Reasoning Web International Summer School

Reasoning Web 2015: Reasoning Web. Web Logic Rules pp 32-74 | Cite as

Higher-Order Modal Logics: Automation and Applications

Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9203)

Abstract

These are the lecture notes of a tutorial on higher-order modal logics held at the 11th Reasoning Web Summer School. After defining the syntax and (possible worlds) semantics of some higher-order modal logics, we show that they can be embedded into classical higher-order logic by systematically lifting the types of propositions, making them depend on a new atomic type for possible worlds. This approach allows several well-established automated and interactive reasoning tools for classical higher-order logic to be applied also to modal higher-order logic problems. Moreover, also meta reasoning about the embedded modal logics becomes possible. Finally, we illustrate how our approach can be useful for reasoning with web logics and expressive ontologies, and we also sketch a possible solution for handling inconsistent data.

Notes

Acknowledgments

We would like to thank João Marcos for consistently useful discussions about discussive logics and paraconsistency. Various persons have contributed or positively influenced this line of research in the past, including, Larry Paulson, Chad Brown, Geoff Sutcliffe, and Jasmin Blanchette.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Christoph Benzmüller
    • 1
  • Bruno Woltzenlogel Paleo
    • 2
  1. 1.Freie Universität BerlinBerlinGermany
  2. 2.Vienna University of TechnologyViennaAustria

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