A quantum computational semantics for epistemic logical operators. Part I: epistemic structures

Some critical open problems of epistemic logics can be investigated in the framework of a quantum computational approach. The basic idea is to interpret sentences like “Alice knows that Bob does not understand that π is irrational” as pieces of quantum information (generally represented by density operators of convenient Hilbert spaces). Logical epistemic operators (to understand, to know. . .) are dealt with as (generally irreversible) quantum operations, which are, in a sense, similar to measurement-procedures. This approach permits us to model some characteristic epistemic processes, that concern both human and artificial intelligence. For instance, the operation of “memorizing and retrieving information” can be formally represented, in this framework, by using a quantum teleportation phenomenon.