On the specification of modal systems: A comparison of three frameworks

Abstract

This paper studies the relationships between three notions of behavioural preorder that have been proposed in the literature: refinement over modal transition systems, and the covariant-contravariant simulation and the partial bisimulation preorders over labelled transition systems. It is shown that there are mutual translations between modal transition systems and labelled transition systems that preserve, and reflect, refinement and the covariant-contravariant simulation preorder. The translations are also shown to preserve the modal properties that can be expressed in the logics that characterize those preorders. A translation from labelled transition systems modulo the partial bisimulation preorder into the same model modulo the covariant-contravariant simulation preorder is also offered, together with some evidence that the former model is less expressive than the latter. In order to gain more insight into the relationships between modal transition systems modulo refinement and labelled transition systems modulo the covariant-contravariant simulation preorder, their connections are also phrased and studied in the context of institutions.

Logical vs. behavioural specifications

“…This finishes some of the work started in [11,33,34]. Recently, the graphical representability of a variant of alternating simulation called covariant-contravariant simulation has been studied in [1].…”

“…Here is the composition-projection operator defined by M M 2 = {(a, t t 2 ) | (a, t) ∈ M, (a, t 2 ) ∈ M 2 } and t t 2 = {(t 1 1 , t 1 2 ), . .…”

Compositionality for Quantitative Specifications

“…Refinement of components is a frequently used design approach in various areas, ranging from subtyping [52] over the Java modeling language JML [41] or correct-by-design class diagram operations [27] to interface theories close to MTS such as interface automata [22] based on alternating simulation. A variant of alternating simulation called covariantcontravariant simulation has been compared to MTS modal refinement in [1]. The graphical representability of these variants was studied in [10,14].…”

“…Indeed, by property (2), a 1 a 2 must be defined for a 1 = a 2 , and by (1), if a 1 a 2 = a 3 is defined, then a 3 = a 1 and a 3 = a 2 .…”

Compositionality for quantitative specifications

“…Refinement of components is a frequently used design approach in various areas, ranging from subtyping [52] over the Java modeling language JML [41] or correct-by-design class diagram operations [27] to interface theories close to MTS such as interface automata [22] based on alternating simulation. A variant of alternating simulation called covariantcontravariant simulation has been compared to MTS modal refinement in [1]. The graphical representability of these variants was studied in [10,14].…”