{"title":"一元不动点逻辑下的社会选择与博弈推理","authors":"Ramit Das, R. Ramanujam, Sunil Simon","doi":"10.4204/EPTCS.297.8","DOIUrl":null,"url":null,"abstract":"Whether it be in normal form games, or in fair allocations, or in voter preferences in voting systems, a certain pattern of reasoning is common. From a particular profile, an agent or a group of agents may have an incentive to shift to a new one. This induces a natural graph structure that we call the improvement graph on the strategy space of these systems. We suggest that the monadic fixed-point logic with counting, an extension of monadic first-order logic on graphs with fixed-point and counting quantifiers, is a natural specification language on improvement graphs, and thus for a class of properties that can be interpreted across these domains. The logic has an efficient model checking algorithm (in the size of the improvement graph).","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"118 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Reasoning about Social Choice and Games in Monadic Fixed-Point Logic\",\"authors\":\"Ramit Das, R. Ramanujam, Sunil Simon\",\"doi\":\"10.4204/EPTCS.297.8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Whether it be in normal form games, or in fair allocations, or in voter preferences in voting systems, a certain pattern of reasoning is common. From a particular profile, an agent or a group of agents may have an incentive to shift to a new one. This induces a natural graph structure that we call the improvement graph on the strategy space of these systems. We suggest that the monadic fixed-point logic with counting, an extension of monadic first-order logic on graphs with fixed-point and counting quantifiers, is a natural specification language on improvement graphs, and thus for a class of properties that can be interpreted across these domains. The logic has an efficient model checking algorithm (in the size of the improvement graph).\",\"PeriodicalId\":118894,\"journal\":{\"name\":\"Theoretical Aspects of Rationality and Knowledge\",\"volume\":\"118 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-07-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theoretical Aspects of Rationality and Knowledge\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4204/EPTCS.297.8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical Aspects of Rationality and Knowledge","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4204/EPTCS.297.8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Reasoning about Social Choice and Games in Monadic Fixed-Point Logic
Whether it be in normal form games, or in fair allocations, or in voter preferences in voting systems, a certain pattern of reasoning is common. From a particular profile, an agent or a group of agents may have an incentive to shift to a new one. This induces a natural graph structure that we call the improvement graph on the strategy space of these systems. We suggest that the monadic fixed-point logic with counting, an extension of monadic first-order logic on graphs with fixed-point and counting quantifiers, is a natural specification language on improvement graphs, and thus for a class of properties that can be interpreted across these domains. The logic has an efficient model checking algorithm (in the size of the improvement graph).