A Quantum Computational Semantics for Epistemic Logical Operators. Part II: Semantics

TL;DR

This paper develops a quantum computational semantics for epistemic logic, capturing complex knowledge expressions and avoiding logical omniscience by leveraging entanglement and holistic meaning structures.

Contribution

It introduces a novel semantics for epistemic language using quantum structures, emphasizing entanglement and holistic interpretation to better model knowledge acquisition.

Findings

Semantic framework reflects limitations of real information processes

Avoids logical omniscience in epistemic reasoning

Utilizes quantum entanglement to determine contextual meanings

Abstract

By using the abstract structures investigated in the first Part of this article, we develop a semantics for an epistemic language, which expresses sentences like "Alice knows that Bob does not understand that PI is irrational". One is dealing with a holistic form of quantum computational semantics, where entanglement plays a fundamental role, thus, the meaning of a global expression determines the contextual meanings of its parts, but generally not the other way around. The epistemic situations represented in this semantics seem to reflect some characteristic limitations of the real processes of acquiring information. Since knowledge is not generally closed under logical consequence, the unpleasant phenomenon of logical omniscience is here avoided.