Higher-Order Modal Logics: Automation and Applications

  • Christoph BenzmüllerEmail author
  • Bruno Woltzenlogel Paleo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9203)


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.


Modal Logic Natural Deduction Ontological Argument Propositional Modal Logic Proof Script 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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
    Email author
  • Bruno Woltzenlogel Paleo
    • 2
  1. 1.Freie Universität BerlinBerlinGermany
  2. 2.Vienna University of TechnologyViennaAustria

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