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Automated Higher-order Reasoning about Quantales

12 pagesPublished: May 16, 2012

Abstract

Originally developed as an algebraic characterisation for quantum mechanics, the algebraic structure of quantales nowadays finds widespread applications ranging from (non-commutative) logics to hybrid systems. We present an approach to bring reasoning about quantales into the realm of (fully) automated theorem proving. This will yield automation in various (new) fields of applications in the future. To achieve this goal and to receive a general approach (independent of any particular theorem prover), we use the TPTP Problem Library for higher-order logic. In particular, we give an encoding of quantales in the typed higher-order form (THF) and present some theorems about quantales which can be proved fully automatically. We further present prospective applications for our approach and discuss practical experiences using THF.

Keyphrases: automated reasoning, higher-order reasoning, quantale, typed higher-order form of TPTP

In: Renate A. Schmidt, Stephan Schulz and Boris Konev (editors). PAAR-2010: Proceedings of the 2nd Workshop on Practical Aspects of Automated Reasoning, vol 9, pages 40--51

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