# A dynamical approach to compatible and incompatible questions

## TL;DR

This paper introduces a quantum-inspired framework for modeling the evolution of compatible and incompatible binary questions using a two-dimensional Hilbert space and Hamiltonian dynamics.

## Contribution

It presents a novel approach applying quantum mechanics principles to analyze question compatibility and their time evolution.

## Key findings

- The framework models question dynamics with non-commutative operators.
- Analysis of simple Hermitian Hamiltonians reveals diverse evolution behaviors.
- The approach bridges quantum formalism and logical question structures.

## Abstract

We propose a natural strategy to deal with compatible and incompatible binary questions, and with their time evolution. The strategy is based on the simplest, non-commutative, Hilbert space $\mathcal{H}=\mathbb{C}^2$, and on the (commuting or not) operators on it. As in ordinary Quantum Mechanics, the dynamics is driven by a suitable operator, the Hamiltonian of the system. We discuss a rather general situation, and analyse the resulting dynamics if the Hamiltonian is a simple Hermitian matrix.