TRIO is a formal notation for the logic-based specification of real-ti
me systems. In this paper the language and its straightforward model-t
heoretic semantics are briefly summarized. Then the need for assigning
a consistent meaning to TRIO specifications is discussed, with refere
nce to a variety of underlying time structures such as infinite-time s
tructures (both dense and discrete) and finite-time structures. The ma
in motivation is the ability to validate formal specifications. A solu
tion to this problem is presented, which gives a new, model-parametric
semantics to the language. An algorithm for constructively verifying
the satisfiability of formulas in the decidable cases is defined, and
several important temporal properties of specifications are characteri
zed.