The least S5-T-Y logic is studied. The language of this logic is formed by addition of the connectives T ( 'tomorrow') and Y ('yesterday') to the language of S5. The T-Y logic axioms (cf. ) and the axioms
oA → TA ∧ YA, TA ∨ YA → ◊A
ToA ↔ oA, YoA ↔ oA
with the rule of the substitution are added to the axiomatic of S5. It is proved, that L∞ is determined of the Kripke frame which is the union of the frames which has the order type
Z (the set of the integers). It is used the reducing of the formulas to perfect disjunctive normal forms (PDNF).
Mathematical problems and theory of numerical methods