Year: 2024
Type: article
Abstract: Quantum logic (QL) is a non-classical logic for analyzing the propositions of quantum physics.Modal logic MB, which is a logic that handles the value of the inner product that appears in quantum mechanics, was constructed with the development of QL.Although the basic properties of this logic have already been analyzed in a previous study, some essential parts still need to be completed.They are concerned with the completeness theorem and the decidability of the validity problem of this logic.This study solves those problems by constructing a nested-sequent calculus for MB.In addition, new logic MB+ with the addition of new modal symbols is discussed. Nested-sequent calculus NSMBThis section discusses the nested-sequent calculus for MB that satisfies the cut-elimination theorem.The nested-sequent calculus NSMB is defined as follows: Axioms:
DOI: 10.4204/eptcs.415.7
Author: Tomoaki Kawano
Institution: Kanagawa University
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4405854008