2 Search Results for "Hirsch, Dean"

Document
Invited Paper
DOI: 10.4230/OASIcs.RW.2024/2025.6
Explaining Reasoning Results for Description Logic Ontologies (Invited Paper)

Authors: Patrick Koopmann

Published in: OASIcs, Volume 138, Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025)

Abstract
The Web Ontology Language (OWL), grounded in description logics, enables reasoning systems to infer implicit knowledge in a transparent manner. However, the expressivity of description logics and the complexity of large ontologies often results in reasoning outcomes that are hard to understand without additional tool support. Explanations of these outcomes are essential for users to understand ontology content, communicate its structure and behavior effectively, and debug undesired or missing inferences. This chapter provides an overview of the central explanation techniques that have been developed for explaining reasoning with description logic ontologies. Here, we consider both explanations for positive entailments (explaining why something can be deduced), as well as negative entailments (why something cannot be deduced). More specifically, we discuss justifications, proofs and interpolation as a means to explain positive entailments, and abduction for explaining negative entailments, where we also have a closer look at practical algorithms as well as practical and theoretical challenges.
Cite as

Patrick Koopmann. Explaining Reasoning Results for Description Logic Ontologies (Invited Paper). In Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025). Open Access Series in Informatics (OASIcs), Volume 138, pp. 6:1-6:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{koopmann:OASIcs.RW.2024/2025.6,
  author =	{Koopmann, Patrick},
  title =	{{Explaining Reasoning Results for Description Logic Ontologies}},
  booktitle =	{Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 \& RW 2025)},
  pages =	{6:1--6:29},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-405-5},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{138},
  editor =	{Artale, Alessandro and Bienvenu, Meghyn and Garc{\'\i}a, Yazm{\'\i}n Ib\'{a}\~{n}ez and Murlak, Filip},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.RW.2024/2025.6},
  URN =		{urn:nbn:de:0030-drops-250514},
  doi =		{10.4230/OASIcs.RW.2024/2025.6},
  annote =	{Keywords: Explanations, Justifications, Proofs, Craig Interpolation, Contrastive Explanations}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.9
Parameterized Sensitivity Oracles and Dynamic Algorithms Using Exterior Algebras

Authors: Josh Alman and Dean Hirsch

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
We design the first efficient sensitivity oracles and dynamic algorithms for a variety of parameterized problems. Our main approach is to modify the algebraic coding technique from static parameterized algorithm design, which had not previously been used in a dynamic context. We particularly build off of the "extensor coding" method of Brand, Dell and Husfeldt [STOC'18], employing properties of the exterior algebra over different fields. For the k-Path detection problem for directed graphs, it is known that no efficient dynamic algorithm exists (under popular assumptions from fine-grained complexity). We circumvent this by designing an efficient sensitivity oracle, which preprocesses a directed graph on n vertices in 2^k poly(k) n^{ω+o(1)} time, such that, given 𝓁 updates (mixing edge insertions and deletions, and vertex deletions) to that input graph, it can decide in time 𝓁² 2^kpoly(k) and with high probability, whether the updated graph contains a path of length k. We also give a deterministic sensitivity oracle requiring 4^k poly(k) n^{ω+o(1)} preprocessing time and 𝓁² 2^{ω k + o(k)} query time, and obtain a randomized sensitivity oracle for the task of approximately counting the number of k-paths. For k-Path detection in undirected graphs, we obtain a randomized sensitivity oracle with O(1.66^k n³) preprocessing time and O(𝓁³ 1.66^k) query time, and a better bound for undirected bipartite graphs. In addition, we present the first fully dynamic algorithms for a variety of problems: k-Partial Cover, m-Set k-Packing, t-Dominating Set, d-Dimensional k-Matching, and Exact k-Partial Cover. For example, for k-Partial Cover we show a randomized dynamic algorithm with 2^k poly(k)polylog(n) update time, and a deterministic dynamic algorithm with 4^k poly(k)polylog(n) update time. Finally, we show how our techniques can be adapted to deal with natural variants on these problems where additional constraints are imposed on the solutions.
Cite as

Josh Alman and Dean Hirsch. Parameterized Sensitivity Oracles and Dynamic Algorithms Using Exterior Algebras. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{alman_et_al:LIPIcs.ICALP.2022.9,
  author =	{Alman, Josh and Hirsch, Dean},
  title =	{{Parameterized Sensitivity Oracles and Dynamic Algorithms Using Exterior Algebras}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{9:1--9:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.9},
  URN =		{urn:nbn:de:0030-drops-163504},
  doi =		{10.4230/LIPIcs.ICALP.2022.9},
  annote =	{Keywords: sensitivity oracles, k-path, dynamic algorithms, parameterized algorithms, set packing, partial cover, exterior algebra, extensor, algebraic algorithms}
}
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