A Quantum Computational Semantics for Epistemic Logical Operators. Part I: Epistemic Structures

TL;DR

This paper introduces a quantum computational framework for epistemic logic, modeling knowledge and understanding as quantum information processes, enabling new insights into epistemic phenomena in AI and human cognition.

Contribution

It proposes a novel quantum approach to epistemic logic, representing sentences as quantum states and operators as quantum operations, bridging quantum information theory and epistemic logic.

Findings

Quantum states represent epistemic sentences.

Quantum operations model knowledge and understanding.

Quantum teleportation simulates memorization and retrieval.

Abstract

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 Pi 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.