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Decidability of Quantum Modal Logic

Kenji Tokuo

Abstract

The decidability of a logical system refers to the existence of an algorithm that can determine whether any given formula in that system is a theorem. In this paper, Harrop's lemma is used to prove the decidability of quantum modal logic.

Decidability of Quantum Modal Logic

Abstract

The decidability of a logical system refers to the existence of an algorithm that can determine whether any given formula in that system is a theorem. In this paper, Harrop's lemma is used to prove the decidability of quantum modal logic.
Paper Structure (11 sections, 7 theorems, 2 equations)

This paper contains 11 sections, 7 theorems, 2 equations.

Table of Contents

  1. Introduction
  2. Background and Objective
  3. QML
  4. Decidability
  5. Objective of This Paper
  6. Our Method
  7. Quantum Modal Logic
  8. Language
  9. Semantics
  10. Axiomatization
  11. Decidability

Key Result

Proposition 1

A logical system that is finitely axiomatizable and has the finite model property is decidable.

Theorems & Definitions (17)

  • Proposition 1: Harrop's Lemma
  • Remark 1
  • Definition 1: Quantum modal structure
  • Definition 2: Truth
  • Definition 3: Axioms and rules
  • Proposition 2: Finite model property
  • Theorem 1: Decidability
  • proof
  • Definition 4: Collapse
  • Lemma 1
  • ...and 7 more