Individuals, Quantifiers and Epistemic Operators

Abstract

The intrinsic informational content that characterizes quantum computational logics has naturally inspired some interesting and intriguing epistemic problems. We investigate the possibility of a quantum computational semantics for a first-order language that can express sentences like “Alice knows that everybody knows that she is pretty”. The basic question is: to what extent is it possible to interpret quantiers and epistemic operators as special examples of Hilbert-space operations? These logical operators turn out to have a similar logical behavior, giving rise to a “reversibility-breaking”. Unlike logical connectives, quantiers and epistemic operators can be represented as special operations that are generally irreversible (as happens in the case of measurement-procedures). An interesting feature of the epistemic quantum semantics is the failure of the unrealistic phenomenon of logical omniscience: Alice might know a given sentence without knowing all its logical consequences.