Bruno Marchal wrote:
What could this mean in a real world example?

Take W as the set of places in Brussels. Take R to be "accessible by walking in a finite number of foot steps". Then each places at Brussels is accessible from itself, giving that you can access it with zero steps, or two steps (forward, backward, ...).

Take W as the set of humans, say that aRb if a can see directly, without mirror, the back of b. Then a can access all humans except themselves. R is said to be irreflexive.

Another important "concrete" example, which will help us latter to study the modal logic of quantum logic. Take the worlds to be the vector of an Hilbert Space (or of the simpler 3-dimensional euclidian space). Say that a is accessible to b, i.e. aRb, if the scalar product of a and b is non null (i.e. a and b are not orthogonal).

These are good illustrative examples, but how do they apply to worlds that just consist of propositions? What is the relation of accessibility in the p,q,r world(s)? Is it negation?

Brent Meeker

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