Re: Why x+y-xy is called probabilistic OR?

Ellen Hisdal (ellen@ifi.uio.no)
Fri, 6 Mar 1998 17:58:52 +0100 (MET)

On March 2 1998 savinov@usa.net (Alexandr A. Savinov)
wrote:

> Could anyone explain a connection between the operation
> x+y-xy and probabilities. That is, the question is
>
> - Why this operation is referred to as probabilistic OR, what is the
> justification of this name, and what is the connection with probabilistic
> theories? I am interested why it is just x+y-xy that is used for
> probabilistic OR, and not x+y, max(x,y) or something else.
>
> I need this since I have formal difficulties in applying it as
> probabilstic OR in my reasoning, it does not work as it should,
> there are some inconsistencies. In particular, it has to be formally
> dual to the probabilistic AND operation.
>
> I would greatly appriciate some explanation and/or references
> (preferebly online).
>
> Thanks.
>
> Sincerely,
>
> Alexandr A. Savinov
>
> --
> Alexandr A. Savinov, PhD -- Scientific Collaborator, Laboratory of AI Systems
> Inst. Math., Moldavian Acad. Sci., str. Academiei 5, MD-2028 Kishinev,
> Moldavia
> Tel: +3732-73-81-30, Fax: +3732-73-80-27, E-mail: savinov@math.moldova.su
> URL: http://www.geocities.com/ResearchTriangle/7220/
>
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See the paper

@article{are,
author = {Hisdal, E.},
title = {Are Grades of Membership Probabilities?},
journal = {Fuzzy Sets and Systems},
year = {1988},
volume = {25},
pages = {325-348} }

and for more details

@techreport{64,
author = {Hisdal, E.},
title = {A Theory of Logic Based on Probability},
institution = {Institute of Informatics, University of Oslo, Box
1080 Blindern, 0316 Oslo 3, Norway},
year = {1984},
type = {Research Report},
note = {ISBN~82-90230-60-5},
number = {64} }

Best greetings,

Ellen