High Level Quantum Structures in Linguistics and Multi Agent Systems

We present two applications to AI of recently introduced high level quantum structures. These structures are the categorical quantum logic of (Abramsky & Coecke 2004) and the quantale quantum logic of (Coecke, Moore, & Stubbe 2001). Firstly, we show how the diagrammatic toolkit of categorical quantum logic, when restricted to its pregroup fragment (Lambek 1999; 2001), 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