ASPaeroFlow: Decomposition Heuristics for Joint Air Traffic Flow & Capacity Management

While mathematical models act as vital decision support systems for operational Air Traffic Flow and Capacity Management (ATFCM), existing approaches isolate Air Traffic Flow Management (ATFM) from Dynamic Airspace Configuration (DAC). This separation introduces an unresolved circular dependency between fixed-demand and fixed-capacity assumptions. Although joint optimization resolves this gap, the enlarged search space renders exact models computationally intractable for medium- to large-scale instances. To bridge this gap, we propose ASPaeroFlow: a heuristic for the joint ATFCM; it combines instance-space decomposition heuristics with a local exact approach using Answer Set Programming. We benchmark ASPaeroFlow from small to industry-sized instances and compare it with exact and alternative approaches. The results indicate that (1) the heuristic provides a computational middle ground between exact methods and operational baselines; (2) simultaneous optimization can outperform sequential optimization on joint ATFCM; and (3) an ablation study indicates that DAC has a larger impact on solution quality than flow measures.

Joint Air Traffic Flow and Capacity Management via Answer Set Programming

Operational Air Traffic Flow and Capacity Management (ATFCM) balances flight demand with available sector capacity, to ensure safe and efficient operations. Mathematical models enhance operational ATFCM performance by framing demand-capacity balancing as an optimization problem, maximizing efficiency while adhering to safety constraints. However, SOTA research optimizes the aircraft trajectories (called ATFM) or the sector configuration (called DAC) separately. This leaves a research gap of whether joint optimization of ATFM and DAC can bring benefits. We partially address this limitation by introducing a joint ATFCM model with an encoding in Answer Set Programming (ASP). The ASP implementation is evaluated against two baselines applied to our joint model: a SOTA Mixed Integer Programming (MIP) model and an iterative CASA-based heuristic. Computational experiments utilize an instance generator fitted to historical OpenSky Network flight data. Our results indicate that the ASP model outperforms the MIP model, while ASP remains competitive against heuristics on small instances. Furthermore, while DAC has the largest improvement on solving performance compared to rerouting and delaying, unrestricted variants of DAC or rerouting lead to search space thrashing.

Intermediate Languages Matter: Formal Languages and LLMs affect Neurosymbolic Reasoning

Large language models (LLMs) achieve astonishing results on a wide range of tasks. However, their formal reasoning ability still lags behind. A promising approach is Neurosymbolic LLM reasoning. It works by using LLMs as translators from natural to formal languages and symbolic solvers for deriving correct results. Still, the contributing factors to the success of Neurosymbolic LLM reasoning remain unclear. This paper demonstrates that one previously overlooked factor is the choice of the formal language. We introduce the intermediate language challenge: selecting a suitable formal language for neurosymbolic reasoning. By comparing four formal languages across three datasets and seven LLMs, we show that the choice of formal language affects both syntactic and semantic reasoning capabilities. We also discuss the varying effects across different LLMs.

Automated Hybrid Grounding Using Structural and Data-Driven Heuristics

The grounding bottleneck poses one of the key challenges that hinders the widespread adoption of Answer Set Programming in industry. Hybrid Grounding is a step in alleviating the bottleneck by combining the strength of standard bottom-up grounding with recently proposed techniques where rule bodies are decoupled during grounding. However, it has remained unclear when hybrid grounding shall use body-decoupled grounding and when to use standard bottom-up grounding. In this paper, we address this issue by developing automated hybrid grounding: we introduce a splitting algorithm based on data-structural heuristics that detects when to use body-decoupled grounding and when standard grounding is beneficial. We base our heuristics on the structure of rules and an estimation procedure that incorporates the data of the instance. The experiments conducted on our prototypical implementation demonstrate promising results, which show an improvement on hard-to-ground scenarios, whereas on hard-to-solve instances we approach state-of-the-art performance.

Making LLMs Reason? The Intermediate Language Problem in Neurosymbolic Approaches

Logical reasoning tasks manifest themselves as a challenge to Large Language Models (LLMs). Neurosymbolic approaches use LLMs to translate logical reasoning problems formulated in natural language into a formal intermediate language. Subsequently, the usage of symbolic reasoners yields reliable solving thereof. However, LLMs often fail in translation due to poorly chosen intermediate languages. We introduce the intermediate language problem, which is the problem of choosing a suitable formal language representation for neurosymbolic approaches. Theoretically, we argue that its origins lie in the inability of LLMs to distinguish syntax from semantics and the relative independence of the problem from its representation. We showcase its existence experimentally by contrasting two intermediate languages, Answer Set Programming and the Python Knowledge Engine. In addition, we demonstrate the effects of varying degrees of supplementary context information. Our results show a maximum difference in overall-accuracy of 53.20% and 49.26% in execution-accuracy. When using the GPT4o-mini LLM we beat the state-of-the-art in overall-accuracy on the ProntoQA dataset by 21.20% and by 50.50% on the ProofWriter dataset.

ASP-driven User-interaction with Clinguin

We present clinguin, a system for ASP-driven user interface design. Clinguin streamlines the development of user interfaces for ASP developers by letting them build interactive prototypes directly in ASP, eliminating the need for separate frontend languages. To this end, clinguin uses a few dedicated predicates to define user interfaces and the treatment of user-triggered events. This simple design greatly facilitates the specification of user interactions with an ASP system, in our case clingo.