoming - Journal of Philosophical Logic:1-16.
    In Bayesian belief revision a Bayesian agent revises his prior belief by conditionalizing the prior on some evidence using Bayes’ rule. We define a hierarchy of modal logics that capture the logical features of Bayesian belief revision. Elements in the hierarchy are distinguished by the cardinality of the set of elementary propositions on which the agent’s prior is defined. Inclusions among the modal logics in the hierarchy are determined. By linking the modal logics in the hierarchy to the strongest modal (...)
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  2.  2
    Standard Bayes Logic is Not Finitely Axiomatizable.Zalán Gyenis - forthcoming - Review of Symbolic Logic:1-13.
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  3.  33
    General Properties of Bayesian Learning as Statistical Inference Determined by Conditional Expectations.Zalán Gyenis & Miklós Rédei - 2017 - Review of Symbolic Logic 10 (4):719-755.
    We investigate the general properties of general Bayesian learning, where “general Bayesian learning” means inferring a state from another that is regarded as evidence, and where the inference is conditionalizing the evidence using the conditional expectation determined by a reference probability measure representing the background subjective degrees of belief of a Bayesian Agent performing the inference. States are linear functionals that encode probability measures by assigning expectation values to random variables via integrating them with respect to the probability measure. If (...)
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  4.  94
    Conditioning Using Conditional Expectations: The Borel–Kolmogorov Paradox.Zalán Gyenis, Gabor Hofer-Szabo & Miklós Rédei - 2017 - Synthese 194 (7):2595-2630.
    The Borel–Kolmogorov Paradox is typically taken to highlight a tension between our intuition that certain conditional probabilities with respect to probability zero conditioning events are well defined and the mathematical definition of conditional probability by Bayes’ formula, which loses its meaning when the conditioning event has probability zero. We argue in this paper that the theory of conditional expectations is the proper mathematical device to conditionalize and that this theory allows conditionalization with respect to probability zero events. The conditional probabilities (...)
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  5.  24
    On the Modal Logic of Jeffrey Conditionalization.Zalán Gyenis - 2018 - Logica Universalis 12 (3-4):351-374.
    We continue the investigations initiated in the recent papers where Bayes logics have been introduced to study the general laws of Bayesian belief revision. In Bayesian belief revision a Bayesian agent revises his prior belief by conditionalizing the prior on some evidence using the Bayes rule. In this paper we take the more general Jeffrey formula as a conditioning device and study the corresponding modal logics that we call Jeffrey logics, focusing mainly on the countable case. The containment relations among (...)
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  6.  61
    Defusing Bertrand’s Paradox.Zalán Gyenis & Miklós Rédei - 2015 - British Journal for the Philosophy of Science 66 (2):349-373.
    The classical interpretation of probability together with the principle of indifference is formulated in terms of probability measure spaces in which the probability is given by the Haar measure. A notion called labelling invariance is defined in the category of Haar probability spaces; it is shown that labelling invariance is violated, and Bertrand’s paradox is interpreted as the proof of violation of labelling invariance. It is shown that Bangu’s attempt to block the emergence of Bertrand’s paradox by requiring the re-labelling (...)
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  7.  80
    Characterizing Common Cause Closed Probability Spaces.Zalán Gyenis & Miklós Rédei - 2011 - Philosophy of Science 78 (3):393-409.
    A classical probability measure space was defined in earlier papers \cite{Hofer-Redei-Szabo1999}, \cite{Gyenis-Redei2004} to be common cause closed if it contains a Reichenbachian common cause of every correlation in it, and common cause incomplete otherwise. It is shown that a classical probability measure space is common cause incomplete if and only if it contains more than one atom. Furthermore, it is shown that every probability space can be embedded into a common cause closed one; which entails that every classical probability space (...)
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  8.  53
    Atomicity and Causal Completeness.Zalán Gyenis & Miklós Rédei - 2014 - Erkenntnis 79 (S3):1-15.
    The role of measure theoretic atomicity in common cause closedness of general probability theories with non-distributive event structures is raised and investigated. It is shown that if a general probability space is non-atomic then it is common cause closed. Conditions are found that entail that a general probability space containing two atoms is not common cause closed but it is common cause closed if it contains only one atom. The results are discussed from the perspective of the Common Cause Principle.
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  9.  38
    Measure Theoretic Analysis of Consistency of the Principal Principle.Miklós Rédei & Zalán Gyenis - 2016 - Philosophy of Science 83 (5):972-987.
    Weak and strong consistency of thePrincipal Principle are defined in terms of classical probability measure spaces. It is proved that the Abstract Principal Principle is both weakly and strongly consistent. The Abstract Principal Principle is strengthened by adding a stability requirement to it. Weak and strong consistency of the resulting Stable Abstract Principal Principle are defined. It is shown that the Stable Abstract Principal Principle is weakly consistent. Strong consistency of the Stable Abstract Principal principle remains an open question.
