[FOM] possibility and probability

[schang.fabien at voila.fr]

Starting from a relational model, I'd say that: 

(1) a proposition p is possible iff p is true at (at least) one model
(2) a proposition p is probable iff its probability is greater than 0

Accordingly, the probabilist version (2) assumes a finite model while the possibilist one (1) does not. 


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> 
> How would you differentiate, mathematically, between the propositions, "It is possible that p," and "It is probable that p," where p is a proposition which may be drawn from a natural language? This deceptively simple question touches upon the fundamental structure of the concepts of possibility and probability. 
> 
> Lotfi Zadeh
> -- Lotfi A. Zadeh Professor Emeritus Director, Berkeley Initiative in Soft Computing (BISC) Address: 729 Soda Hall #1776 Computer Science Division Department of Electrical Engineering and Computer Sciences University of California Berkeley, CA 94720-1776 zadeh at eecs.berkeley.edu Tel.(office): (510) 642-4959 Tel.(home): (510) 526-2569 Fax (home): (510) 526-2433 URL: http://www.cs.berkeley.edu/~zadeh/ BISC Homepage URLs URL: http://zadeh.cs.berkeley.edu/ 

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