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A NOTE ON INDEPENDENCE OF EFFECT ALGEBRAS' AXIOMATIC SYSTEM

English

2018
*
Journal of Pure and Applied Mathematics: Advances and Applications
*

English

In this paper, we mention about

doi:10.18642/jpamaa_7100121912
fatcat:aeepkugtpnb63nue43b2yrg3iq
*the*significance of*the**independence*of axiomatic systems and how is obtained. ... Afterwards, we scrutinize*the**independence*of*the*axiomatic system of effect algebras which is given by Foulis and Bennett [6] . ... We prove here that*the**axioms*(E1) through (E4)*are**independent*. To see this, we construct a model for each*axiom*in which that*axiom*is false while*the*others*are*true. ...##
###
Characterizing NTU-bankruptcy rules using bargaining axioms

2020
*
Annals of Operations Research
*

In particular, we derive new axiomatic characterizations of

doi:10.1007/s10479-020-03828-w
fatcat:oecoaucyrjc3dakmggbotkungi
*the*proportional rule,*the*truncated proportional rule, and*the*constrained relative*equal*awards rule, using properties which concern changes ... in*the*estate or in*the*claims. ...*The*relations between all estate*axioms*can be summarized by*the*following diagram.*The**axioms**independence*of irrelevant alternatives and*independence*of undominating alternatives*are**independent*. ...##
###
On the consistency and independence of some set-theoretical axioms

1978
*
Notre Dame Journal of Formal Logic
*

, Replacement, and Power-Set is

doi:10.1305/ndjfl/1093888220
fatcat:ulcqzp2byfbshgozggfl6zdbgu
*independent*from*the*remaining four*axioms*. ...*The*abovementioned*axioms**are*five of*the*six*axioms*of*the*Zermelo-Fraenkel Theory of Sets,*the*sixth being*Axiom*of Infinity. ... Thus, in*the*model given by (9) and (10),*equal*sets*are**not*elements of*the*same sets. Hence,*the**Axiom*of Extensionality is*not*valid. ...##
###
Basic independence axioms for the publication-citation system

2012
*
Journal of Scientometric Research
*

Among

doi:10.5530/jscires.2012.1.6
fatcat:pva5dbpkc5daxbshbpqzxnmsli
*the*indicators considered here only*the*number of publications and*the*number of citations satisfy*the*requirements of this*axiom*. Weaker forms of*the*basic*independence**axiom**are*considered. ... Following*the*idea of*the*Bouyssou-Marchant*independence**axiom*, a basic*independence**axiom*for an indicator is introduced. ... ACKNOWLEDGEMENT We acknowledge*the*National Natural Science Foundation of China (NSFC Grant No No.7101017006 and 71173187) for financial support.*The*authors thank Raf Guns for useful remarks. ...##
###
Ranking Opportunity Sets, Indirect Utility and Indifferences

2012
*
Social Science Research Network
*

If

doi:10.2139/ssrn.2159172
fatcat:dyknqziqkbgzjmmdlabhva62oi
*the*best alternatives*are**equally*good, then we count*the*number of maximal options in both sets. ... One of*the**axioms*, which we label simple indirect preference, requires for each pair x and y of different options, that x is*equally*good as y =⇒ {x, y} is ranked above {y}. ... or larger than k*are**equally*good: when*the*k + 1'th option becomes available*the*level of well-being does*not*increase. ...##
###
Evaluation of Arguments in Weighted Bipolar Graphs
[chapter]

2017
*
Lecture Notes in Computer Science
*

We introduce

doi:10.1007/978-3-319-61581-3_3
fatcat:n35naoydrzhbtdnile7obi6xqm
*axioms*that an evaluation method (or semantics) could satisfy. Such*axioms**are*very useful for judging and comparing semantics. ... We then analyze existing semantics on*the*basis of our*axioms*, and finally propose a new semantics for*the*class of acyclic graphs. ... Similarly, when*the*attack relation is empty,*the**axiom*coincides with strengthening*axiom*in [10] . Almost all*axioms**are**independent*, i.e., they do*not*follow from others. ...##
###
Sharpening independence results for Huntington's affine geometry
[article]

2013
*
arXiv
*
pre-print

*the*same intended class of structures, which employs weak betweenness (

*the*arguments

*are*permitted to be

*equal*). ... We carry out a systematic investigation of

*the*strict notion of betweenness that Huntington employs (

*the*three arguments

*are*supposed to be distinct) by comparing it to McPhee's three

*axiom*systems for ... Acknowledgements

*The*results reported here were achieved thanks to

*the*hard work that goes into developing and maintaining a number of automated reasoning systems, in particular

*the*...

