Generalized Quantifiers in Logic Programs

  • Authors:

  • Thomas Eiter;Georg Gottlob;Helmut Veith

  • Affiliations:

  • -;-;-

  • Venue:
  • ESSLLI '97 Revised Lectures from the 9th European Summer School on Logic, Language, and Information: Generalized Quantifiers and Computation
  • Year:
  • 1997

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Abstract

Generalized quantifiers are an important concept in model-theoretic logic which has applications in different fields such as linguistics, philosophical logic and computer science. In this paper, we consider a novel application in the field of logic programming, which has been presented recently. The enhancement of logic programs by generalized quantifiers is a convenient tool for interfacing extra-logical functions and provides a natural framework for the definition of modular logic programs. We survey the expressive capability of syntactical classes of logic programs with generalized quantifiers over finite 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 different 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 efficiently recognizable syntactic restrictions.