Generalized Quantifiers in Logic Programs

Generalized quantiiers are an important concept in model-theoretic logic which has applications in diierent elds such as linguistics , philosophical logic and computer science. In this paper, we consider a novel application in the eld of logic programming, which has been presented recently. The enhancement of logic programs by generalized quantiiers is a convenient tool for interfacing extra-logical functions and provides a natural framework for the deenition of modular logic programs. We survey the expressive capability of syntactical classes of logic programs with generalized quantiiers over nite structures, and pay particular attention to modular logic programs. Moreover, we study the complexity of such programs. It appears that modular logic programming has the expressive power of second-order logic and captures the polynomial hierarchy, and diierent natural syntactical fragments capture the classes therein. The program complexity parallels the expressive power in the weak exponential hierarchy. Modular logic programming proves to be a rich formalism whose expressiveness and complexity can be controlled by eeciently recognizable syntactic restrictions.