{"title":"被遗忘事物的幽灵遗忘后的大小研究","authors":"Paolo Liberatore","doi":"10.1016/j.apal.2024.103456","DOIUrl":null,"url":null,"abstract":"<div><p>Forgetting is removing variables from a logical formula while preserving the constraints on the other variables. In spite of reducing information, it does not always decrease the size of the formula and may sometimes increase it. This article discusses the implications of such an increase and analyzes the computational properties of the phenomenon. Given a propositional Horn formula, a set of variables and a maximum allowed size, deciding whether forgetting the variables from the formula can be expressed in that size is <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-hard in <span><math><msubsup><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>p</mi></mrow></msubsup></math></span>. The same problem for unrestricted CNF propositional formulae is <span><math><msubsup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>p</mi></mrow></msubsup></math></span>-hard in <span><math><msubsup><mrow><mi>Σ</mi></mrow><mrow><mn>3</mn></mrow><mrow><mi>p</mi></mrow></msubsup></math></span>.</p></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"175 8","pages":"Article 103456"},"PeriodicalIF":0.6000,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S016800722400054X/pdfft?md5=664e39c8c02a1bed0bfc7e9414e88499&pid=1-s2.0-S016800722400054X-main.pdf","citationCount":"0","resultStr":"{\"title\":\"The ghosts of forgotten things: A study on size after forgetting\",\"authors\":\"Paolo Liberatore\",\"doi\":\"10.1016/j.apal.2024.103456\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Forgetting is removing variables from a logical formula while preserving the constraints on the other variables. In spite of reducing information, it does not always decrease the size of the formula and may sometimes increase it. This article discusses the implications of such an increase and analyzes the computational properties of the phenomenon. Given a propositional Horn formula, a set of variables and a maximum allowed size, deciding whether forgetting the variables from the formula can be expressed in that size is <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-hard in <span><math><msubsup><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>p</mi></mrow></msubsup></math></span>. The same problem for unrestricted CNF propositional formulae is <span><math><msubsup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>p</mi></mrow></msubsup></math></span>-hard in <span><math><msubsup><mrow><mi>Σ</mi></mrow><mrow><mn>3</mn></mrow><mrow><mi>p</mi></mrow></msubsup></math></span>.</p></div>\",\"PeriodicalId\":50762,\"journal\":{\"name\":\"Annals of Pure and Applied Logic\",\"volume\":\"175 8\",\"pages\":\"Article 103456\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-05-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S016800722400054X/pdfft?md5=664e39c8c02a1bed0bfc7e9414e88499&pid=1-s2.0-S016800722400054X-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Pure and Applied Logic\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S016800722400054X\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"LOGIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Pure and Applied Logic","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S016800722400054X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"LOGIC","Score":null,"Total":0}
The ghosts of forgotten things: A study on size after forgetting
Forgetting is removing variables from a logical formula while preserving the constraints on the other variables. In spite of reducing information, it does not always decrease the size of the formula and may sometimes increase it. This article discusses the implications of such an increase and analyzes the computational properties of the phenomenon. Given a propositional Horn formula, a set of variables and a maximum allowed size, deciding whether forgetting the variables from the formula can be expressed in that size is -hard in . The same problem for unrestricted CNF propositional formulae is -hard in .
期刊介绍：
The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.
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