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

David Kastrup (dak@fsnif.neuroinformatik.ruhr-uni-bochum.de)
Mon, 2 Mar 1998 18:30:08 +0100 (MET)

savinov@usa.net writes:

> 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.

Probabilistic AND is xy, probabilistic NOT is 1-x.

Dualism implies that NOT (A AND B) = (NOT A) OR (NOT B),
namely that 1-xy = (1-x) + (1-y) - (1-x)(1-y)
which holds just perfectly.

```--
David Kastrup                                     Phone: +49-234-700-5570
Email: dak@neuroinformatik.ruhr-uni-bochum.de       Fax: +49-234-709-4209
Institut für Neuroinformatik, Universitätsstr. 150, 44780 Bochum, Germany
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