Universality of Univariate Mixed Fractions in Divisive Meadows

This is to announce a new electronic preprint concerning meadows. The paper entitled “Universality of univariate mixed fractions in divisive meadows” (arXiv:1707.00499v1 [math.RA] ) has now been archived. This preprint shows that univariate fractions, i.e. terms over the signature of divisive meadows with at most one variable that are of the form p/q, can be transformed to sums of a polynomial and a simple fraction, i.e. a fraction without proper subterms that are fractions, in the equational theory of meadows of characteristic zero.

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Adams Conditioning and Likelihood Ratio Transfer Mediated Inference

This is to announce a new version of an electronic preprint concerning an application of meadows. The preprint “Adams Conditioning and Likelihood Ratio Transfer Mediated Inference” has been updated (arXiv:1611.09351v3 [cs.AI]). This preprint presents different ways in which information about likelihoods or likelihood ratios which one agent transfers to another agent may be accommodated by the latter agent in its belief state. It is the result of a study motivated by contemporary ideas in forensic science about courtroom reasoning. Moreover, it is written as a contribution to the development of probability theory in the setting of signed meadows — which started with the papers “Probability Functions in the Context of Signed Involutive Meadows” (arXiv:1307.5173v3 [math.LO]) and “Conditional Values in Signed Meadow Based Axiomatic Probability Calculus” (arXiv:1609.02812v3 [math.LO]).

 

 

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Conditional Values in Signed Meadow Based Axiomatic Probability Calculus

This is to announce a new version of an electronic preprint concerning an application of meadows. The preprint “Conditional Values in Signed Meadow Based Axiomatic Probability Calculus” has been updated (arXiv:1609.02812v3 [math.LO]). In this preprint, an account of some basic elements of probability calculus, including expectation value, probability mass function, variance, covariance, correlation, independence, configuration, sample space, and random variable, is provided. This account is based  on a rephrasing of Kolmogorov’s axioms for probability functions in the setting of signed meadows.  In the presentation, use is made of the special properties of meadows, most notably 1/0 = 0.

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Probability Functions in the Context of Signed Involutive Meadows

This is to announce a new version of an electronic preprint concerning an application of meadows. The preprint “Signed Meadow Valued Probability Functions” has now been replaced by a substantial revision with the new title “Probability functions in the context of signed involutive meadows” (arXiv:1307.5173v3 [math.LO]).  An equation that was mentioned as an axiom before is in fact derivable from the other axioms. This fact called for a significant change in emphasis and presentation. In addition a survey has been
provided of some options to turn conditional probability into a total operator.

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Fracpairs and Fractions over a Reduced Commutative Ring

This is to announce the publication of a paper concerning an application of fractions. The paper “Fracpairs and Fractions over a Reduced Commutative Ring” (doi:10.1016/j.indag.2016.01.007) has now been published. In this paper, the principle of fractions as pairs is elaborated in case denominators may be zero. The resulting mathematical structure is essentially that of a common meadow.

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Signed Meadow Valued Probability Functions

This is to announce a new version of an electronic preprint concerning an application of meadows. The preprint “Signed Meadow Valued Probability Functions” has now been replaced by a substantial revision (arXiv:1307.5173v2 [math.LO]). In this preprint,  Kolmogorov’s probability axioms for probability functions are phrased in the setting of Boolean algebras and signed meadows. A completeness theorem is proved for the resulting equational axiom system.

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Transformation of Fractions into Simple Fractions in Divisive Meadows

This is to announce the publication of a paper concerning fractions. The paper “Transformation of fractions into simple fractions in divisive meadows” (doi:10.1016/j.jal.2016.03.001) has now been published. In this paper, it is investigated which divisive meadows admit transformation of fractions into simple fractions, i.e. fractions whose numerator and denominator do not contain fractions.

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Related Work

This is to announce the addition of a page entitled “Related Work” to this website. On this page, references are given to work  in which the multiplicative inverse operation is totalized by imposing that the multiplicative inverse of zero is an additional value that can be interpreted as infinity.

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Subvarieties of the Variety of Meadows

This is to announce a new version of an electronic preprint concerning meadows. The preprint “Subvarieties of the variety of meadows” has now been updated (arXiv:1510.04021v4 [math.RA]). In this preprint, subvarieties of the variety of meadows
obtained by extending the equational axiomatization of meadows and expanding the signature of meadows are studied.

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Transformation of Fractions into Simple Fractions in Divisive Meadows

This is to announce a new version of an electronic preprint concerning meadows. The preprint “Transformation of fractions into simple fractions in divisive meadows” has now been updated (arXiv:1510.06233v3 [math.RA]). In this preprint, it is investigated which divisive meadows admit transformation of fractions into simple fractions, i.e. fractions whose numerator and denominator do not contain fractions.

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