Signed interval logic

Abstract

Signed Interval Logic (SIL) is an extension of Interval Temporal Logic (ITL) with the introduction of the notion of a direction of an interval. We develop syntax, semantics, and proof system of SIL, and show that this proof system is sound and complete. The proof system of SIL is not more complicated than that of ITL but SIL is (contrary to ITL) capable of specifying liveness properties. Other interval logics capable of this (such as Neighbourhood Logic) have more complicated proof systems. We discuss how to define future intervals in SIL for the specification of liveness properties. To characterize the expressive power of SIL we relate SIL to arrow logic and relational algebra.