Supported Semantics for Modular Systems

ABSTRACT. Modular systems offer a language-independent declarative framework in which modules from different languages are combined to describe a conceptually and/or computationally complex problem. The original semantics developed to combine modules in a modular system is a model-theoretical semantics with close ties to relational algebraic operations.

In this paper, we introduce a new semantics for modular systems, called supported model semantics, that extends the original model-theoretic semantics of modular systems and captures non-monotonic reasoning on the level of modular system (rather than the level of individual modules). Moreover, we also use supported model semantics for modular systems to compare the expressiveness of modular systems with that of heterogeneous non-monotonic multi-context systems [BE'07]. We show that, under very few conditions, all multi-context systems can be translated into equivalent modular systems. Our result is true for both major semantics of multi-context systems, i.e., the equilibrium semantics and the grounded equilibrium semantics. Thus, we show that modular systems under supported model semantics generalize multi-context systems under either of its major semantics.