Statecharts: From Visual Syntax to Model-Theoretic Semantics

This paper presents a novel model–theoretic account of Harel, Pnueli and Shalev’s original step semantics of the visual specification language Statecharts. The graphical syntax of a Statechart is read, directly and structurally, as a formula in propositional logic. This proposition captures all the logical constraints imposed by the diagram on the Statechart’s semantics, i.e., the possible sets of transitions that can be taken together to perform a valid Statecharts step, and their effects on Statecharts configurations. The paper’s main result shows that the correct semantics is uniquely described by the intuitionistic interpretation of Statecharts formulas, whereas the naive classical interpretation is insufficient. The advocated intuitionistic approach not only gives a correct, clear and direct logical account of Statecharts’ semantics, but also permits the integration of Statecharts with formal validation tools, such as theorem provers.