A Logic for the Specification of Continuous Systems

The paper proposes a first-order logic for the specification of continuous components of hybrid systems. The particularity of the approach lies in its interpretation of individual variables not as functions over time or as point-based values, but as environment-based values. An environment-based value closely models the local behavior of a function defined on a continuous time domain. The advantage of the approach is that it enables us to consider the derivation operator as an ordinary unary logical function. Thus, the logic is free from any built-in operators; they can all be defined on the elements of the carrier set of environment-based values.