{"title":"游戏中的过渡系统","authors":"P. Levy, S. Staton","doi":"10.1145/2603088.2603150","DOIUrl":null,"url":null,"abstract":"We describe a framework for game semantics combining operational and denotational accounts. A game is a bipartite graph of \"passive\" and \"active\" positions, or a categorical variant with morphisms between positions. The operational part of the framework is given by a labelled transition system in which each state sits in a particular position of the game. From a state in a passive position, transitions are labelled with a valid O-move from that position, and take us to a state over the updated position. Transitions from states in an active position are likewise labelled with a valid P-move, but silent transitions are allowed, which must take us to a state in the same position. The denotational part is given by a \"transfer\" from one game to another, a kind of program that converts moves between the two games, giving an operation on strategies. The agreement between the two parts is given by a relation called a \"stepped bisimulation\". The framework is illustrated by an example of substitution within a lambda-calculus.","PeriodicalId":20649,"journal":{"name":"Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"67 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2014-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"16","resultStr":"{\"title\":\"Transition systems over games\",\"authors\":\"P. Levy, S. Staton\",\"doi\":\"10.1145/2603088.2603150\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We describe a framework for game semantics combining operational and denotational accounts. A game is a bipartite graph of \\\"passive\\\" and \\\"active\\\" positions, or a categorical variant with morphisms between positions. The operational part of the framework is given by a labelled transition system in which each state sits in a particular position of the game. From a state in a passive position, transitions are labelled with a valid O-move from that position, and take us to a state over the updated position. Transitions from states in an active position are likewise labelled with a valid P-move, but silent transitions are allowed, which must take us to a state in the same position. The denotational part is given by a \\\"transfer\\\" from one game to another, a kind of program that converts moves between the two games, giving an operation on strategies. The agreement between the two parts is given by a relation called a \\\"stepped bisimulation\\\". The framework is illustrated by an example of substitution within a lambda-calculus.\",\"PeriodicalId\":20649,\"journal\":{\"name\":\"Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)\",\"volume\":\"67 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-07-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"16\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/2603088.2603150\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2603088.2603150","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We describe a framework for game semantics combining operational and denotational accounts. A game is a bipartite graph of "passive" and "active" positions, or a categorical variant with morphisms between positions. The operational part of the framework is given by a labelled transition system in which each state sits in a particular position of the game. From a state in a passive position, transitions are labelled with a valid O-move from that position, and take us to a state over the updated position. Transitions from states in an active position are likewise labelled with a valid P-move, but silent transitions are allowed, which must take us to a state in the same position. The denotational part is given by a "transfer" from one game to another, a kind of program that converts moves between the two games, giving an operation on strategies. The agreement between the two parts is given by a relation called a "stepped bisimulation". The framework is illustrated by an example of substitution within a lambda-calculus.