On the relationship between one-point frames and degrees of unsatisfiability of modal formulas (Q1057257)

Let \(A, V\), a range respectively over Kripke frames for a given normal modal logic \(L\), the valuations for \(A\) and points (worlds) of \(A\). A \(U\)-set of \(L\) is defined to be any set of formulas \(F\) given by an expression of the form \(Q_ 1AQ_ 2VQ_ 3a(aRF)\), where \(Q_ i\) are quantifiers and \(aRF\) is any of the relations ''\(F\) is true at \(a\)'', ''\(F\) is false at \(a\)''. A lot of necessary and sufficient conditions for various inclusion relations between \(U\)-sets are formulated.