I should not necessarily care about the reality of things and facts. There are also possibility, causality and unknown things in the real world, so it is better to reduce the phrase “real world” to world.

There is also some wrong information which is based on lies. In spite of uncertainty of information and concept of trust, we face some facts, some proposition with semantic in our world, which are lies. Lies are not going to be possible in the future and also are not counterfactuals. They are our incorrect belief that existed in world and possible world.

I wonder why not to separate them in to other world, or how can we place them beside the other proposition showing their difference.

P.S. I really enjoyed while I was reading about possible world semantic for counterfactuals. Counterfactuals express the reflection on what might have been. Considering causality we can mention this counterfactual: "If c had not occurred, e would not have occurred"

P.S.2. “The rough idea is that a counterfactual of the form "If it had been the case that A, it would have been the case that C" is true if and only if there is an auxiliary set S of true statements consistent with the antecedent A, such that the members of S, when conjoined with A, entail the consequent C. Much debate centered on the issue of the precise specification of the set S. Most empiricists agreed that S would have to include statements of laws of nature, while some thought that it would have to include statements of singular causation.”