##
###
Characterizing NTU-Bankruptcy Rules Using Bargaining Axioms

2018
*
Social Science Research Network
*

In particular, we derive new axiomatic characterizations of

doi:10.2139/ssrn.3118951
fatcat:urcgeks4cnex5ir3r5wnskqpge
*the*proportional rule,*the*truncated proportional rule, and*the*constrained relative*equal*awards rule using properties which concern changes ... in*the*estate or*the*claims. ... and*independence*of unclaimed alternatives*are**independent*of any claims*axiom*. ...##
###
The Axiomatic Approach to Population Ethics

2003
*
Politics, Philosophy and Economics
*

In addition,

doi:10.1177/1470594x030023004
fatcat:lnmcipmkona33npomisor53t3m
*the*two alternatives*are**equally*good if and only if their values*are**the*same.*Not*all population principles that satisfy our basic*axioms*have value functions. ... If critical levels*are**not*all*the*same, utility*independence*is satisfied but existence*independence*is*not*. ...##
###
Ranking Opportunity Sets, Averaging Versus Preference for Freedom

2013
*
Social Science Research Network
*

*Axioms*that involve no more than two alternatives capture

*the*differences between

*the*two rules. JEL Classification Number: D71, D81. ... First, a modified version of indirect utility takes into account

*the*number of maximal elements in

*the*opportunity set. This rule meets Puppe's

*axiom*of preference for freedom. ... By repeated application of

*independence*we obtain that {a 1 } and A

*are*

*equally*good. ...

##
###
Page 79 of Mathematical Gazette Vol. 3, Issue 47
[page]

1904
*
Mathematical Gazette
*

nNOS it tu
ON

*THE**AXIOMS*AND POSTULATES. 79 be reproduced, for*the*reason that, if they*are**not*new, they*are**not*generally known. ... It also follows from*the**axiom*that all or none of*the*straight lines of*the*plane*are*closed. If they*are**not*closed two straight lines through a point A do*not*cut again. ...##
###
Page 116 of MIND Vol. 6, Issue 21
[page]

1897
*
MIND
*

If this

*axiom*were really*independent*of division into units, it would hold*equally*of intensive quantities, but this is*not**the*case.*The*sum of two temperatures, for example, is meaningless. ... Chapters i. and ii. of this book give*the**axioms*of*equality*and addition, which*are*declared a priori, and*are*stated in a form apparently free from reference to number. ...##
###
A new single transferable vote method and its axiomatic justification

2012
*
Social Choice and Welfare
*

*The*results

*are*extended to

*the*methods, allowing fractional numbers of votes. ... We also propose a modification for quota definition that improves

*the*theoretical properties of

*the*procedures.

*The*method is justified by utilising a new set of

*axioms*. ... Acknowledgements

*The*partial support of

*the*Academic Foundation of

*the*National Research University Higher School of Economics (project # 10-04-0030) and

*the*International Laboratory of Decision Choice ...

##
###
Rényi entropy yields artificial biases not in the data and incorrect updating due to the finite-size data

2019
*
Physical review. E
*

It is demonstrated that this is so because it does

doi:10.1103/physreve.99.032134
fatcat:dmrhxb4mezb7zocpuktm2frx7e
*not*conform to*the*system and subset*independence**axioms*of Shore and Johnson. ... We finally show that*the*escort averaged constraints do*not*remedy*the*situation. ... T.O. acknowledges*the*state-targeted program "Center of Excellence for Fundamental and Applied Physics" (BR05236454) by*the*Ministry of Education and Science of*the*Republic of Kazakhstan. ...##
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Boole cebirleri için bağımsız aksiyom kümeleri

2018
*
Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi
*

Also we prove

doi:10.25092/baunfbed.433895
fatcat:fn3guokrwzevbnb6pl6kvlf6eu
*the**independence*of three*axioms*, proposed by Huntington and then by Robbins, which form a minimal set of*axioms*for Boolean algebras. ... In this work, we review axiomatic systems and prove some of*the*equivalent axiomatizations of Boolean algebras. ... Hence*the*left sides of (1) and (4)*are**equal*by commutativity, so*the*right sides must also be*equal*, and this gives (B 5 ). ...
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