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Higher-order modal logics: automation and applications. (English) Zbl 1358.68273
Faber, Wolfgang (ed.) et al., Reasoning web. Web logic rules. 11th international summer school 2015, Berlin, Germany, July 31 – August 4, 2015. Tutorial lectures. Cham: Springer (ISBN 978-3-319-21767-3/pbk; 978-3-319-21768-0/ebook). Lecture Notes in Computer Science 9203, 32-74 (2015).
Summary: 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.
For the entire collection see [Zbl 1358.68011].

MSC:
68T27 Logic in artificial intelligence
03B35 Mechanization of proofs and logical operations
03B45 Modal logic (including the logic of norms)
68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)
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