{"type":"ScholarlyArticle","title":"Do We Need Many-valued Logics for Incomplete Information?","authors":[{"name":"Marco Console","slug":"marco-console","given":"Marco","family":"Console","affiliation":"University of Edinburgh"},{"name":"Paolo Guagliardo","slug":"paolo-guagliardo","given":"Paolo","family":"Guagliardo","affiliation":"University of Edinburgh"},{"name":"Leonid Libkin","slug":"leonid-libkin","given":"Leonid","family":"Libkin","affiliation":"University of Edinburgh"}],"abstract":"One of the most common scenarios of handling incomplete information occurs in relational databases. They describe incomplete knowledge with three truth values, using Kleene's logic for propositional formulae and a rather peculiar extension to predicate calculus. This design by a committee from several decades ago is now part of the standard adopted by vendors of database management systems. But is it really the right way to handle incompleteness in propositional and predicate logics? Our goal is to answer this question. Using an epistemic approach, we first characterize possible levels of partial knowledge about propositions, which leads to six truth values. We impose rationality conditions on the semantics of the connectives of the propositional logic, and prove that Kleene's logic is the maximal sublogic to which the standard optimization rules apply, thereby justifying this design choice. For extensions to predicate logic, however, we show that the additional truth values are not necessary: every many-valued extension of first-order logic over databases with incomplete information represented by null values is no more powerful than the usual two-valued logic with the standard Boolean interpretation of the connectives. We use this observation to analyze the logic underlying SQL query evaluation, and conclude that the many-valued extension for handling incompleteness does not add any expressiveness to it.","doi":"10.24963/ijcai.2019/851","url":"https://ijcai.org/proceedings/2019/851","pdf":"https://ijcai.org/proceedings/2019/0851.pdf","markdown":"https://ijcai.org/proceedings/2019/851.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/851","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Best Sister Conferences","track":"Best Sister Conferences","number":851,"pages":{"first":6141,"last":6145},"keywords":["Knowledge Representation and Reasoning: Logics for Knowledge Representation","Knowledge Representation and Reasoning: Reasoning about Knowlege and Belief","Multidisciplinary Topics and Applications: Databases"],"videos":[],"references":[{"position":1,"raw":"[Arenas et al., 2014] Marcelo Arenas, Pablo Barceló, Leonid Libkin, and Filip Murlak. 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