[Paper Review] On the cost-complexity of multi-context systems

Peter Novák, Cees Witteveen|arXiv (Cornell University)|May 28, 2014

Logic, Reasoning, and Knowledge5 references3 citations

TL;DR

This paper introduces cost-aware multi-context systems (C-MCS), extending non-monotonic multi-context systems by integrating execution costs of semantic operators. It proposes an incremental reasoning algorithm for definite MCSs that reduces redundant computation by reusing partial equilibria, significantly lowering cost-complexity in systems like maritime surveillance where sensor and database access incurs high operational costs.

ABSTRACT

Multi-context systems provide a powerful framework for modelling information-aggregation systems featuring heterogeneous reasoning components. Their execution can, however, incur non-negligible cost. Here, we focus on cost-complexity of such systems. To that end, we introduce cost-aware multi-context systems, an extension of non-monotonic multi-context systems framework taking into account costs incurred by execution of semantic operators of the individual contexts. We formulate the notion of cost-complexity for consistency and reasoning problems in MCSs. Subsequently, we provide a series of results related to gradually more and more constrained classes of MCSs and finally introduce an incremental cost-reducing algorithm solving the reasoning problem for definite MCSs.

Motivation & Objective

• To address the high operational costs—such as bandwidth, energy, and database access—in large-scale information-aggregation systems using multi-context systems.
• To formalize cost-complexity as a metric for consistency and reasoning in multi-context systems, shifting focus from time-complexity to resource cost.
• To design and implement an incremental reasoning algorithm that reuses previously computed equilibria to minimize repeated computation in definite multi-context systems.
• To evaluate the framework in real-world deployments, particularly in maritime traffic surveillance systems like Metis, where cost efficiency is critical.

Proposed method

• Extends non-monotonic multi-context systems with a cost function $\mathit{cost}: \mathsf{KB} \rightarrow \mathbb{R}^+$ assigning execution cost to each knowledge base's semantic operator.
• Introduces the notion of cost-complexity as the worst-case total cost of computing equilibria across different classes of MCSs: general, definite, and acyclic.
• Proposes Algorithm 3 for incremental reasoning in definite MCSs, which computes equilibria fragment by fragment, reusing results from previously processed fragments.
• Uses the concept of supports and grounded equilibria to incrementally build a global equilibrium, ensuring correctness via monotonicity in definite MCSs.
• Employs a fragment selection strategy that prioritizes the cheapest available fragments in stratified definite MCSs to minimize cost.
• Validates the approach through implementation and deployment in Metis, a maritime traffic surveillance system, demonstrating practical cost reduction.

Experimental results

Research questions

• RQ1 How can the cost of executing semantic operators in multi-context systems be formally modeled and analyzed to guide efficient system design?
• RQ2 What are the worst-case cost-complexity bounds for consistency and reasoning in general, definite, and acyclic multi-context systems?
• RQ3 Can incremental reasoning over fragments reduce the total cost of query answering in definite multi-context systems compared to monolithic computation?
• RQ4 How does the structure of information flow (e.g., overlaps in context supports) affect the performance of incremental reasoning algorithms?
• RQ5 To what extent can cost-aware reasoning improve scalability in real-world systems like maritime surveillance platforms?

Key findings

• The paper establishes worst-case cost-complexity upper bounds for consistency and reasoning in general, definite, and acyclic multi-context systems, providing theoretical foundations for cost-aware system design.
• For definite multi-context systems, the incremental reasoning algorithm (Algorithm 3) ensures correctness by leveraging monotonicity and reusing partial equilibria, reducing redundant computation.
• The algorithm achieves cost reduction by processing fragments in order of increasing cost, particularly effective when context supports have low overlap.
• In practice, the algorithm was successfully implemented and deployed in Metis, a maritime traffic surveillance system, demonstrating real-world applicability and cost savings.
• High redundancy—where most contexts depend on most others—can limit the algorithm’s effectiveness due to frequent recomputation, though such cases are rare in real deployments.
• The framework enables scalable reasoning in knowledge-intensive systems by shifting focus from time-complexity to cost-complexity, offering a practical alternative for resource-constrained environments.