We present two applications to AI of recently introduced high level quantum structures. These structures are the categorical quantum logic of Abramsky and Coecke and the quantale quantum logic of Coecke Moore and Stubbe. Firstly, we show how the diagrammatic toolkit of categorical quantum logic, when restricted to its pregroup fragment introduced by Lambek, simplifies analysis of sentence structure of different languages. Moreover, the quantitative values that arise in these diagrams signify different degrees of complexity of sentences, which turn out to vary for different languages. Secondly, we show how expanding the quantale quantum logic with epistemic modalities provides a powerful system to reason about information update in multi-agent systems. Finally, we indicate how the above two applications to non-quantum domains can themselves be `re-quantized', providing applications to quantum informatics of distributed systems.
Subjects: 7.1 Multi-Agent Systems; 13. Natural Language Processing
Submitted: Jan 23, 2007