{"title":"描述逻辑中的统一 $\\mathcal{FL}_\\bot$","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":"{\"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}","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}
Unification in the description logic $\mathcal{FL}_\bot$
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.
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