Automated Higher-Order Reasoning in Quantales

  • 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.

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Metadaten
Author:Han Hing Dang, Peter HöfnerGND
URN:urn:nbn:de:bvb:384-opus4-10463
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/1222
Series (Serial Number):Reports / Technische Berichte der Fakultät für Angewandte Informatik der Universität Augsburg (2010-03)
Type:Report
Language:English
Publishing Institution:Universität Augsburg
Release Date:2010/10/22
Institutes:Fakultät für Angewandte Informatik
Fakultät für Angewandte Informatik / Institut für Informatik
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
Licence (German):Deutsches Urheberrecht