The Complexity of the Constructive Master Modality

2026-03-05

AI Summary

This study addresses the computational complexity of the constructive modal logics CK* and WK*. By introducing their semantic characterizations and establishing mutual interpretability with fragments of propositional dynamic logic (PDL), the authors combine modal semantics with complexity-theoretic techniques to analyze these systems. They prove for the first time that both CK* and WK* are EXPTIME-complete and enjoy the exponential finite model property. Furthermore, the work confirms a conjecture by Afshari et al. regarding the EXPTIME-completeness of the diamond-free fragments of these logics and extends the result to show that the validity problems for CS4 and WS4 also reside in EXPTIME.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic 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
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We introduce the semantically-defined constructive master-modality logics $\sf CK^*$ and $\sf WK^*$, extending the basic constructive modal logic $\sf CK$ and the Wijesekera-style logic $\sf WK$ obtained by impossing infallibility. Using translations between our logics and fragments of $\sf PDL$, we show that both $\sf CK^*$ and $\sf WK^*$ are EXPTIME-complete and admit an exponential-size finite model property. In particular, for their diamond-free fragment, also studied by Afshari et al. and Celoni, we establish EXPTIME-completeness, thereby settling the conjecture of Afshari et al. As an application, we embed $\sf CS4$ and $\sf WS4$ into the master-modality logics, showing that their validity problems are in EXPTIME.

Problem

• constructive modal logic
• EXPTIME-completeness
• master modality
• finite model property
• validity problem

Innovation

• constructive modal logic
• master modality
• EXPTIME-completeness
• finite model property
• propositional dynamic logic