Interconnections between classes of sequentially compositional temporal formulas

Interval Temporal Logic (ITL) is an established formalism for reasoning about time periods. We elucidate here the relationship between various kinds of compositional propositional ITL formulas. Several are closed under conjunction and the standard temporal operator known as “box” and “always”.

► We elucidate the relationship between various classes of compositional ITL formulas.
► Classes involve both basic sequential composition (chop) and iteration (chop-star).
► Some classes are closed under conjunction and the standard temporal operator “box”.
► The techniques help to modularly obtain safety and liveness formulas.
► Our incremental proofs about the classes avoid redundant reasoning.