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  10.  11
    The Bayes Blind Spot of a Finite Bayesian Agent is a Large Set.Zalán Gyenis & Miklós Rédei - unknown
    The Bayes Blind Spot of a Bayesian Agent is the set of probability measures on a Boolean algebra that are absolutely continuous with respect to the background probability measure of a Bayesian Agent on the algebra and which the Bayesian Agent cannot learn by conditionalizing no matter what evidence he has about the elements in the Boolean algebra. It is shown that if the Boolean algebra is finite, then the Bayes Blind Spot is a very large set: it has the (...)
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  11.  32
    General Properties of General Bayesian Learning.Miklós Rédei & Zalán Gyenis - unknown
    We investigate the general properties of general Bayesian learning, where ``general Bayesian learning'' means inferring a state from another that is regarded as evidence, and where the inference is conditionalizing the evidence using the conditional expectation determined by a reference probability measure representing the background subjective degrees of belief of a Bayesian Agent performing the inference. States are linear functionals that encode probability measures by assigning expectation values to random variables via integrating them with respect to the probability measure. If (...)
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  12.  8
    On Atomicity of Free Algebras in Certain Cylindric-Like Varieties.Zalán Gyenis - 2011 - Logic Journal of the IGPL 19 (1):44-52.
    In this paper we show that the one-generated free three dimensional polyadic and substitutional algebras Fr1PA3 and Fr1SCA3 are not atomic. What is more, their corresponding logics have the Gödel’s incompleteness property. This provides a partial solution to a longstanding open problem of Németi and Maddux going back to Alfred Tarski via the book [12].
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  13.  34
    Defusing Bertrand's Paradox.Zalán Gyenis & Rédei Miklós - unknown
    The classical interpretation of probability together with the Principle of Indifference are formulated in terms of probability measure spaces in which the probability is given by the Haar measure. A notion called Labeling Irrelevance is defined in the category of Haar probability spaces, it is shown that Labeling Irrelevance is violated and Bertrand's Paradox is interpreted as the very proof of violation of Labeling Invariance. It is shown that Bangu's attempt to block the emergence of Bertrand's Paradox by requiring the (...)
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  14.  17
    Categorial Subsystem Independence as Morphism Co-Possibility.Zalán Gyenis & Miklós Rédei - unknown
    This paper formulates a notion of independence of subobjects of an object in a general category. Subobject independence is the categorial generalization of what is known as subsystem independence in the context of algebraic relativistic quantum field theory. The content of subobject independence formulated in this paper is morphism co-possibility: two subobjects of an object will be defined to be independent if any two morphisms on the two subobjects of an object are jointly implementable by a single morphism on the (...)
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  15.  19
    Can Bayesian Agents Always Be Rational? A Principled Analysis of Consistency of an Abstract Principal Principle.Miklós Rédei & Zalán Gyenis - unknown
    The paper takes thePrincipal Principle to be a norm demanding that subjective degrees of belief of a Bayesian agent be equal to the objective probabilities once the agent has conditionalized his subjective degrees of beliefs on the values of the objective probabilities, where the objective probabilities can be not only chances but any other quantities determined objectively. Weak and strong consistency of the Abstract Principal Principle are defined in terms of classical probability measure spaces. It is proved that the Abstract (...)
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  16.  3
    Finite Jeffrey Logic is Not Finitely Axiomatizable.Zalán Gyenis - unknown
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  17.  16
    Upward Morley's Theorem Downward.Gábor Sági & Zalán Gyenis - 2013 - Mathematical Logic Quarterly 59 (4-5):303-331.
  18.  2
    Common Cause Completability of Non-Classical Probability Spaces.Zalán Gyenis & Miklós Rédei - unknown
    We prove that under some technical assumptions on a general, non-classical probability space, the probability space is extendible into a larger probability space that is common cause closed in the sense of containing a common cause of every correlation between elements in the space. It is argued that the philosophical significance of this common cause completability result is that it allows the defence of the Common Cause Principle against certain attempts of falsification. Some open problems concerning possible strengthening of the (...)
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  19. Algebraic Characterization of the Local Craig Interpolation Property.Zalán Gyenis - 2018 - Bulletin of the Section of Logic 47 (1):45-58.
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  20. 10. Discussion: Problems for Natural Selection as a Mechanism Discussion: Problems for Natural Selection as a Mechanism (Pp. 512-523). [REVIEW]Marc Lange, Raphael van Riel, Maximilian Schlosshauer, Gregory Wheeler, Zalán Gyenis, Miklós Rédei, John Byron Manchak, James Owen Weatherall, Bruce Glymour & Bradford Skow - 2011 - Philosophy of Science 78 (3).
     
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