{"title":"Unification in the description logic $\\mathcal{FL}_\\bot$","authors":"Barbara Morawska","doi":"arxiv-2405.00912","DOIUrl":null,"url":null,"abstract":"Description Logics are a formalism used in the knowledge representation,\nwhere the knowledge is captured in the form of concepts constructed in a\ncontrolled way from a restricted vocabulary. This allows one to test\neffectively for consistency of and the subsumption between the concepts.\nUnification of concepts may likewise become a useful tool in analysing the\nrelations between concepts. The unification problem has been solved for the\ndescription logics $\\mathcal{FL}_0$ and $\\mathcal{EL}$. These small logics do\nnot provide any means to express negation. Here we show an algorithm solving\nunification in $\\mathcal{FL}_\\bot$, the logic that extends $\\mathcal{FL}_0$\nwith the bottom concept. Bottom allows one to express that two concepts are\ndisjoint. Our algorithm runs in exponential time, with respect to the size of\nthe problem.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"22 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Symbolic Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2405.00912","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Description Logics are a formalism used in the knowledge representation,
where the knowledge is captured in the form of concepts constructed in a
controlled way from a restricted vocabulary. This allows one to test
effectively for consistency of and the subsumption between the concepts.
Unification of concepts may likewise become a useful tool in analysing the
relations between concepts. The unification problem has been solved for the
description logics $\mathcal{FL}_0$ and $\mathcal{EL}$. These small logics do
not provide any means to express negation. Here we show an algorithm solving
unification in $\mathcal{FL}_\bot$, the logic that extends $\mathcal{FL}_0$
with the bottom concept. Bottom allows one to express that two concepts are
disjoint. Our algorithm runs in exponential time, with respect to the size of
the problem.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
