Inheritance of Temporal Logic Properties

Abstract

Abstract. Inheritance is one of the key features for the success of object-oriented languages. Inheritance (or specialisation) supports incremental design and re-use of already written specifications or programs. In a formal approach to system design the interest does not only lie in re-use of class definitions but also in re-use of correctness proofs. If a provably correct class is specialised we like to know those correctness properties which are preserved in the subclass. This can avoid re-verification of already proven properties and may thus substantially reduce the verification effort. In this paper we study the question of inheritance of correctness properties in the context of state-based formalisms, using a temporal logic (CTL) to formalise requirements on classes. Given a superclass and its specialised subclass we develop a technique for computing the set of formulas which are preserved in the subclass. For specialisation we allow addition of attributes, modification of existing as well as extension with new methods.

The Challenges of Building Advanced Mechatronic Systems

“…Currently, such techniques take the following approach: correctness properties are proven for the initial states (of the system) and in addition shown to be preserved under transitions of the state. Examples of this are inductive verification techniques like [14,28,7] or methods for change analysis and property preservation for inheritance [32,33]. For volatile mechatronic systems, such methods need to be lifted to transformations of the model itself.…”

Embedding of Biological Regulatory Networks and Property Preservation

“…CTL is a branching-time temporal logic where the structure representing all possible executions is tree-like rather than linear while LTL is a linear temporal logic that implicitly quantifies universally over paths starting from a given state and modelizes linearly all possible executions. Here, we consider actually the restriction of CTL ⋆ by removing the next operator X, noted respectively CTL ⋆ -X [18,31]. For biological applications, the time mandatory for a biological system to change of qualitative state, i.e the time for a neXt transition, has a large variance.…”

Property Preservation along Embedding of Biological Regulatory Networks

“…It is well-adapted to specify and reason about non-deterministic and/or concurrent processes. Here, we consider actually a restriction of CTL by removing the next operator X, noted CTL-X [14,15]. The reason is for biological applications, the logical connector X is not of big relevance.…”