PPT Slide
Basic idea is to give a mathematical characterization of a ‘world’ in just enough detail to assign a meaning to every expression.
Exactly what counts as ‘just enough’ depends on the language.
Eg. for propositional logic, all you need to know is the truthvalues of the proposition letters, so an interpretation (“possible world”) is a truth-assignment to the proposition letters.
For first-order logic, you need to know
1.what the quantifiers range over (the universe);
2.for each name, what thing it names;
3.for each relation symbol, what combinations of things make it true (a set of n-tuples).
For maps, you need to know the topological structure of the terrain, the projection function, and for each map symbol, what property of the terrain region it indicates.