On Angels and Demons: Strategic (De)Construction of Dynamic Models

2026-01-12

AI Summary

This study addresses the problem of strategic reasoning by agents who modify graph structures in dynamically evolving systems, with applications in communication networks, security protocols, and multi-agent planning. The work proposes three modal logics that formally capture: (1) a “demon” agent deleting edges under cost constraints, (2) an “angel” agent adding edges within a budget, and (3) their collaborative or competitive interactions through update operations. For the first time, strategic graph modifications are unified within a single logical framework that explicitly distinguishes between constructive and destructive actions. By introducing cost-constrained graph-altering operators, the paper precisely characterizes the expressive power and computational complexity of model checking for all three logics.

Technology Category

• Knowledge Representation and Reasoning: Action, Change, and Causality
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Graphical Models

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
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

In recent years, there has been growing interest in logics that formalise strategic reasoning about agents capable of modifying the structure of a given model. This line of research has been motivated by applications where a modelled system evolves over time, such as communication networks, security protocols, and multi-agent planning. In this paper, we introduce three logics for reasoning about strategies that modify the topology of weighted graphs. In Strategic Deconstruction Logic, a destructive agent (the demon) removes edges up to a certain cost. In Strategic Construction Logic, a constructive agent (the angel) adds edges within a cost bound. Finally, Strategic Update Logic combines both agents, who may cooperate or compete. We study the expressive power of these logics and the complexity of their model checking problems.

Problem

• strategic reasoning
• model modification
• weighted graphs
• dynamic topology
• multi-agent systems

Innovation

• strategic reasoning
• graph modification
• modal logic
• model checking
• multi-agent systems