Although it is widely accepted that every system should be robust, in the
sense that "small" violations of environment assumptions should lead to "small"
violations of system guarantees, it is less clear how to make this intuitive
notion of robustness mathematically precise. In this paper, we address this
problem by developing a robust version of Linear Temporal Logic (LTL), which we
call robust LTL and denote by rLTL. Formulas in rLTL are syntactically
identical to LTL formulas but are endowed with a many-valued semantics that
encodes robustness. In particular, the semantics of the rLTL formula φ⇒ψ is such that a "small" violation of the environment
assumption φ is guaranteed to only produce a "small" violation of the
system guarantee ψ. In addition to introducing rLTL, we study the
verification and synthesis problems for this logic: similarly to LTL, we show
that both problems are decidable, that the verification problem can be solved
in time exponential in the number of subformulas of the rLTL formula at hand,
and that the synthesis problem can be solved in doubly exponential time