Automated Higher-order Reasoning about Quantales

erschienen 2010 in Workshop on Practical Aspects of Automated Reasoning, 2010.

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 in quantales into the realm of (fully) automated theorem proving. Hence the paper paves the way for automation 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.