De Alfaro and Henzinger's Interface Automata (IA) and Nyman et al.'s recent
combination IOMTS of IA and Larsen's Modal Transition Systems (MTS) are
established frameworks for specifying interfaces of system components. However,
neither IA nor IOMTS consider conjunction that is needed in practice when a
component shall satisfy multiple interfaces, while Larsen's MTS-conjunction is
not closed and Bene\v{s} et al.'s conjunction on disjunctive MTS does not treat
internal transitions. In addition, IOMTS-parallel composition exhibits a
compositionality defect. This article defines conjunction (and also
disjunction) on IA and disjunctive MTS and proves the operators to be
'correct', i.e., the greatest lower bounds (least upper bounds) wrt. IA- and
resp. MTS-refinement. As its main contribution, a novel interface theory called
Modal Interface Automata (MIA) is introduced: MIA is a rich subset of IOMTS
featuring explicit output-must-transitions while input-transitions are always
allowed implicitly, is equipped with compositional parallel, conjunction and
disjunction operators, and allows a simpler embedding of IA than Nyman's. Thus,
it fixes the shortcomings of related work, without restricting designers to
deterministic interfaces as Raclet et al.'s modal interface theory does.Comment: 28 page