Visualising CTL Witnesses and Counterexamples -- Extended Version

2026-04-22

AI Summary

This work addresses the limited interpretability of Computation Tree Logic (CTL) model checking results, which stems from the absence of intuitive, visualizable evidence forms—CTL counterexamples being notably harder to comprehend than Linear Temporal Logic (LTL) traces. The paper proposes a unified evidence framework for CTL over explicit-state models, capable of representing both witnesses for satisfied properties and counterexamples for violations. Minimal evidence structures are formally defined for each temporal operator, and a human-centric visualization scheme is developed by integrating formal reasoning with graphical techniques. A complete toolchain implementing this approach is presented. All theoretical claims are rigorously proven, significantly enhancing the readability and explainability of CTL model checking outcomes.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

One of the advantages of LTL over CTL is that the notion of a counterexample is easy to grasp, visualise and process: it is a trace that violates the property at hand. In this paper we propose a notion of evidence for CTL properties on explicit-state models -- which equally serves as witness for satisfied properties and counterexample for violated ones -- and how to visualise it, with the main aim of (human) comprehension. The main contribution consists of a formal model of evidence, a characterisation of minimal evidence per temporal operator, and a concrete, implemented proposal for its visualisation. This is the extended version of a paper published in SPIN 2026, containing the proofs of all results.

Problem

• CTL
• counterexample
• witness
• visualization
• explicit-state models

Innovation

• CTL evidence
• counterexample visualization
• witness generation
• temporal logic verification
• explicit-state model