{"title":"Forcing and Calculi for Hybrid Logics","authors":"Daniel Găină","doi":"10.1145/3400294","DOIUrl":null,"url":null,"abstract":"The definition of institution formalizes the intuitive notion of logic in a category-based setting. Similarly, the concept of stratified institution provides an abstract approach to Kripke semantics. This includes hybrid logics, a type of modal logics expressive enough to allow references to the nodes/states/worlds of the models regarded as relational structures, or multi-graphs. Applications of hybrid logics involve many areas of research, such as computational linguistics, transition systems, knowledge representation, artificial intelligence, biomedical informatics, semantic networks, and ontologies. The present contribution sets a unified foundation for developing formal verification methodologies to reason about Kripke structures by defining proof calculi for a multitude of hybrid logics in the framework of stratified institutions. To prove completeness, the article introduces a forcing technique for stratified institutions with nominal and frame extraction and studies a forcing property based on syntactic consistency. The proof calculus is shown to be complete and the significance of the general results is exhibited on a couple of benchmark examples of hybrid logical systems.","PeriodicalId":17199,"journal":{"name":"Journal of the ACM (JACM)","volume":"27 1","pages":"1 - 55"},"PeriodicalIF":0.0000,"publicationDate":"2020-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the ACM (JACM)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3400294","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 10
Abstract
The definition of institution formalizes the intuitive notion of logic in a category-based setting. Similarly, the concept of stratified institution provides an abstract approach to Kripke semantics. This includes hybrid logics, a type of modal logics expressive enough to allow references to the nodes/states/worlds of the models regarded as relational structures, or multi-graphs. Applications of hybrid logics involve many areas of research, such as computational linguistics, transition systems, knowledge representation, artificial intelligence, biomedical informatics, semantic networks, and ontologies. The present contribution sets a unified foundation for developing formal verification methodologies to reason about Kripke structures by defining proof calculi for a multitude of hybrid logics in the framework of stratified institutions. To prove completeness, the article introduces a forcing technique for stratified institutions with nominal and frame extraction and studies a forcing property based on syntactic consistency. The proof calculus is shown to be complete and the significance of the general results is exhibited on a couple of benchmark examples of hybrid logical systems.