Local and global metrics for the semantics of counterfactual conditionals
Karl Schlechta, David Makinson · Journal of Applied Non-Classical Logics · 1994
The semantics for counterfactual conditionals employs indexed relations a between possible worlds, with x >a y read intuitively as «x is closer to a than is y». This paper considers the question how far these different «closeness» relations of a model may be derived from a common source. Despite some well-known negative observations, we show that there is also quite a strong positive answer. Our main result is that for any model equiped with modular relations derived from multiple metrics da via the equation x a y iff da(a, x) da(a, y), there is a model that validates exactly the same formulae of the logic of counterfactuals, and whose relations a are determined by a common metric d, via the equation x a y iff da(a, x) da(a, y).