Decidability of Quantum Modal Logic

2026-03-18

AI Summary

This study addresses the decidability problem in quantum modal logic—specifically, whether there exists an effective algorithm to determine if an arbitrary formula is a theorem. To this end, the paper introduces Harrop’s lemma into this logical framework for the first time, combining formal reasoning techniques with decidability analysis to rigorously establish the decidability of quantum modal logic. This result not only fills a critical gap in the proof-theoretic understanding of the system but also provides a solid theoretical foundation for future work on automated reasoning and algorithmic implementation within this logic.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

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.

Problem

• decidability
• quantum modal logic
• theorem
• logical system
• algorithm

Innovation

• quantum modal logic
• decidability
• Harrop's lemma
• theorem proving
• logical systems