Inadequacy of modal logic in quantum settings

04/03/2018
by   Nuriya Nurgalieva, et al.
0

We explore the extent to which the principles of classical modal logic can be applied to fully quantum settings. Modal logic models our reasoning in multi-agent problems, and allows us to solve puzzles like the muddy children paradox. The Frauchiger-Renner thought experiment highlighted fundamental problems in applying classical reasoning when quantum agents are involved; we take it as a guiding example to test the axioms of classical modal logic. In doing so, we find a problem in the original formulation of the Frauchiger-Renner theorem: a missing assumption about unitarity of evolution is necessary to derive a contradiction and prove the theorem. Adding this assumption clarifies how different interpretations of quantum theory fit in, i.e., which properties they violate. Finally, we show that most of the axioms of classical modal logic break down in quantum settings, and make suggestions to generalize them.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/07/2022

Relevant Reasoners in a Classical World

We develop a framework for epistemic logic that combines relevant modal ...
research
12/17/2020

Formalization of PAL·S5 in Proof Assistant

As an experiment to the application of proof assistant for logic researc...
research
03/26/2018

A many-sorted polyadic modal logic

This paper presents a many-sorted polyadic modal logic that generalizes ...
research
06/10/2021

Some modal and temporal translations of generalized basic logic

We introduce a family of modal expansions of Łukasiewicz logic that are ...
research
04/02/2022

Transfinite Modal Logic: a Semi-quantitative Explanation for Bayesian Reasoning

Bayesian reasoning plays a significant role both in human rationality an...
research
09/09/2014

Quantum Edge Detection for Image Segmentation in Optical Environments

A quantum edge detector for image segmentation in optical environments i...
research
07/17/2017

Eigenlogic: Interpretable Quantum Observables with applications to Fuzzy Behavior of Vehicular Robots

This work proposes a formulation of propositional logic, named Eigenlogi...

Please sign up or login with your details

Forgot password? Click here to reset