# circularity of possibility defined over possible worlds

I have just checked similar questions that have been asked(and answered) before but I am still confused. How is it that the notion of possibility defined over as being True in some possible world not a circular definition? I mean if we assume that I need to explain some alien race that does not have a conception of the notion of possibility , it seems as though an explanation of it over some 'possible' world does not do the trick. Is this circularity dismissable? (Do you know of any papers that discuss such issues?) Thanks in advance

"Possible worlds" must be read as a façon de parler (manner of speech).

See Kripke semantics:

A Kripke frame or modal frame is a pair (W,R), where W is a set, and R is a binary relation on W. Elements of W are called nodes (or worlds) and R is known as the accessibility relation.

See: Saul Kripke, A Completeness Theorem in Modal Logic, JSL (1959).

The same in E.Zalta, Basic Concepts in Modal Logic:

A standard model M for a set of atomic formulas shall be any triple (W;R;V) satisfying the following conditions:

1. W is a non-empty set,
1. R is a binary relation on W, [...]

Remark: For any given model M, we call W the set of worlds in M, R the accessibility relation for M.