\input zb-basic
\input zb-ioport
\iteman{io-port 06080386}
\itemau{Demey, Lorenz}
\itemti{Algebraic aspects of duality diagrams.}
\itemso{Cox, Philip (ed.) et al., Diagrammatic representation and inference. 7th international conference, Diagrams 2012, Canterbury, UK, July 2--6, 2012. Proceedings. Berlin: Springer (ISBN 978-3-642-31222-9/pbk). Lecture Notes in Computer Science 7352. Lecture Notes in Artificial Intelligence, 300-302 (2012).}
\itemab
Summary: Duality phenomena are widespread in logic and language; their behavior is visualized using square diagrams. This paper shows how our recent algebraic account of duality can be fruitfully used to study these diagrams. A duality cube is constructed, and it is shown that 14 duality squares can be embedded into this cube (two of which were hitherto unknown). This number is also an upper bound.
\itemrv{~}
\itemcc{}
\itemut{duality; negation; logic; linguistics; logical geometry}
\itemli{doi:10.1007/978-3-642-31223-6\_32}
\end