Cone semantics for logics with negation

Özgür Lütfü Özçep; Mena Leemhuis; Diedrich Wolter

doi:10.24963/ijcai.2020/252

Cone semantics for logics with negation

Özgür Lütfü Özçep, Mena Leemhuis, Diedrich Wolter

University of Bamberg

25 Citations (Scopus)

Abstract

This paper presents an embedding of 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. Our 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.

Original language	English
Pages	1820 - 1826
Number of pages	7
DOIs	https://doi.org/10.24963/ijcai.2020/252
Publication status	Published - 08.07.2020
Event	29th International Joint Conference on Artificial Intelligence - Yokohama, Japan Duration: 01.01.2021 → 01.01.2021 Conference number: 165342

Conference

Conference	29th International Joint Conference on Artificial Intelligence
Abbreviated title	IJCAI 2020
Country/Territory	Japan
City	Yokohama
Period	01.01.21 → 01.01.21

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

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10.24963/ijcai.2020/252

Cite this

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title = "Cone semantics for logics with negation",

abstract = "This paper presents an embedding of 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. Our 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.",

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AU - Özçep, Özgür Lütfü

AU - Leemhuis, Mena

AU - Wolter, Diedrich

N1 - Conference code: 165342

PY - 2020/7/8

Y1 - 2020/7/8

N2 - This paper presents an embedding of 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. Our 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.

AB - This paper presents an embedding of 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. Our 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.

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M3 - Conference Papers

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T2 - 29th International Joint Conference on Artificial Intelligence

Y2 - 1 January 2021 through 1 January 2021

ER -

Cone semantics for logics with negation

Abstract

Conference

UN SDGs

Research Areas and Centers

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