Definition
Standard translation is defined as follows: *, where is anExample
As an example, when standard translation is applied to , we expand the outer box to get : meaning that we have now moved from to an accessible world and we now evaluate the remainder of the formula, , in each of those accessible worlds. The whole standard translation of this example becomes : which precisely captures the semantics of two boxes in modal logic. The formula holds in when for all accessible worlds from and for all accessible worlds from , the predicate is true for . Note that the formula is also true when no such accessible worlds exist. In case has no accessible worlds then is false but the whole formula isStandard translation and modal depth
TheReferences
* Patrick Blackburn and Johan van Benthem (1988), ''Modal Logic: A Semantic Perspective''. Modal logic Predicate logic