Thursday, December 6, 2018
Roberto Giuntini (University of Cagliari)
Classical and quantum degrees of truth: a new look at the effects of a Hilbert space
Abstract: We investigate certain Brouwer-Zadeh lattices that serve as abstract counterparts of lattices of effects in Hilbert spaces under the spectral ordering. These algebras, called $PBZ^*$-lattices, can also be seen as generalisations of orthomodular lattices and are remarkable for the collapse of three notions of “sharpness” that are distinct in general Brouwer-Zadeh lattices. We investigate the structure theory of $PBZ^*$-lattices and their reducts; in particular, we prove some embedding results for $PBZ^*$-lattices and provide an initial description of the lattice of $PBZ^*$-varieties.