An interval logic for real-time system specification

Formal techniques for the specification of real time systems must be capable of describing system behavior as a set of relationships expressing the temporal constraints among events and actions, including properties of invariance, precedence, periodicity, liveness, and safety conditions. The paper describes a Temporal-Interval Logic with Compositional Operators (TILCO) designed expressly for the specification of real time systems. TILCO is a generalization of classical temporal logics based on the operators, eventually and henceforth; it allows both qualitative and quantitative specification of time relationships. TILCO is based on time intervals and can concisely express temporal constraints with time bounds, such as those needed to specify real time systems. This approach can be used to verify the completeness and consistency of specifications, as well as to validate system behavior against its requirements and general properties. TILCO has been formalized by using the theorem prover Isabelle/HOL. TILCO specifications satisfying certain properties are executable by using a modified version of the Tableaux algorithm. The paper defines TILCO and its axiomatization, highlights the tools available for proving properties of specifications and for their execution, and provides an example of system specification and validation.