Lenses for Partially-Specified States (Extended Version)

2026-01-08

arXiv.org

AI Summary

When multiple views share a common data source, concurrent updates often lead to loss of user intent or view inconsistency. To address this, this work proposes a framework based on partial-state lenses, which precisely captures user update intentions by introducing partially specified states and their partial order structure. The framework defines a notion of update preservation that is compatible with intent merging, thereby enabling semantic merging and compositional reasoning over multi-view updates. This approach establishes a novel bidirectional transformation theory with strong behavioral guarantees. Formal verification and case studies demonstrate that the proposed framework significantly outperforms existing methods in both expressiveness and practical utility.

Technology Category

• Machine Learning: Multi-instance/Multi-view Learning
• Computer Vision: Multi-modal Vision
• Knowledge Representation and Reasoning: Preferences

Application Category

• Security and Privacy: Data transparency and provenance
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

A bidirectional transformation is a pair of transformations satisfying certain well-behavedness properties: one maps source data into view data, and the other translates changes on the view back to the source. However, when multiple views share a source, an update on one view may affect the others, making it hard to maintain correspondence while preserving the user's update, especially when multiple views are changed at once. Ensuring these properties within a compositional framework is even more challenging. In this paper, we propose partial-state lenses, which allow source and view states to be partially specified to precisely represent the user's update intentions. These intentions are partially ordered, providing clear semantics for merging intentions of updates coming from multiple views and a refined notion of update preservation compatible with this merging. We formalize partial-state lenses, together with partial-specifiedness-aware well-behavedness that supports compositional reasoning and ensures update preservation. In addition, we demonstrate the utility of the proposed system through examples.

Problem

• bidirectional transformation
• multiple views
• update preservation
• consistency
• compositional reasoning

Innovation

• partial-state lenses
• bidirectional transformation
• update preservation
• compositional reasoning
• partially-specified states