输入/输出逻辑的复杂性

Q1 Mathematics

Journal of Applied Logic Pub Date : 2017-12-01 DOI:10.1016/j.jal.2017.03.002

Xin Sun , Livio Robaldo

{"title":"输入/输出逻辑的复杂性","authors":"Xin Sun , Livio Robaldo","doi":"10.1016/j.jal.2017.03.002","DOIUrl":null,"url":null,"abstract":"<div>Input/output logic is a formalism in deontic logic and normative reasoning. Unlike deontic logical frameworks based on possible-world semantics, input/output logic adopts norm-based semantics in the sense of [13], specifically operational semantics. It is well-known in theoretical computer science that complexity is an indispensable component of every logic. So far, previous literature in input/output systems focuses on proof theory and semantics, while neglects complexity. This paper adds the missing component by giving the complexity results of main decision problems in input/output logic. Our results show that input/output logic is coNP hard and in the 2nd level of the polynomial hierarchy.</div>","PeriodicalId":54881,"journal":{"name":"Journal of Applied Logic","volume":"25 ","pages":"Pages 69-88"},"PeriodicalIF":0.0000,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jal.2017.03.002","citationCount":"16","resultStr":"{\"title\":\"On the complexity of input/output logic\",\"authors\":\"Xin Sun , Livio Robaldo\",\"doi\":\"10.1016/j.jal.2017.03.002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>Input/output logic is a formalism in deontic logic and normative reasoning. Unlike deontic logical frameworks based on possible-world semantics, input/output logic adopts norm-based semantics in the sense of [13], specifically operational semantics. It is well-known in theoretical computer science that complexity is an indispensable component of every logic. So far, previous literature in input/output systems focuses on proof theory and semantics, while neglects complexity. This paper adds the missing component by giving the complexity results of main decision problems in input/output logic. Our results show that input/output logic is coNP hard and in the 2nd level of the polynomial hierarchy.</div>\",\"PeriodicalId\":54881,\"journal\":{\"name\":\"Journal of Applied Logic\",\"volume\":\"25 \",\"pages\":\"Pages 69-88\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.jal.2017.03.002\",\"citationCount\":\"16\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Logic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1570868317300046\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Logic","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1570868317300046","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 16

摘要

输入/输出逻辑是道义逻辑和规范推理中的一种形式主义。与基于可能世界语义的道义逻辑框架不同，输入/输出逻辑采用了[13]意义上的基于规范的语义，即操作语义。在理论计算机科学中，复杂性是每一种逻辑不可缺少的组成部分，这是众所周知的。到目前为止，以前的输入/输出系统的文献主要集中在证明理论和语义上，而忽略了复杂性。本文通过给出输入/输出逻辑中主要决策问题的复杂度结果，增加了缺失的部分。我们的结果表明，输入/输出逻辑是coNP困难的，并且处于多项式层次的第二层。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On the complexity of input/output logic

Input/output logic is a formalism in deontic logic and normative reasoning. Unlike deontic logical frameworks based on possible-world semantics, input/output logic adopts norm-based semantics in the sense of [13], specifically operational semantics. It is well-known in theoretical computer science that complexity is an indispensable component of every logic. So far, previous literature in input/output systems focuses on proof theory and semantics, while neglects complexity. This paper adds the missing component by giving the complexity results of main decision problems in input/output logic. Our results show that input/output logic is coNP hard and in the 2nd level of the polynomial hierarchy.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