Modularity Aspects of Disjunctive Stable Models

Practically all programming languages used in software engineering allow to split a program into several modules. For fully declarative and nonmonotonic logic programming languages, however, the modular structure of programs is hard to realise, since the output of an entire program cannot in general be composed from the output of its component programs in a direct manner. In this paper, we consider these aspects for the stable-model semantics of disjunctive logic programs (DLPs). We define the notion of a DLP-function, where a welldefined input/output interface is provided, and establish a novel module theorem enabling a suitable compositional semantics for modules. The module theorem extends the well-known splitting-set theorem and allows also a generalisation of a shifting technique for splitting shared disjunctive rules among components.