Cones, Negation, and All That

Özgür Lütfü Özçep; Mena Leemhuis; Diedrich Wolter

doi:10.1007/978-3-030-58285-2_17

Cones, Negation, and All That

Özgür Lütfü Özçep^*, Mena Leemhuis, Diedrich Wolter

^*Corresponding author for this work

University of Bamberg

Abstract

This paper summarizes results on embedding ontologies expressed in the ALC description logic into a real-valued vector space, comprising restricted existential and universal quantifiers, as well as concept negation and concept disjunction. The main result states that an ALC ontology is satisfiable in the classical sense iff it is satisfiable by a partial faithful geometric model based on cones. The line of work to which we contribute aims to integrate knowledge representation techniques and machine learning. The new cone-model of ALC proposed in this work gives rise to conic optimization techniques for machine learning, extending previous approaches by its ability to model full ALC. This is an extended abstract of the paper “Cone Semantics for Logics with Negation” to be published in the proceedings of the 29th International Joint Conference on Artificial Intelligence (IJCAI 2020).

Original language	English
Title of host publication	KI 2020: KI 2020: Advances in Artificial Intelligence
Editors	Ute Schmid, Franziska Klügl, Diedrich Wolter
Number of pages	5
Volume	12325 LNAI
Publisher	Springer, Cham
Publication date	09.09.2020
Pages	235-239
ISBN (Print)	978-3-030-58284-5
ISBN (Electronic)	978-3-030-58285-2
DOIs	https://doi.org/10.1007/978-3-030-58285-2_17
Publication status	Published - 09.09.2020
Event	43rd German Conference on Artificial Intelligence - Bamberg, Germany Duration: 21.09.2020 → 25.09.2020 Conference number: 245059

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 4 Quality Education
SDG 9 Industry, Innovation, and Infrastructure
SDG 11 Sustainable Cities and Communities
SDG 12 Responsible Consumption and Production
SDG 14 Life Below Water
SDG 15 Life on Land

Research Areas and Centers

Centers: Center for Artificial Intelligence Luebeck (ZKIL)
Research Area: Intelligent Systems

Access to Document

10.1007/978-3-030-58285-2_17

Cite this

Özçep, Ö. L., Leemhuis, M., & Wolter, D. (2020). Cones, Negation, and All That. In U. Schmid, F. Klügl, & D. Wolter (Eds.), KI 2020: KI 2020: Advances in Artificial Intelligence (Vol. 12325 LNAI, pp. 235-239). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12325 LNAI). Springer, Cham. https://doi.org/10.1007/978-3-030-58285-2_17

Özçep, Özgür Lütfü ; Leemhuis, Mena ; Wolter, Diedrich. / Cones, Negation, and All That. KI 2020: KI 2020: Advances in Artificial Intelligence. editor / Ute Schmid ; Franziska Klügl ; Diedrich Wolter. Vol. 12325 LNAI Springer, Cham, 2020. pp. 235-239 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "This paper summarizes results on embedding ontologies expressed in the ALC description logic into a real-valued vector space, comprising restricted existential and universal quantifiers, as well as concept negation and concept disjunction. The main result states that an ALC ontology is satisfiable in the classical sense iff it is satisfiable by a partial faithful geometric model based on cones. The line of work to which we contribute aims to integrate knowledge representation techniques and machine learning. The new cone-model of ALC proposed in this work gives rise to conic optimization techniques for machine learning, extending previous approaches by its ability to model full ALC. This is an extended abstract of the paper “Cone Semantics for Logics with Negation” to be published in the proceedings of the 29th International Joint Conference on Artificial Intelligence (IJCAI 2020).",

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note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2020. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.; 43rd German Conference on Artificial Intelligence <br/>, KI 2020 ; Conference date: 21-09-2020 Through 25-09-2020",

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Özçep, ÖL, Leemhuis, M & Wolter, D 2020, Cones, Negation, and All That. in U Schmid, F Klügl & D Wolter (eds), KI 2020: KI 2020: Advances in Artificial Intelligence. vol. 12325 LNAI, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12325 LNAI, Springer, Cham, pp. 235-239, 43rd German Conference on Artificial Intelligence
, Bamberg, Bavaria, Germany, 21.09.20. https://doi.org/10.1007/978-3-030-58285-2_17

Cones, Negation, and All That. / Özçep, Özgür Lütfü; Leemhuis, Mena; Wolter, Diedrich.
KI 2020: KI 2020: Advances in Artificial Intelligence. ed. / Ute Schmid; Franziska Klügl; Diedrich Wolter. Vol. 12325 LNAI Springer, Cham, 2020. p. 235-239 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12325 LNAI).

Research output: Chapters in Books/Reports/Conference Proceedings › Conference contribution › peer-review

TY - GEN

T1 - Cones, Negation, and All That

AU - Özçep, Özgür Lütfü

AU - Leemhuis, Mena

AU - Wolter, Diedrich

N1 - Conference code: 245059

PY - 2020/9/9

Y1 - 2020/9/9

N2 - This paper summarizes results on embedding ontologies expressed in the ALC description logic into a real-valued vector space, comprising restricted existential and universal quantifiers, as well as concept negation and concept disjunction. The main result states that an ALC ontology is satisfiable in the classical sense iff it is satisfiable by a partial faithful geometric model based on cones. The line of work to which we contribute aims to integrate knowledge representation techniques and machine learning. The new cone-model of ALC proposed in this work gives rise to conic optimization techniques for machine learning, extending previous approaches by its ability to model full ALC. This is an extended abstract of the paper “Cone Semantics for Logics with Negation” to be published in the proceedings of the 29th International Joint Conference on Artificial Intelligence (IJCAI 2020).

AB - This paper summarizes results on embedding ontologies expressed in the ALC description logic into a real-valued vector space, comprising restricted existential and universal quantifiers, as well as concept negation and concept disjunction. The main result states that an ALC ontology is satisfiable in the classical sense iff it is satisfiable by a partial faithful geometric model based on cones. The line of work to which we contribute aims to integrate knowledge representation techniques and machine learning. The new cone-model of ALC proposed in this work gives rise to conic optimization techniques for machine learning, extending previous approaches by its ability to model full ALC. This is an extended abstract of the paper “Cone Semantics for Logics with Negation” to be published in the proceedings of the 29th International Joint Conference on Artificial Intelligence (IJCAI 2020).

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DO - 10.1007/978-3-030-58285-2_17

M3 - Conference contribution

SN - 978-3-030-58284-5

VL - 12325 LNAI

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 235

EP - 239

BT - KI 2020: KI 2020: Advances in Artificial Intelligence

A2 - Schmid, Ute

A2 - Klügl, Franziska

A2 - Wolter, Diedrich

PB - Springer, Cham

T2 - 43rd German Conference on Artificial Intelligence <br/>

Y2 - 21 September 2020 through 25 September 2020

ER -

Özçep ÖL, Leemhuis M, Wolter D. Cones, Negation, and All That. In Schmid U, Klügl F, Wolter D, editors, KI 2020: KI 2020: Advances in Artificial Intelligence. Vol. 12325 LNAI. Springer, Cham. 2020. p. 235-239. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-58285-2_17

Cones, Negation, and All That

Abstract

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