Cas Proost | Searcharxiv

arXiv2026

Incremental, inconsistency-resilient reasoning over Description Logic Abox streams

More and more, data is being produced in a streaming fashion. This has led to increased interest into how actionable insights can be extracted in real time from data streams through Stream Reasoning. Reasoning over data streams raises multiple challenges, notably the high velocity of data, the real time requirement of the reasoning, and the noisy and volatile nature of streams. This paper proposes novel semantics for incremental reasoning over streams of Description Logic ABoxes, in order to tackle these challenges. To address the first two challenges, our semantics for reasoning over sliding windows on streams allow for incrementally computing the materialization of the window based on the materialization of the previous window. Furthermore, to deal with the volatile nature of streams, we present novel semantics for inconsistency repair on such windows, based on preferred repair semantics. We then detail our proposed semi-naive algorithms for incremental materialization maintenance in the case of OWL2 RL, both in the presence of inconsistencies and without.

cs.AI↗

arXiv2024

Toric degenerations and Newton-Okounkov bodies

In recent times, a wide variety of combinatorics has been introduced in order to solve problems from algebraic geometry. Newton-Okounkov bodies and tropical geometry are two such combinatorial theories. As shown by Kaveh and Manon, there is a certain correspondence between these two. Building on this correspondence, and exploiting the link of both theories to toric degenerations, Harada and Escobar obtained their wall-crossing result for prime cones. This result states that moving between two adjacent prime maximal cones in a tropical variety corresponds to a mutation between the associated Newton-Okounkov bodies of these cones. In this thesis, we provide a method for applying the wall-crossing result to non-prime cones. Our approach uses a procedure developed by Bossinger, Lamboglia, Mincheva and Mohammadi in order to compute an embedding which changes a tropical variety in such a way that a non-prime cone becomes prime. Assuming that adjacent cones stay adjacent, the wall-crossing result can then be applied in this new embedding. Building on computations by Clarke, Mohammadi and Zaffalon, we show that for Gr(3,6), this approach works. We compute the new embedding and its tropicalization in this case, and study the relation between cones in the new embedding and the original embedding.

math.AG↗