  Quantum information has suggested new forms of quantum logic, called quantum
computational logics, where meanings of sentences are represented by pieces of
quantum information (generally, density operators of some Hilbert spaces),
which can be stored and transmitted by means of quantum particles. This
approach can be applied to a semantic characterization of epistemic logical
operations, which may occur in sentences like "At time t0 Bob knows that at
time t Alice knows that the spin-value is up". Each epistemic agent (say,
Alice, Bob,...) has a characteristic truth-perspective, corresponding to a
particular orthonormal basis of the Hilbert space C^2. From a physical point of
view, a truth-perspective can be associated to an apparatus that allows one to
measure a given observable. An important feature that characterizes the
knowledge of any agent is the amount of information that is accessible to
him/her (technically, a special set of density operators, which also represents
the internal memory of the agent in question). One can prove that interesting
epistemic operations are special examples of quantum channels, which generally
are not unitary. The act of knowing may involve some intrinsic irreversibility
due to possible measurement procedures or to a loss of information about the
environment. We also illustrate some relativistic-like effects that arise in
the behavior of epistemic agents.
