Automated Higher-order Reasoning in Quantales

H.-H. Dang, P. Höfner

in: Universität Augsburg Technical Report, Institute of Computer Science, University of Augsburg, April 2010

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 in quantales into the realm of (fully) automated theorem proving. Hence the paper paves the way for automatisation in various (new) fields of applications. 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.