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Logic, Inference, Probability and Paradox
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Logic, Inference, Probability and Paradox

A special issue of Philosophies (ISSN 2409-9287).

Deadline for manuscript submissions: closed (30 November 2017) | Viewed by 14882

Special Issue Editors

Prof. Dr. Julio Stern

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Guest Editor
Department of Applied Mathematics, Institute of Mathematics and Statistics, University of São Paulo, São Paulo 05508-900, Brazil
Interests: Bayesian inference; foundations of statistics; significance measures; evidence; logic and epistemology of significance measures
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Walter Carnielli

E-Mail Website
Guest Editor
Centre for Logic, Epistemology and the History of Science, State University of Campinas, Campinas, SP 13083-970, Brazil
Interests: logic foundations of probability and posibility; probabilistic reasoning; philosophy of probability; combinatorics and probability
Dr. Juliana Bueno-Soler

E-Mail Website
Guest Editor
School of Technology, State University of Campinas, Limeira, SP 13484-332, Brazil
Interests: Bayesian inference; probabilistic reasoning; logic foundations of probability; interpretations of probability; statistical models

Special Issue Information

Dear Colleagues,

Reasoning with uncertain knowledge is a growing area of interest, involving several tendencies, such as reasoning with non-standard theories of probability (e.g., theories of probability based on non-classical logics) and combining argumentation systems, is more qualitative in nature, with probabilities or probabilistic semantics. All such tendencies and areas of investigation are naturally generalized to possibility systems and other credal calculi. This poses new and intriguing questions on the philosophy of probability and credal calculi in general, amplifying the discussions around the correct formal theories of probability and on the interpretations of probability, among the classical, logical, frequentist, propensity, and subjectivist (and possibly others). Dilemmas and paradoxes in probabilities and credal calculi are also a relevant area of research. This Special Issue intends to contribute to the state-of-the-art of such research topics by gathering together the contribution of authors in interconnected areas including logical, mathematical and conceptual aspects.

Prof. Dr. Julio Michael Stern
Prof. Dr. Walter Alexandre Carnielli
Dr. Juliana Bueno-Soler
Guest Editors

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Keywords

  • interpretations of probability, possibility and other credal calculi
  • philosophy of probability, possibility and other credal calculi
  • probabilistic and possibilistic argumentation and inference
  • probability, possibility and uncertain reasoning
  • paradoxes in probability, possibility and other credal calculi

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Published Papers (3 papers)

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Research

13 pages, 287 KiB  
Article
Probabilistic Justification Logic
by Joseph Lurie
Philosophies 2018, 3(1), 2; https://doi.org/10.3390/philosophies3010002 - 16 Feb 2018
Cited by 6 | Viewed by 3100
Abstract
Justification logics are constructive analogues of modal logics. They are often used as epistemic logics, particularly as models of evidentialist justification. However, in this role, justification (and modal) logics are defective insofar as they represent justification with a necessity-like operator, whereas actual evidentialist [...] Read more.
Justification logics are constructive analogues of modal logics. They are often used as epistemic logics, particularly as models of evidentialist justification. However, in this role, justification (and modal) logics are defective insofar as they represent justification with a necessity-like operator, whereas actual evidentialist justification is usually probabilistic. This paper first examines and rejects extant candidates for solving this problem: Milnikel’s Logic of Uncertain Justifications, Ghari’s Hájek–Pavelka-Style Justification Logics and a version of probabilistic justification logic developed by Kokkinis et al. It then proposes a new solution to the problem in the form of a justification logic that incorporates the essential features of both a fuzzy logic and a probabilistic logic. Full article
(This article belongs to the Special Issue Logic, Inference, Probability and Paradox)
220 KiB  
Article
The Interpretation of Probability: Still an Open Issue? 1
by Maria Carla Galavotti
Philosophies 2017, 2(3), 20; https://doi.org/10.3390/philosophies2030020 - 29 Aug 2017
Cited by 5 | Viewed by 6483
Abstract
Probability as understood today, namely as a quantitative notion expressible by means of a function ranging in the interval between 0–1, took shape in the mid-17th century, and presents both a mathematical and a philosophical aspect. Of these two sides, the second is [...] Read more.
Probability as understood today, namely as a quantitative notion expressible by means of a function ranging in the interval between 0–1, took shape in the mid-17th century, and presents both a mathematical and a philosophical aspect. Of these two sides, the second is by far the most controversial, and fuels a heated debate, still ongoing. After a short historical sketch of the birth and developments of probability, its major interpretations are outlined, by referring to the work of their most prominent representatives. The final section addresses the question of whether any of such interpretations can presently be considered predominant, which is answered in the negative. Full article
(This article belongs to the Special Issue Logic, Inference, Probability and Paradox)
442 KiB  
Article
Entrance Fees and a Bayesian Approach to the St. Petersburg Paradox
by Diego Marcondes, Cláudia Peixoto, Kdson Souza and Sergio Wechsler
Philosophies 2017, 2(2), 11; https://doi.org/10.3390/philosophies2020011 - 10 May 2017
Cited by 1 | Viewed by 4466
Abstract
In An Introduction to Probability Theory and its Applications, W. Feller established a way of ending the St. Petersburg paradox by the introduction of an entrance fee, and provided it for the case in which the game is played with a fair [...] Read more.
In An Introduction to Probability Theory and its Applications, W. Feller established a way of ending the St. Petersburg paradox by the introduction of an entrance fee, and provided it for the case in which the game is played with a fair coin. A natural generalization of his method is to establish the entrance fee for the case in which the probability of heads is θ ( 0 < θ < 1 / 2 ) . The deduction of those fees is the main result of Section 2. We then propose a Bayesian approach to the problem. When the probability of heads is θ ( 1 / 2 < θ < 1 ) the expected gain of the St. Petersburg game is finite, therefore there is no paradox. However, if one takes θ as a random variable assuming values in ( 1 / 2 , 1 ) the paradox may hold, which is counter-intuitive. In Section 3 we determine necessary conditions for the absence of paradox in the Bayesian approach and in Section 4 we establish the entrance fee for the case in which θ is uniformly distributed in ( 1 / 2 , 1 ) , for in this case there is a paradox. Full article
(This article belongs to the Special Issue Logic, Inference, Probability and Paradox)
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