{"title":"两个Alt逻辑乘积中可采性的不可判定性","authors":"Philippe Balbiani, Çiğdem Gencer","doi":"10.1093/jigpal/jzad021","DOIUrl":null,"url":null,"abstract":"Abstract The product of two $\\textbf {Alt}$ logics possesses the polynomial product finite model property and its membership problem is $\\textbf {coNP}$-complete. Using a reduction from an undecidable domino-tiling problem, we prove that its admissibility problem is undecidable.","PeriodicalId":51114,"journal":{"name":"Logic Journal of the IGPL","volume":"27 7","pages":"0"},"PeriodicalIF":0.6000,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Undecidability of admissibility in the product of two Alt logics\",\"authors\":\"Philippe Balbiani, Çiğdem Gencer\",\"doi\":\"10.1093/jigpal/jzad021\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract The product of two $\\\\textbf {Alt}$ logics possesses the polynomial product finite model property and its membership problem is $\\\\textbf {coNP}$-complete. Using a reduction from an undecidable domino-tiling problem, we prove that its admissibility problem is undecidable.\",\"PeriodicalId\":51114,\"journal\":{\"name\":\"Logic Journal of the IGPL\",\"volume\":\"27 7\",\"pages\":\"0\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-10-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Logic Journal of the IGPL\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/jigpal/jzad021\",\"RegionNum\":4,\"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":"Logic Journal of the IGPL","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/jigpal/jzad021","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"LOGIC","Score":null,"Total":0}
Undecidability of admissibility in the product of two Alt logics
Abstract The product of two $\textbf {Alt}$ logics possesses the polynomial product finite model property and its membership problem is $\textbf {coNP}$-complete. Using a reduction from an undecidable domino-tiling problem, we prove that its admissibility problem is undecidable.
期刊介绍：
Logic Journal of the IGPL publishes papers in all areas of pure and applied logic, including pure logical systems, proof theory, model theory, recursion theory, type theory, nonclassical logics, nonmonotonic logic, numerical and uncertainty reasoning, logic and AI, foundations of logic programming, logic and computation, logic and language, and logic engineering.
Logic Journal of the IGPL is published under licence from Professor Dov Gabbay as owner of the journal.
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