Paraconsistent Probabilities: Consistency, Contradictions and Bayes’ Theorem

Bueno-Soler, Juliana; Carnielli, Walter

doi:10.3390/e18090325

Cited by 15 publications

(9 citation statements)

References 29 publications

(23 reference statements)

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“…This approach is appealing for its theoretical simplicity, for allowing computer-efficient implementations of specific models, etc. For historical analyzes of this approach, see [45,91,92,184], for recent works from Walter's group following this line, see [31,176]. Notwithstanding their usefulness, simplicity and popularity, finitary or countable sentential formalisms also have their limitations, for example, being unable to express measure theoretic arguments used in mathematical statistics.…”

Section: Statistics In (Un)countable Sentential Probabilitymentioning

confidence: 99%

The e-value and the Full Bayesian Significance Test: Logical Properties and Philosophical Consequences

Stern¹,

Pereira²,

Lauretto³

et al. 2022

Preprint

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This article gives a conceptual review of the e-value, ev (H | X) -the epistemic value of hypothesis H given observations X. This statistical significance measure was developed in order to allow logically coherent and consistent tests of hypotheses, including sharp or precise hypotheses, via the Full Bayesian Significance Test (FBST). Arguments of analysis allow a full characterization of this statistical test by its logical or compositional properties, showing a mutual complementarity between results of mathematical statistics and the logical desiderata lying at the foundations of this theory.

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Section: Statistics In (Un)countable Sentential Probabilitymentioning

confidence: 99%

The e-value and the Full Bayesian Significance Test: Logical Properties and Philosophical Consequences

Stern¹,

Pereira²,

Lauretto³

et al. 2022

Preprint

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show abstract

“…Currently, there are several types of nonclassical logics, and in general, we can consider that only those logics that are indestructible in the presence of the contradiction are paraconsistent. Therefore, a paraconsistent logic (PL) is a nonclassical logic that has, as its fundamental characteristic, the opposition to the principle of noncontradiction [15][16][17][18].…”

Section: Paraconsistent Logicmentioning

confidence: 99%

Application of Shannon Entropy in the Construction of a Paraconsistent Model of the Atom

Filho¹

2020

Preprint

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In this work, we present a model of the atom that is based on a nonclassical logic called paraconsistent logic (PL), which has the main property of accepting the contradiction in logical interpretations without the conclusions being annulled. The proposed model is constructed with an extension of PL called paraconsistent annotated logic with annotation of two values (PAL2v), which is associated with an interlaced bilattice of four vertices. We use the logarithmic function of the Shannon entropy H(s) to construct the paraconsistent equations and thus adapt a probabilistic model for representations in quantum physics. Through analyses of the interlaced bilattice, comparative values are obtained for some of the phenomena and effects of quantum mechanics, such as superposition of states, quantum entanglement, wave functions, and equations that determine the energy levels of the layers of an atom. At the end of this article, we use the hydrogen atom as a basis of the representation of the PAL2v model, where the values of the energy levels in six orbital layers are obtained. As an example, we present a possible method of applying the PAL2v model to the use of Raman spectroscopy signals in the detection of lubricating mineral oil quality.

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“…This will shed new light on formal representations of belief, on Bayesian epistemology, and on novel applications in statistics. There is a huge literature on such topics; I can only wisely advise a couple of references with distinctive objectives, that somehow represent this view: Against All Odds: When Logic Meets Probability 21 and Paraconsistent Probabilities: Consistency, Contradictions and Bayes' Theorem 22 .…”

Section: Logics and Probability And Probability Logicmentioning

confidence: 99%