L. K. Dillon
G. Kutty
Abstract
This article describes a graphical interval logic that is the foundation of a tool set supporting formal specification and verification of concurrent software systems. Experience has shown that most software engineers find standard temporal logics difficult to understand and use. The objective of this article is to enable software engineers to specify and reason about temporal properties of concurrent systems more easily by providing them with a logic that has an intuitive graphical representation and with tools that support its use. To illustrate the use of the graphical logic, the article provides some specifications for an elevator system and proves several properties of the specifications. The article also describes the tool set and the implementation.
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Index Terms
- A graphical interval logic for specifying concurrent systems
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Reviews
Andreas Ramses Heckler
A graphical interval logic called “GIL” and the “GIL tool set” are described. GILs name stems from its two essential characteristics: the graphical syntax and the “interval-based” semantics of GIL formulas. GIL specifications are intended to be more readable than textual specifications and more comprehensible than specifications founded on standard temporal logics. The purpose of the GIL tool set is highlighted by the following quotation: The GIL tool set is a prototype. …Both the logic and the display of formulas have evolved based on our experience with the tools. We expect this process of experimentation and revision to continue as we refine the current tool set into a working environment for specification, validation, and design of concurrent software systems. A robust, user-friendly environment will permit empirical studies needed to determine whether software designers find a visual logic, such as GIL, easier to use than a textual logic. The GIL tool set includes a visual (syntax-directed) editor (GILED), a proof checker, and a model generator. The logic has a formal model-theoretic semantics and is as expressive as propositional temporal logic with until and without next [1]. Unfortunately, it is not possible to give an impression of GILs graphical syntax in this review. To get an impression of its interval-based semantics, consider the most fundamental form of a GIL-formula F in its textual version: F:= [ f &vbm0; f,g ) F 1 . The essential parts of F are the interval I:= [ f &vbm0; f,g ) (where f and g are GIL-formulas) and the GIL-formula F 1 . Together they form the new GIL-formula F . Evaluation of GIL-formulas needs a given (infinite) sequence s of states and a given index i , and yields either true or false. In our case, F s,i = true holds if the following conditions are fulfilled. Let li be the least index such that f s,l = true, let rl be the least index such that g s,r = true, and let s be the subsequence of s determined by l and r , that is, s :=s l ,s l+1 ,&ldots;,s r-1 ,s r-1 ,s r-1 ,&ldots; Then F l s ,0 = true must hold. The meaning of a GIL-formula F depends on further (graphical) syntactic details—a formula F describes either all sequences s such that F s,0 = true holds or all sequences s such that F s,i = true holds for all i . The paper consists of eight main sections: “Introduction,” “Graphical Interval Logic,” “An Example Specification,” “Graphical Proofs of System Properties,” “The Graphical Interval Logic Tool Set, “Implementation of the Tool Set,” “Related Work,” and “Conclusion.” Appendix A contains a formal definition of the syntax and its model-theoretic semantics. The paper has no serious deficiencies, but readers, especially those who are not familiar with the topic, should not ignore the appendix. The best way to understand the concepts of GIL is to read section 2 (which gives an informal introduction) and A ppendix A (which gives the formal definitions) simultaneously.
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